Natural Convection Heat Transfer in Heated Vertical

Natural Convection Heat Transfer in Heated Vertical Tubes with Internal Rings

Abstract: Experimental investigation of natural convection heat transfer in heated vertical tubes dissipating heat from the internal surface is presented. The test section is electrically heated and constant wall heat flux is maintained both circumferentially and axially. Four different test sections are taken having 45mm internal diameter and 3.8mm thickness. The length of the test sections are 450 mm, 550 mm, 700 mm and 850 mm. Ratios of length to diameter of the test sections are taken as L/D = 10, 12.22, 15.56, and 18.89. Wall heat fluxes are maintained at = 250 to 3341 W/m2. Experiments are also conducted on channels with internal rings of rectangular section placed at various distances. Thickness of the rings are taken as t = 4 mm, 6 mm and 8 mm. The step size of the rings varies from 75 mm to 283.3mm. The non-dimensional ring spacing are taken as s/D = 1.67 to 6.29 and the nondimensional ring thickness are taken as t/D = 0.089 to 0.178. The ratios of ring spacing to ring thickness are taken as s / t = 9.375 to 70.82. The effects of various parameters such as L/D ratio, wall heat flux, ring thickness and ring spacing on local steady-state heat transfer behavior are observed. From the experimental data a correlation is developed for average Nusselt number and modified Rayleigh number. Another correlation is also developed for modified Rayleigh number and modified Reynolds number. These correlations can predict the data accurately within ± 10% error. Keywords: heat transfer, heat flux, natural convection, ring spacing, ring thickness

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Natural Convection Heat Transfer in Heated Vertical Tubes with

2

Internal Rings

3

Ramesh Chandra Nayaka, Manmatha K. Roulb and Saroj Kumar Sarangic

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a,cDepartment

5

bDepartment

of Mechanical Engineering, SOA University, Bhubaneswar, INDIA,PIN-751030

of Mechanical Engineering, GITA, Bhubaneswar, ODISHA, INDIA, PIN-752054

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Corresponding Author:

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Email: [email protected]

8

1

Manuscript body Download source file (1.27 MB)

9

ABSTRACT

10

Experimental investigation of natural convection heat transfer in heated vertical tubes dissipating heat

11

from the internal surface is presented. The test section is electrically heated and constant wall heat flux

12

is maintained both circumferentially and axially. Four different test sections are taken having 45mm

13

internal diameter and 3.8mm thickness. The length of the test sections are 450 mm, 550 mm, 700 mm

14

and 850 mm. Ratios of length to diameter of the test sections are taken as L/D = 10, 12.22, 15.56, and

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18.89. Wall heat fluxes are maintained at

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channels with internal rings of rectangular section placed at various distances. Thickness of the rings are

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taken as t = 4 mm, 6 mm and 8 mm. The step size of the rings varies from 75 mm to 283.3mm. The

18

non-dimensional ring spacing are taken as s/D = 1.67 to 6.29 and the non-dimensional ring thickness are

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taken as t/D = 0.089 to 0.178. The ratios of ring spacing to ring thickness are taken as s / t = 9.375 to

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70.82. The effects of various parameters such as L/D ratio, wall heat flux, ring thickness and ring

21

spacing on local steady-state heat transfer behavior are observed. From the experimental data a

22

correlation is developed for average Nusselt number and modified Rayleigh number. Another

23

correlation is also developed for modified Rayleigh number and modified Reynolds number. These

24

correlations can predict the data accurately within ± 10% error.

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Keywords: - Heat flux; Heat transfer; Natural convection; Ring spacing; Ring thickness

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1 INTRODUCTION

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Application of natural convection heat transfer can be observed in many areas of engineering fields,

28

such as solar collectors, environmental engineering and electronic equipments. This is the common

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method used in electronics cooling, where a large number of thermal connection modules are

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accommodated on a small base. This category includes stand-alone packages such as modems and small

31

computers having an array of printed circuit boards (PCB) mounted within an enclosure. As the density

32

of these heat producing modules increases day by day, for more compactness, the heat released should

33

be transferred from the surface not only to protect them but also for longer life. Natural convection is a

34

type of heat transfer, in which the fluid motion is not generated by any external source but only by

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density differences in the fluid occurring due to temperature gradients. In natural convection, fluid

36

surrounding a heat source receives heat, becomes less dense and rises. The surrounding cooler fluid then

37

moves to replace it. This cooler fluid is then heated and the process continues, forming convection

38

current. The driving force for natural convection is buoyancy which arises as a result of differences in

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fluid density. Since the fluid velocity associated with natural convection is relatively low, the heat

40

2

= 250 to 3341 W/m2 . Experiments are also conducted on


transfer coefficient encountered in natural convection is also low. Natural convection heat transfer

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depends on the geometry of the surface as well as its orientation. It also depends on the variation of

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temperature on the surface and the thermo physical properties of the fluid. At present, flow of gaseous

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heat carriers in vertical channels with natural convection is extensively encountered in science and

45

engineering. For example, its application can be observed in domestic convectors, cooling systems of

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radio electronic and electrical equipment, nuclear reactors with passive cooling systems, dry cooling

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towers, ground thermo siphons, etc. In such applications, it is required to cool the internal surfaces of

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vertical open-ended pipes by natural convection, despite the low rates of heat transfer that this

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convection process affords. The amount of heat that can be removed from an electronic component that

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is cooled by natural convection can be substantially increased by increasing the surface area of the

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components. In recent years, the natural convection heat transfer problem has received increasing

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attention in the literature due to its wide applications.

