Fundamentals of Heat and Mass Transfer
Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated


Textbook Question
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Chapter 3, Problem 3.1P

Consider the plane wall of Figure 3.1, separating hot and cold fluids at temperatures T , 1 and T , 2 , respectively. Using surface energy balances as boundary conditions at x = 0 and x = L (see Equation 2.34). obtain the temperature distribution within the wall and the heat flux in terms of T , 1 , T , 2 , h 1 , h 2 , k , and L.

Expert Solution & Answer
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To determine

The temperature distribution within the wall and heat flux.

Answer to Problem 3.1P

The expression of temperature distribution is T(x)=h1h2kh1+kh2+h1h2Lx+kh1T,1+kh2T,2+h2Lh1T,1kh1+kh2+h1h2L and heat flux is q=h1kh21h2+1h1+Lk(T,1T,2) .

Explanation of Solution


The temperature of hot fluid is T,1

The temperature of cold fluid is T,2

Formula Used:

The expression of one dimensional heat equation is given by,


The expression of convection heat rate is given by,



Assume steady state, constant material properties with no heat generation.

The heat equation is calculated as,


Integrate the above equation once.


Integrate above equation again.


Apply boundary condition at x=0 and x=L .

At x=0 , q=k( dT dx)x=0=h1(T ,1T s,1)

At x=L , q=k( dT dx)x=L=h2(T s,2T ,2)

The surface temperature at x=0 is given by,


The surface temperature at x=L is given by,

  Ts,2=C1L+C2 .

Solve all the equation to find unknown.




The temperature distribution is calculated as,


The heat flux is calculated as,



Therefore, the expression of temperature distribution is T(x)=h1h2kh1+kh2+h1h2Lx+kh1T,1+kh2T,2+h2Lh1T,1kh1+kh2+h1h2L and heat flux is q=h1kh21h2+1h1+Lk(T,1T,2) .

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Chapter 3 Solutions

Fundamentals of Heat and Mass Transfer

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