Introduction to Heat Transfer

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Fourth edition. Solutions manual. School of Mechanical Engineering. Purdue University. Introduction to. Heat. Transfer. Frank P. Incropera. David P. Dewitt ...

Introduction to Heat Transfer Fourth edition

Solutions manual Frank P. Incropera David P. Dewitt School of Mechanical Engineering Purdue University

PROBLEM 1.1 KNOWN: Heat rate, q, through one-dimensional wall of area A, thickness L, thermal conductivity k and inner temperature, T1. FIND: The outer temperature of the wall, T2. SCHEMATIC:

ASSUMPTIONS: (1) One-dimensional conduction in the x-direction, (2) Steady-state conditions, (3) Constant properties. ANALYSIS: The rate equation for conduction through the wall is given by Fourier’s law,

q cond = q x = q ′′x ⋅ A = -k

T −T dT ⋅ A = kA 1 2 . dx L

Solving for T2 gives

T2 = T1 −

q cond L . kA

Substituting numerical values, find

T2 = 415$ C -

3000W × 0.025m 0.2W / m ⋅ K × 10m2

T2 = 415$ C - 37.5$ C T2 = 378$ C. COMMENTS: Note direction of heat flow and fact that T2 must be less than T1.