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Iyi and Hasan [1] studied on Natural Convection Flow and Heat Transfer in an Enclosure Containing

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Staggered Arrangement of Blockages they found numerical results allow a better understanding on the

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influence of blockages arrangement within a low turbulent natural convection flow in an enclosure. The

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influence on fluid flow and heat transfer for the different stacking of arrangement of the blockages

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within the enclosure was identified and detailed profiles at the mid-height and mid-width of the

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rectangular enclosure have been analyzed. Buonomo and Manca [2] numerically investigated the

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transient natural convection in parallel-plate vertical micro channels. The vertical micro channel is

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considered asymmetrically or symmetrically heated at uniform heat flux. The first-order model for slip

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velocity and jump temperature is assumed in micro-scale conditions. The analysis is performed under

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laminar boundary layer assumption for different values of Knudsen number, Rayleigh number and the

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ratio of wall heat flux in order to evaluate their effects on wall temperatures, mass flow rate, velocity

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profiles and Nusselt number. Mallik and Sastri [3] studied experimentally the natural convection heat

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transfer over an array of staggered discrete vertical plates and found that the use of discrete vertical

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plates in lieu of continuous plates gives rise to enhancement of natural convection heat transfer. The

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highest local heat transfer values are encountered at the leading edge and least at the trailing edge of

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each plate for a particular temperature level and spacing. The highest value corresponds to the thinnest

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thermal boundary layer and as the thermal boundary layer starts growing from the leading edge of each

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plate, the heat transfer values starts decreasing and reach a minimum at the trailing edge. Had the plates

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been continuous, there would have been decrease in the heat transfer values continuously along the

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height of the vertical plate for same input conditions. They also found that the heat transfer quantities at

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the leading edge of the top plate are more than that at the trailing edge but less than that at the leading

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edge of the bottom plate. Degree of enhancement increases with increase in spacing.

75

3


Huang et al. [4] studied overall convective heat transfer coefficients of the perforated fin arrays lie

77

between two limits corresponding to an imperforate fin arrays and vertical parallel plates, respectively.

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The overall convective heat transfer coefficients of the perforated fin arrays increase with increasing

79

total perforation length. Cheng [5] Studied effects of the modified Darcy number, the buoyancy ratio

80

and the inner radius-gap ratio on the fully developed natural convection heat and mass transfer in a

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vertical annular non-Darcy porous medium with asymmetric wall temperatures and concentrations. The

82

exact solutions for the important characteristics of fluid flow, heat transfer, and mass transfer are

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derived by using a non-Darcy flow model. The modified Darcy number is related to the flow resistance

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of the porous matrix. For the free convection heat and mass transfer in an annular duct filled with

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porous media, increasing the modified Darcy number tends to increase the volume flow rate, total heat

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rate added to the fluid, and the total species rate added to the fluid. Moreover, an increase in the

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buoyancy ratio or in the inner radius-gap ratio leads to an increase in the volume flow rate, the total heat

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rate added to the fluid, and the total species rate added to the fluid. Capobianchi and Aziz [6] analyzed

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natural convective flows over vertical surfaces and found that the local Nusselt number is an implicit

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function of the Biot number characterizing the convective heating on the backside of the plate. The

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order of magnitude of the local Nusselt number was therefore evaluated numerically for three values

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each of the Boussinesq, Prandtl, and Biot number.

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Experimental study of Sparrow and Bahrami [7] encompasses three types of hydrodynamic boundary

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conditions along the lateral edges of the channel. Lee [8] Carried

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investigation of laminar natural convection heat and mass transfer in open vertical parallel plates with

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unheated

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temperature/uniform wall concentration (UWT/UWC) and

98

(UHF/UMF) are considered. Results of dimensionless induced volume rate Q, average Nusselt number

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NuE and Sherwood number ShE are obtained for air flow under various buoyancy ratio N, Grashof

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number GrL, Schmidt number Sc and combinations of unheated entry, heated section and unheated exit

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length. Theoretical solutions for Q, NuE and ShE for both UWT/UWC and UHF/UMF cases are derived

102

under fully developed conditions. Mobedi and Sunden [9] Investigated a steady state conjugate

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conduction–convection on vertical plate fin in which a small heat source is located. Heat from the fin

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surface is transferred to the surroundings by laminar natural convection. The governing equations for

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the problem are the heat conduction equation for the fin and the boundary layer equations, which are

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continuity, momentum and energy equations, for the fluid. A computer program is written by using the

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finite difference method in order to solve the governing equations which are nonlinear and coupled. The

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best location of the heat source in the fin for maximum heat transfer rate depends on two parameters

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which are the conduction–convection parameter and the Prandtl number. The obtained results have

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4

entry and

unheated

exit is presented.

a combined numerical and theoretical

Both boundary conditions of uniform wall uniform heat flux/uniform mass flux


shown that for the fin with large conduction–convection parameter, a heat source location for maximum

112

heat transfer rate exists. Levy et al. [10] address the problem of optimum plate spacing for laminar

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natural convection flow between two plates. Churchill, using the theoretical and experimental results

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obtained by a number of authors for the mean rate of heat transfer in laminar buoyancy-driven flow

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through vertical channels, developed general correlation equations for these results.

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Lewandowski and Radziemska [11] Presented a theoretical solution of natural convective heat transfer

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from isothermal round plates mounted vertically in unlimited space. With simplifying assumptions

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typical for natural heat transfer process, equations for the velocity profile in the boundary layer and the

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average velocity were obtained. Using this velocity, the energy flow within the boundary layer was

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balanced and compared with the energy transferred from the surface of the vertical plate according to

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the Newton's law. The solution of the resulting differential equation is presented in the form of a

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correlation between the dimensionless Nusselt and Rayleigh numbers. The theoretical result is

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compared with the correlation of numerical results obtained using fluent. Experimental measurements

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of heat transfer from a heated round vertical plate 0.07 m in diameter were performed in both water and

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air. The theoretical, numerical, and experimental results are all in good agreement. Dey et al [12] found

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that the local flow field around a fin can substantially enhance the forced convection heat transfer from

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a conventional heat sink. A fin is set into oscillation leading to rupture of the thermal boundary layer

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developed on either side of the fin. This enhancement in heat transfer is demonstrated through an

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increase in the time-averaged Nusselt Number (Nu) on the fin surfaces.

