Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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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
Assuming constant properties and no internal heat generation, determine the regions where the temperature changes with time.
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Students have asked these similar questions
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.)
Suppose that as a body cools, the temperature of the surrounding medium increases because it
completely absorbs the heat being lost by the body. Let T(t) and Tm (t) be the temperatures of
the body and the medium at time t, respectively. If the initial temperature of the body is T1 and
the initial temperature of the medium is T2, then it can be shown in this case that Newton's law
of cooling is dT/dt = k(T - Tm ), k 0 is a constant.
(a) The foregoing DE is autonomous. Determine the limiting value of the temperature T(t)
as t→ o What is the limiting value of Tm (t) as t→o?
(b) Verify your answers in part (a) by actually solving the differential equation.
(c) Discuss a physical interpretation of your answers in part (a).
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.
The initial temperature of the object at time t = = 0 is T(t = 0) = 200°C.
°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 =
Chapter 2 Solutions
Fundamentals of Heat and Mass Transfer
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