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
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Chapter 4, Problem 4.49P
(a)
To determine
Finite − difference equation for any interior node
(b)
To determine
Finite − difference equation for node
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The diagram (below) illustrate an object of a thermal conductivity 236 W/m-K. The
circular cross section is having a radius r = ax, where a = 0.4. The small end is
located at x1= 24 mm and the large end at x2 = 124 mm. End temperatures are Ti=
600 K and T2 = 400 K (as shown by figure), while lateral surface is well insulated.
(1) Please find the temperature distribution equation (in terms of temperature (T)
and distance (x)). (2) Calculate conduction heat rate (q.) in kW.
2. A rectangular block has thickness B in the x-direction. The side at x = 0 is held at temperature
T, while the side at x = B is held at T2. The other four sides are well insulated. Heat is generated
in the block at a uniform rate per unit volume of [.
(a) Use the conduction equation to derive an expression for the steady-state temperature profile,
T(x). Assume constant thermal conductivity.
(b) Use the result of part (a) to calculate the maximum temperature in the block for the following
values of the parameters:
T₁-120 °C k-0.2 W/(m K) B-1.0 m T₂-0 F-100 W/m³
1. Question 1- Laplace Equation: Leibmann's Method
The four sides of a square plate of side 12cm, made of homogenous material, are kept at a constant
temperature 0°C and 100°C as shown in Figure 1. Using a grid of mesh 4cm and applying Leibmann's
method, perform up to four (4) iteration to find the temperature at the various mesh points.
12cm
U=100
➤U=0
R
u=100
U=100
·X
12cm
Figure 1 Showing Boundary Conditions for Given Problem.
Chapter 4 Solutions
Fundamentals of Heat and Mass Transfer
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