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Awasarmol and Pise [13] reported that the perforated fin can enhance heat transfer. The magnitude of

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heat transfer enhancement depends upon angle of orientation, diameter of perforations and heater input.

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The perforation of fins enhances the heat dissipation rates and at the same time decreases the

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expenditure for fin materials. It helps making fin arrays light weight. Kundu and Wongwises [14]

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studied decomposition analysis on convecting–radiating rectangular plate fins for variable thermal

135

conductivity and heat transfer coefficient. They concluded that the variable thermal conductivity did not

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make a significant role on the temperature and fin-wall performances in radiative and convective

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environment. Kundu and Lee [15] determined the minimum shape of porous fins with convection and

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radiation modes of heat transfer taken place on its surfaces. They proposed that optimum shape of

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porous fins as strong function with porosity. Singh and Patil [16] reported the heat dissipation ability of

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the naturally cooled heat sink hasbeen found to increase by the application of impressions on the fin

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body. Roul and Nayak [17] also studied experimentally the natural convection heat transfer from the

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internal surface of heated vertical tubes. Deshmukh and Warkhedkar [18] investigated the effects of

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design parameters of the fully shrouded elliptical pin fin heat sinks. On the basis of experimental

144

measurements, the overall heat transfer coefficient and the thermal performance characteristics are

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5


obtained for various parameters with the inline and staggered layout of the pin fin heat sinks in mixed

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convection with assisting flow.

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Taler [19] presented a numerical method for determining heat transfer coefficients in cross-ﬂow heat

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exchangers with extended heat exchange surfaces. He used a nonlinear regression method to determine

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coefficients in the correlations deﬁning heat transfer on the liquid and air-side. Correlation coefficients

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were determined from the condition that the sum of squared liquid and air temperature differences at the

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heat exchanger outlet, obtained by measurements and those calculated, achieved minimum. Minimum

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of the sum of the squares was found using the Levenberg-Marquardt method. The uncertainty in

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estimated parameters was determined using the error propagation rule by Gauss. The outlet temperature

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of the liquid and air leaving the heat exchanger was calculated using the analytical model of the heat

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exchanger.

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Taler and Teler [20] presented different approaches for steady-state and transient analysis of

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temperature distribution and efficiency of continuous-plate fins. They suggested that for a constant heat

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transfer coefficient over the fin surface, the plate fin can be divided into imaginary rectangular or

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hexangular fins. They computed the transient temperature distributions in continuous fins attached to

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oval tubes using the finite volume methods. The developed method can be used in the transient analysis

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of compact heat exchangers to calculate accurately the heat flow transferred from the finned tubes to the

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fluid. Duda and Mazurkiewicz [21] presented the numerical modeling of steady state heat and mass

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transfer in cylindrical ducts for both laminar and hydro dynamically fully developed turbulent flow.

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Numerical results were compared with values obtained from analytical solution of such problems. The

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problems under consideration are often denoted as extended Graetz problems. Calculations were carried

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out gradually decreasing the mesh size in order to examine the convergence of numerical method to

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analytical solution.

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When a vertical plate is heated a free-convection boundary layer is formed over the surface, as shown in

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fig. 1. Inertial, viscous and buoyant forces are predominant in this layer. The velocity profile in this

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boundary layer is quite unlike the velocity profile in a forced convection boundary layer. At the wall,

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the velocity is zero because of no slip condition; it increases to some maximum value and then

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decreases to zero at the edge of the boundary layer since the free stream conditions are at rest in the

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free-convection system. The initial boundary layer development is laminar; but at some distance from

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the leading edge, depending on the fluid properties and temperature levels to which the wall is

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subjected, turbulent eddies are formed, and transition to a turbulent boundary layer begins. After certain

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distance up the plate the boundary layer may become fully turbulent.

178

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Manuscript body Download source file (1.27 MB)

Turbulent

179

u

180

TW

181

T∞ Laminar

182

(a)

183

TW

184

T

185 186

T∞

T, u

u

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δ

188

(b)

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Fig. 1(a) Boundary layer on a vertical flat plate (b) Velocity and Temperature distribution in the boundary layer

190 191

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Over the years it has been found that average free-convection heat transfer coefficients can be

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represented in the following functional form for a variety of circumstances:

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Nu f  C  Grf Pr f



m

(1)

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where the subscript f indicates that the properties in the dimensionless groups are evaluated at the film

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temperature, which is given by:

197

198

199

200

Tf  

Tw  T 2

(2)

The product of the Grashof and Prandtl is called Rayleigh number: Ra = Gr Pr

(3)

7


The characteristic dimensions used in the Nusselt and Grashof numbers depend on the geometry of the

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problem. For a vertical plate it is the height of the plate L; for a horizontal cylinder it is the diameter d;

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and so forth. Experimental data for free convection problems appear in a number of references as given

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in the following paragraph.

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For vertical surfaces, the Nusselt and Grashof numbers are formed with L, the height of the surface as

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the characteristic dimension. If the boundary layer thickness is not large compared to the diameter of the

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cylinder, the heat transfer may be calculated with the same relations used for vertical plates. The general

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criterion is that a vertical cylinder may be treated as a vertical flat plate [22], when,

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D 35  L Gr 1 4 L

(4)

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where D is the diameter of the cylinder. For isothermal surfaces, the values of the constants are given by

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Vliet [22]. There are some indications from the analytical work of various investigators that the

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following relation may be preferable.

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Nu f  0.10  Grf Pr f



1

3

(5)

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More complete relations have been provided by Churchill and Chu [23] and are applicable over wider

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ranges of the Rayleigh number: Nu  0.68 

216

1

Nu  0.825 

0.670 Ra

1

4

1   0.492 / Pr   0.387 Ra

2

1

9

6

1   0.492 / Pr  16    9

217

16

8

 

for RaL 109

(6)

for 101  RaL 1012

(7)

4

9

27

218

This equation is also a satisfactory representation for constant heat flux. Properties for these equations

219

are evaluated at the film temperature.

