Introduction to Heat Transfer
6th Edition
ISBN: 9780470501962
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 2, Problem 2.26P
At a given instant of time, the temperature distribution within an infinite homogeneous body is given by the function
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The initial temperature of a 50 cm long silver wire is 50 °C. The circumference of the wire in question is completely insulated, but both ends are kept at a temperature of 0 °C (zero degrees Celsius). Obtain the heat conduction along the wire as a function of time and position and, taking a single term in the solution, determine how many degrees Celsius the temperature in the middle of the rod will be after 7 minutes. (For silver wire, α=1.70 cm2/s.)
The time evolution of the temperature of an object follows the Newton's cooling laws
dT
dx
=
-k(T - Ts),
where the term k = 2.2 (1/s) is the heat transfer constant, and Tg = 25.6° C is the ambient temperature.
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°C
Use the Euler's method, and a time step of h=0.2s, calculate:
When t = = 0.2s, T =
°C
When t 1s, T =
A curved surface of a rod of length L is perfectly insulated against the flow of heat . The rod , which is so thin that heat flow in it can be assumed to be one dimensional , is initially at the temperature U(x,0 ) = 20 x / 3L ° C . Find the temperature at any point in the road at any subsequent time if at t = 0 the temperature at each end of the rod is suddenly reduced to 0 ° C and maintained at that temperature thereafter .
Chapter 2 Solutions
Introduction to Heat Transfer
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