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Extensive experiments have been reported in the literature for free convection from vertical and inclined

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surfaces to water under constant heat-flux conditions. In such experiments, the results are presented in

222

terms of a modified Grashof number, Gr* :

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Grx*  Grx Nux 

g  qw x 4 k 2

(8)

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Where qw is the wall heat flux in watts per square meter. The local heat transfer coefficients are

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correlated by the following relation for the laminar range:

226 227

Nuxf 

hx  0.60  Grx* Pr f kf



1

5

for 105  Gx* 1011 ;

(9) 8


For the turbulent region, the local heat-transfer coefficients are correlated with Nux  0.17  Grx* Pr 

229

1

4

for 2 103  Grx* Pr 1016 ;

(10)

230

All properties in the above correlation are evaluated at the local film temperature. Although these

231

experiments were conducted for water, the resulting correlations are shown to work for air as well.

232

Writing Eq. (10) as a local heat transfer form gives. Nu x  C  Grx Pr 

233 234

m

(11)

Substituting the value of Grx : Nux  C

235

1

1 m 

Gr Pr  * x

m

1 m 

(12)

236

The value of m for laminar and turbulent flow are taken as ¼ and 1/3 respectively. Churchill and Chu

237

[23] suggested that Eq.(6) may be modified to apply to the constant heat flux case if the average Nusselt

238

number is based on the wall heat flux and the temperature difference at the center of the plate (x = L/2).

239

The result is 1

Nu L 4  Nu L  0.68 

240

241

Where



0.67  GrL*  1   0.492 / Pr 9 /16   

4/9

(13)



NuL  qw L / k T and T  Tw  at L / 2  T

242

Nu L

243

T = Temperature difference between the wall and the fluid at the center of the plate.

244

The purpose of this work is to study experimentally the natural convection heat transfer from the

245

internal surface of heated vertical pipes at different heating levels. The test section is a vertical, open-

246

ended cylindrical pipe dissipating heat from the internal surface. The test section is electrically heated

247

imposing the circumferentially as well as axially constant wall heat flux. As a result of the heat transfer

248

to air from the internal surface of the pipe, the temperature of the air increases. As a result of which the

249

density of air inside the pipe decreases which causes the air to rise. Although extensive work has been

250

done on the study of natural convection heat transfer and hydrodynamics in heated vertical open-ended

251

channels without internal rings, but the works on heat transfer from internal surfaces with presence of

252

internal rings of different thicknesses are not adequate in literature.

253

Four different test sections having 45mm internal diameter and 3.8mm thickness are taken. The length

254

of the test sections varies from 450 mm to 850 mm. Ratios of length to diameter of the test sections are

255

taken as L/D = 10, 12.22, 15.56, and 18.89. Wall heat fluxes are maintained at q // = 250 to 3341 W/m2 .

256

9

= Average Nusselt number which is based on the constant wall heat flux.


Experiments are also conducted on channels with internal rings of rectangular section placed at various

258

distances. Thickness of the rings are taken as t = 4.0, 6.0, 8 mm. The step size s of the rings is varied

259

from 75mm to 283.3mm. Other dimensions are taken as: s / D = 1.67 to 6.29, t / D = 0.089 to 0.178 and

260

s / t = 9.375 to 70.82.

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2 EXPERIMENTAL SET-UP AND PROCEDURE

262

The experimental set-up consists of a test section, an electrical circuit of heating and a measuring

263

system as shown in fig.2. The cross-sectional view of the test section is shown in fig. 3. In this study, a

264

hollow tube is made of aluminium which is 45mm in diameter and 3.8mm thick. Nine Copper-

265

Constantan thermocouples are fixed to monitor temperatures on the internal surface at various locations

266

as shown in the figure. Holes of 0.8 mm diameter are drilled at these locations for inserting the

267

thermocouples. After inserting the thermocouple junction, the holes are filled with aluminium powder

268

for getting good thermal contact with the tube. Then the openings of the thermocouple wells are closed

269

by punching with a dot punch. Epoxy is used for sealing the opening of the thermocouple wells and for

270

holding the thermocouples in position.

271

After mounting the thermocouples, a layer of asbestos paste (10mm thick) is provided on the outer

272

surface of the tube. A layer of glass tape is provided over the asbestos paste and then the nichrome wire

273

heater coil is helically wound around the external surface with equal spacing. Then asbestos rope of

274

diameter approximately 7mm is wound over the heater coil with close fitting. After that another layer of

275

asbestos paste is provided. A layer of glass-fibers of approximately 15mm thickness is wrapped around

276

it. A thick cotton cloth is wrapped over the glass fibers. It is covered with a very thin aluminium foil for

277

reducing the radiation heat transfer. Two traversing type thermocouples are provided; one at the

278

entrance and the other at the exit, to determine the temperature profile of fluid entering and leaving the

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tube at different radial distances. Another traversing type thermocouple is also used for measuring the

280

external surface temperature of the test section to find out the heat loss from the external surface.

281

Four different test sections with length varying from 450 mm to 850 mm were considered. For each test

282

section experiments were conducted for eight different heat flux values. Internal rings were provided at

283

different locations with thickness varying from 4 mm to 8 mm, spacing varying from 75mm to 283.3

284

and heat flux varying from 250 to 3341 W/m2 . Total 320 numbers of experiments were conducted and

285

to perform each experiment around 4 hours were required for steady state conditions to be reached.

286

Even after four hours, it was very difficult to obtain steady state condition. So, a number of observations

287

were taken for each experiment and average data was reported. This average value was found to have

288

deviations within ± 2%.

289

10


290

6

291

1

292

4

293

7

294

2

295

5

296 297

11 8

298

9

299

10

300

Fig. 2. Experimental Set-up

301 302 303 304

1. Test section, 2. System of thermocouples, 3. Selector switch, 4. Millivoltmeter, 5. Thermometer, 6. Ammeter, 7 & 9. Volt meter, 8. Variac, 10. Transformer, 11. Traversing type thermocouples 7

305

3

2

5

306

307

308

309

310 311 312 313

10

8

9

4

1

6

Fig. 3 Cross sectional view of test section 1. Aluminium tube, 2. Position of thermocouples, 3. Heater coil, 4. Glass tape, 5. Asbestos rope, 6. Asbestos paste, 7. Glass fibre, 8. Cotton cloth, 9. Aluminium foil, 10. Internal rings 11


Wall temperatures at different locations are found out from the milli-voltmeter readings to which

315

thermocouples are connected. The fluid temperatures at the channel exit and entrance are found out at

316

various radial distances by two traversing type thermocouples provided at the top and bottom of the

317

channel respectively. The electric power input to the test section is determined from the measured

318

voltage drop across the test section and the current along the test section.

319

Though adequate thermal insulation is provided on the outer surface of the tube, there is still some heat

320

rejection from the external surface and this heat loss by natural convection from the test section through

321

the insulation is evaluated by measuring the outer surface temperature of the insulation and the ambient

322

temperature. At different axial locations along the pipe the outer surface temperature of the insulator are

323

measured by thermocouples and the average insulation temperature is determined. Heat loss from the

324

external surface is then computed by the suggested correlation [24] for natural convection from a

325

vertical cylinder in air. Now heat dissipated from the internal surface can be found out by subtracting

326

this heat loss from the heat input to the test section. The wall heat flux q // can be found out by dividing

327

this heat by the internal surface area. From the measured temperature profiles at the channel entrance

328

and exit, the approximate temperature profile at any other axial distance can be calculated.

329

Let the local wall temperatures at different axial distance along the pipe be Tw1 , Tw2 , Tw3 , …..etc, and

330

the fluid temperature at these distances be Tb1 , Tb2 , Tb3 , …..etc. respectively, then local heat transfer

331

coefficient at these locations can be calculated by the relation: h1 

332

qn Tw1  Tb1 

(14)

333

Similarly, h2 , h3 , h4,

334

The average Nusselt number can be found from the average heat transfer coefficient by using the

335

relation:

336

...

Nu 

etc. can be calculated and from which average heat transfer coefficient is found.

hD k

(15)

337

Now modified Rayleigh number based on constant heat flux and average wall temperature can be

338

calculated by using the following formulas:

339

340

Ra #  Gr Pr

D g  q // D5  L  kL

(16)

12

Manuscript body Download source file (1.27 MB) Ra  #

341





g  2 c p  Tw  Tb D 4 Lk 

(17)

342

Since the wall temperature is difficult to be maintained constant, we will consider the constant wall heat

343

flux case only.

344

A vane type anemometer [25] is used to measure the velocity of fluid at the exit of the channel. The

345

modified Reynolds number can be calculated by using the relation: Re # 

346

 uD 2 L

(18)

347

Thermal boundary conditions of uniform wall heat flux q // = constant is considered. Wall heat fluxes are

348

maintained at q// = 250 to 3341 W/m2 . Spatial variations of the measured local wall temperatures are

349

plotted for the smooth channel for different wall heat fluxes and non dimensional measured temperature

350

profiles at the channel exit for various heat fluxes and for different channel length are plotted.

351

Similarly studies are also carried out on intensified channels of the same geometrical sizes with

352

providing the discrete rings of height t = 4.0, 6.0, 8 mm; step size (s) of the rings are varying from75mm

353

to 283.3mm and the different non-dimensional ratios are taken as : ratio s / D = 1.67 to 6.29, ratio t / D

354

= 0.089 to 0.178 and ratio s / t =9.375 to 70.82.

355

SAMPLE CALCULATIONS:

356

For q // = 2188 W/m2 , L = 450mm, L/D = 10;

357

(a)

358

Average surface temperature excess over ambient,  T = 180 C, t∞ = 270 C

359

Average temperature of fluid, t f =27 + 18/2 = 36 0 C

360

The different property values of air at one atm. Pressure can be found out from the data table as follows:

361

362

Heat loss from external surface:

 1/ T f 

1  3.236 103 / K 36  273

13

381

Manuscript body

382

Download source file (1.27 MB) 383

Now, Rayleigh Number,

Ra = Gr.Pr  

g  Tw  T  D13

2

 Pr

9.81 3.236 103 18   0.12 

384

16.576 10 

6 2

3

 0.6998

 2.515 106 1

Nu 2  0.825  385 386

Nu  21.198

387 388

h

389

0.387 Ra

1

6

  0.494  916  1       Pr  

8

 4.604 27

Nu.k 21.198  0.027236   4.811W / m 2 K D1 0.12

Heat lost from theexternalsurface, q2  h    D1  L  T

390

 4.811   0.12  0.45 18  14.69W

391

(b)

392

Heat input, q1 = V x I = 90 x 1.71 = 153.9W

393

Heat rejected from the internal surface, q = q 1 – q2 = 153.9 – 14.69 = 139.21 W

394

Wall heat flux =

395

( C ) Heat transfer coefficient: The local and average heat transfer coefficient is calculated in a tabular

396 397

Wall heat flux:

q 139.21   2188W / m2 A   0.045  0.45

form as given in table 1. Table 1: Thermocouple positions

Local wall

Fluid temp.

in mm

temp. excess

Excess over

399

over amb. in

amb. in 0 C

400

0C

398

h

q // in W/m2 .0 C T  T  w1 b1 

401

0

128.1

0

17.08

402

65

137.2

5

16.55

403

129

144.2

9.5

16.244

404

193

147.8

14

16.353

405

257

153.3

18

16.17

406

321

155.5

23.5

16.5757

407

385

155.8

28.5

17.1877

408

450

155

34

18.083

409

14


Tw  147.52 0C

411

Tb  17 0 C

412

h

413

414

(d)

134.243  16.78W / m 2 . 0C 8

Different non-dimensional numbers: T f 1  27 

Tw  Tb 147.52  17  27   92.260 C 2 2

415

The properties of air corresponding to this temperature are:

416

  22.3328 106 m 2 / s

417

  32.2845 106 m 2 / s k  0.031465W / m.K

418 419



1  2.7378 103 / K 92.26  273 hD 16.78  0.045   23.998 k 0.031465

420

Nusselt Number, Nu =

421

Modified Rayleigh number, Ra# =

g  q // D 5  kL

9.81 2.7378 103  2188   0.045   0.45  22.3328 106  32.2845 10 6  0.031465 5

422 423

424

1.062182 106

Mean stream velocity, u = 13.5m/min = 0.225 m/s

0.225   0.045  uD2 =   45.337  L 22.3328 106  0.45 2

Re#

425

Modified Reynolds number,

426

3 RESULTS AND DISCUSSION

427

Fig. 4(a) and 4(b) illustrate the typical axial variations of local wall temperatures for various L/D ratios

428

and for various heat fluxes for smooth tubes. It can be seen from these figures that the wall temperature

429

increases along the height of the cylinder, which is in accordance with the theoretical predictions done

430

by various investigators. But it slightly decreases towards the end, which may be due to the heat

431

rejection from the end of the tubes as the thickness of the tube is not negligible.

432

15


468

2

409 W/m 2 762 W/m 2 1012 W/m 2 1377 W/m 2 1723 W/m 2 2188 W/m 2 2655 W/m 2 3158 W/m

0

Temperature in c

200

150

100

50

0 0

50 100 150 200 250 300 350 400 450 500 550 600

Distance in mm 469

Fig. 4(a) Variation of wall temperature for different heat fluxes for L = 450 mm 250 2


Temperature in

oc

200

150

100

50

0 0

100

200

300

400

500

600

700

800

900

Distance in mm 470

Fig. 4(b) Variation of wall temperature for different heat fluxes for L = 700 mm

471

Experimental temperature profiles at the channel exit for different heat fluxes and for different L/D ratio

472

for smooth tubes are indicated in fig. 5(a), (b). The radial distances are taken as abscissa whereas the

473

fluid temperatures are taken as the ordinate. Here the distances are measured from the center of the pipe

474

towards the wall at the exit of the test section. At the center r = 0 and at the wall r = R =22.5 mm. It is

475

evident from these figures that the fluid temperature is maximum at the wall which is nearly equal to the

476

wall temperature at the exit of the pipe and it minimum at the center of the pipe. This is due to the fact

477

that heat is transferred from the wall of the heated pipe to the air by natural convection. So, the air in the

478

vicinity of the wall is hotter as compared to the air farther the wall.

479

16

Manuscript body Download source file (1.27 MB) 250 2


o

Temperature in c

200

150

100

50

0 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

Radial distance in mm

506 507

Fig. 5(a) Temperature profile at channel exit for different wall heat fluxes for smooth tubes with L = 450 mm

250 2

o

Temperature in c

200

508

509

150


100

50

0 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

Radial Distance in mm 511

Fig. 5(b) Temperature profile at channel exit for different wall heat fluxes for smooth tubes with L = 700 mm

512

Similarly, studies are also carried out on intensified channels of the same geometrical sizes by providing

513

internal rings of same material of different heights such as t = 4 mm, 6 mm, and 8mm. Step size (s) of

514

the rings are varying from75mm to 283.3mm. Other non-dimensional ratios are taken as: s / D = 1.67 to

515

6.29, t / D = 0.089 to 0.178 and s / t = 9.375 to 70.82. Experimental temperature profiles at the channel

516

exit for different heat fluxes and for different L/D ratio for tubes with internal rings are indicated in

517

figures 6 (a) to 6 (k). It is evident from these figures that the fluid temperature is maximum at the wall

518

which is nearly equal to the wall temperature and minimum at the center of the pipe. It can also be seen

519

from these figures that the air temperature at the center of the pipe is more in case of pipes with internal

520

rings as compared to that of smooth pipes. This is due to the fact that there is enhancement of heat

521

transfer from the wall to the air when internal rings are provided. As hot layers diffuse to the center of

522

17

510

Manuscript body 545

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flow, and the cold ones move to wall area, the gradient of temperature in the boundary layer increases, and thus heat transfer increases. 546

It can also be seen that the average heat transfer rate increases with increasing the thickness of the rings

547

up to a certain limit, beyond which it decreases. When ring thickness increases from 4 mm to 6 mm

548

there is enhancement of heat transfer from the wall to air. But by further increasing the ring thickness

549

from 6 mm to 8 mm there is slight decrease in heat transfer. This may be due to the fact that when the

550

ring thickness increases, the intensity of pulsation will increase and the pulsation arising behind the ring

551

will have no time to fade sufficiently on the way to the following ring and will defuse to the flow core.

552

Thus intensity of pulsation will increase and consequently the turbulence of flow will occur. This results

553

in significant growth of hydraulic resistance with small increase of heat transfer.

250 2


o

Temperature in c

200

150

100

50

0 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

Radial distance in mm 554 555

Fig.6 ( a) Distribution of temperature of flow at the exit of the tube with internal rings (L/D = 10, t = 6 mm, s = 250mm).

250 2

o

Temperature in c

200

150


100

50

0 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

Radial distance in mm 556 557 558

Fig. 6 ( b). Distribution of temperature of flow at the exit of the tube with internal rings (L/D = 10, t = 6 mm, s = 150mm). 18

Manuscript body 580

Download source file (1.27 MB)

250 2


0

Temperature in c

200

150

100

50

0 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0


Fig. 6 ( c) Distribution of temperature of flow at the exit of the tube with internal rings (L/D = 10, t = 6 mm, s = 112.5mm). 250 2

0

Temperature in c

200

583

150

100


50

0 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0


Fig. 6 ( d) Distribution of temperature of flow at the exit of the tube with internal rings (L/D = 10, t = 6 mm, s = 75mm). 250 2

0

Temperature in c

200

150

664 W/m 2 892 W/m 2 1028 W/m 2 1227 W/m 2 1460W/m 2 1637 W/m 2 1980 W/m 2 2596 W/m

100

50

0 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0


588

Fig. 6 ( e). Distribution of temperature of flow at the exit of the smooth tube with internal rings (L/D = 18.89, t = 4 mm, s = 425mm). 19

Manuscript body 612

Download source file (1.27 MB) 2


0

Temperature in c

200

150

100

50

0 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0


Fig. 6 ( f). Distribution of temperature of flow at the exit of the smooth tube with internal rings (L/D = 18.89, t = 4 mm, s = 283.33mm).

250 2


0

Temperature in c

200

150

100

50

0 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0


Fig. 6 ( g) Distribution of temperature of flow at the exit of the smooth tube with internal rings (L/D = 18.89, t = 4 mm, s = 212.5mm) 250 2

0

Temperature in c

200

150

664 W/m 2 892 W/m 2 1028 W/m 2 1227 W/m ) 2 1460 W/m 2 1637 W/m 2 1980 W/m 2 2596 W/m

100

50

0 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0


619

Fig.6 ( h). Distribution of temperature of flow at the exit of the smooth tube with internal rings (L/D = 18.89, t = 6 mm, s = 425mm).

20

Manuscript body 639

Download source file (1.27 MB) 250 2


0

Temperature in c

200

150

100

50

0 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

Radial distance in mm

640 641

Fig. 6 ( i). Distribution of temperature of flow at the exit of the smooth tube with internal rings (L/D = 18.89, t = 6 mm, s = 283.33mm) 250 2

0

Temperature in c

200

150


100

50

0 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0


Fig. 6 ( j). Distribution of temperature of flow at the exit of the smooth tube with discrete rings (L/D = 18.89, t = 6 mm, s = 212.5mm). 250 2

0

Temperature in c

200

150


100

50

0 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

Radial distance in mm 644 645 646

Fig. 6 ( k). Distribution of temperature of flow at the exit of the smooth tube with internal rings (L/D = 18.89, t = 8 mm, s = 212.5mm). 21


The fig. 7 shows the distribution of temperatures of flow at outlet of channels for various L/D ratio, i.e;

676

for different length of the tube. It is clear from the graph that heat transfer increases with increase in

677

tube length. This is because by increasing the length of the test sections the surface area increases as a result of which the heat transfer from the wall to air increases. 220

678

L/D L/D L/D L/D

200 180

0

Temperature in C

160

= = = =

10 12.22 15.56 18.89

140 120 100 80 60 40 20 0 0

5

10

15

20

25

Distance in mm 679

Fig. 7. Temperature profiles at the channel exit for smooth tubes with different length

680

The fig. 8 and 9 shows the distribution of temperatures of flow at outlet of channels for various heat

681

fluxes and various thickness and spacing of rings inside the tube. It can be seen that the average heat

682

transfer rate increases with increasing the thickness of the rings up to a certain limit, beyond which it

683

decreases, which is shown in the fig. 9. Fig. 8 shows that when the spacing between the rings decreases

684

beyond a certain limit, the heat transfer rate decreases. This may be due to the fact that with an often

685

arrangement of rings the pulsation arising behind the ring will have no time to fade sufficiently on the

686

way to the following ring and will defuse to the flow core. Thus, intensity of pulsation will increase and

687

consequently the turbulence of flow will occur. This results in significant growth of hydraulic resistance

688

with small increase of heat transfer. 140

Empty s = 225mm s = 150mm s = 112mm s = 75mm

0

Temperature in C

120 100 80 60 40 20 0 0

5

10

15

20

25

Radial distance in mm 689

690

Fig. 8. Temperature profiles at the channel exit for tubes with discrete rings 22


Empty t = 4 mm t = 6 mm t = 8 mm

120

0

Temperature in C

140

100 80 60 40 20 0

5

10

15

20

25

Radial Distance in mm

719

Fig. 9. Temperature profiles at the channel exit for different ring spacing

720

Relationship between Nusselt number and Rayleigh number:

721

Fig. 10 shows the relationship between the experimentally obtained average Nusselt number and

722

modified Rayleigh number, which is plotted on log-log scale. A correlation between average Nuusselt

723

number and modified Rayleigh number for laminar natural convection in smooth vertical tubes has been

724

developed as shown in Eq. (19): Nu  0.33   Ra # 

725

0.31

(19)

726

Average Nusselt Number

100

10

1 100000

L/D = 10 L/D = 12.22 L/D = 15.56 L/D = 18.89 Eq. 19

1000000

1E7

Modified Rayleigh Number 727 728 729

Fig. 10 Relationships between the experimentally obtained average Nusselt number and modified Rayleigh number 23


Relationship between Reynolds number and Rayleigh number:

753

Fig. 11 shows the relationship between experimentally obtained modified Reynolds number and

754

modified Rayleigh number, which are plotted on logarithmic scale. This correlation can be obtained as:

755

Re #  0.49   Ra # 

1

3

(20)

Modified Reynolds Number

100

756

757

L/D = 10 L/D = 12.22 L/D = 15.56 L/D = 18.89 Eq. 20

10

1 100000

1000000

1E7

Modified Rayleigh Number

Fig. 11 Relationship between experimentally obtained modified Reynolds number and modified Rayleigh number

758 759 760

4 CONCLUSIONS

761

Experimental investigation of natural convection heat transfer in a vertical pipe has been conducted both

762

for smooth pipes and for pipes with internal rings. The effects of channel length, wall heat flux, ring

763

thickness and ring spacing on the characteristics of natural convection heat transfer are examined in

764

detail. The following conclusions have been drawn from the present investigation.

765 766 767 768 769 770

(i) Average heat transfer rate from the internal surfaces of a heated vertical pipe increases with increase in length of the test section. (ii) Average heat transfer rate from the internal surfaces of a heated vertical pipe increases discrete rings are provided. (iii)Average heat transfer rate increases with increasing the thickness of the rings up to certain value, beyond which it decreases.

771

(iv) Average heat transfer rate increases with increasing the number of rings i.e. reducing the spacing

772

between the rings up to a certain value of spacing, but further reduction in ring spacing, reduces

773

the heat transfer rate from the internal wall to air.

774

24

Manuscript body Download source file (1.27 MB) 775 776 777 778

779

780 781 782 783

(v) A correlation between average Nusselt number and modified Rayleigh number was proposed as given in Eq. (19), which can predict the data accurately within ± 5% error. (vi) Another correlation between modified Rayleigh number and modified Reynolds number was proposed as given in Eq. (20), which can predict the data within ± 10% error. REFERENCES : [1] Iyi D., Hasan R.: Natural Convection Flow and Heat Transfer in an Enclosure Containing Staggered Arrangement of Blockages. Procedia Engineering 105, (2015), 176-183. [2] Buonomo B., Manca O.: Transient natural convection in a vertical micro channel heated at uniform heat flux. International Journal of Thermal Sciences 56, (2012), 35-47.

784

[3] Malik S.K., Sastri, V. M. K.: Experimental investigation of natural convection heat transfer over

785

an array of staggered discrete vertical plates. Journal of Energy Heat and Mass transfer, Vol. 18,

786

(1996), 127-133.

787

[4] Huang G.J., Wong S.C., Lin C.P.: Enhancement of natural convection heat transfer from

788

horizontal rectangular fin arrays with perforations in fin base. International Journal of Thermal

789

Sciences 84, (2014), 164-174.

790

[5] Cheng C. Y.: Fully developed natural convection heat and mass transfer in a vertical annular

791

porous medium with asymmetric wall temperatures and concentrations. Applied Thermal

792

Engineering 26, (2006), 2442-2447.

793

[6] Capobianchi M., Aziz A.: A scale analysis for natural convective flows over vertical surfaces,

794

International Journal of Thermal Sciences. International Journal of Thermal Sciences 54 (2012),

795

82-88.

796 797 798 799 800 801

[7] Sparrow E. M., Bahrami P. A.: Experiments in natural convection from vertical parallel plates with either open or closed edges. ASME Journal of Heat Transfer Vol. 102, (1980), 221-227. [8] Lee K.T.: Natural convection heat and mass transfer in partially heated vertical parallel plates. International Journal of Heat and Mass Transfer 42, (1999), 4417-4425. [9] Mobedi M., Sunden B.: Natural convection heat transfer from a thermal heat source located in a vertical plate fin. International Communications in Heat and Mass Transfer 33, (2006),943-950.

802

[10] Levy E. K., Eichen P.A., Cintani W. R., and Shaw R. R.: Optimum plate spacing for laminar

803

natural convection heat transfer from parallel vertical isothermal flat plates: experimental

804

verification. ASME J. Heat Transfer, Vol. 97, (1975),474-476.

805 806

807

[11] Lewandowski W.M., Radziemska E.: Heat transfer by free convection from an isothermal vertical round plate in unlimited space. Applied Energy 68, (2001),187-201. 25

Manuscript body Download source file (1.27 MB) 808 809

[12] Dey S., Chakrborty D.: Enhancement of convective cooling using oscillating fins. International Communications in Heat and Mass Transfer 36 (2009), 508–512.

810

[13] Awasarmol U. V., Pise A. T.: An experimental investigation of natural convection heat transfer

811

enhancement from perforated rectangular fins array at different inclinations. Experimental

812

Thermal and Fluid Science 68 (2015), 145–154.

813

[14] Kundu B., Wongwises S.: Decomposition analysis on convecting– radiating rectangular plate

814

fins for variable thermal conductivity and heat transfer coefficient. J. Franklin Inst. 349 (2012),

815

966–984.

816 817

[15] Kundu B., Lee K.S.: Exact analysis for minimum shape of porous fins under convection and radiation heat exchange with surrounding. Int. J. Heat Mass Transfer 81 (2015), 439–448.

818

[16] Singh P., Patil A. K.: Experimental investigation of heat transfer enhancement through

819

embossed fin heat sink under natural convection. Experimental Thermal and Fluid Science 61

820

(2015), 24–33.

821

[17] Roul M.K., Nayak R.C.: Experimental Investigation of Natural Convection Heat Transfer

822

through Heated Vertical Tubes. International Journal of Engineering Research and Applications,

823

Vol. 2(2012), 1088-1096.

824 825 826 827 828 829 830 831 832 833 834 835

[18] Deshmukh P.A., Warkhedkar R.M.: Thermal performance of elliptical pin fin heat sink under combined natural and forced convection. Exp. Thermal Fluid Sci. 50 (2013), 61–68. [19] Taler D.: Experimental determination of correlations for mean heat transfer coefficients in plate fin and tube heat exchangers. Archives of thermodynamics Vol. 33(2012), 1-24. [20] Taler D., Taler J.: Steady-state and transient heat transfer through fins of complex geometry. Archives of Thermodynamics, 35 (2014), 117–133. [21] Duda P., Mazurkiewicz G.: Numerical modeling of heat and mass transfer in cylindrical ducts. Archives of Thermodynamics, 31 (2010), 33–43. [22] Vliet, G.C.:

Natural convection local heat transfer on constant-heat-flux inclined surfaces.

Journal of Heat Transfer 91(1969), 511-516. [23] Churchill S.W., Chu H.H.S.: Correlating Equations for Laminar and Turbulent Free Convection from a Vertical Plate. International Journal of Heat Mass Transfer 18 (1975), 1323–1329.

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[24] Holman J. P.: Heat Transfer. McGraw-Hill, Tenth Edition 2010.

837

[25] Velmurugan, P., Kalaivanan, R.:

838

Sadhana 41(2016), 369–376.

839

Energy and exergy analysis in double-pass solar air heater.

26

Index

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