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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Question
Chapter 2, Problem 2.43P
(a)
To determine
The differential equation for variation in temperature with angular coordinate.
(b)
To determine
The expression for temperature distribution
(c)
To determine
The expression for heat rate
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under steady-state conditions. If you are given T1 = 200 °C and T2 = 164 °C, determine:
a) the conduction heat flux, q,.cond, in
m2
W
from x = 0 to x = L
b) if the dimensions of the triangle ares 15 mm and h 13 mm, calculate the heat
transfer due to convection, q,y, in W at x = L
Finsulation
T2
T
T = 20°C
h = 500 W/m2.K
Triangular Prism
x L
x 0
L= 50 mm
k = 100 W/m-K
Q1
Passage of an electric current through a long conducting
rod of radius r; and thermal conductivity k, results in
uniform volumetric heating at a rate of ġ. The conduct-
ing rod is wrapped in an electrically nonconducting
cladding material of outer radius r, and thermal conduc-
tivity k, and convection cooling is provided by an
adjoining fluid.
Conducting
rod, ġ, k,
11
To
Čladding, ke
For steady-state conditions, write appropriate forms of
the heat equations for the rod and cladding. Express ap-
propriate boundary conditions for the solution of these
equations.
#4: A rod of length L. coincides with the interval [0, L] on the x-axis. Let u(x, t) be the
temperature. Consider the following conditions.
(A) The left end is held at temperature 0°.
(B) The right end is insulated.
(C) There is heat transfer from the lateral surface of the rod into the
surrounding medium, which is held at temperature 0°
(D) The left end is insulated.
(E) The initial temperature is 0° throughout.
(F) The right end is held at temperature 0°.
(G) There is heat transfer from the right end into the surrounding medium,
which is held at a constant temperature of 0°.
(H) There is heat transfer from the left end into the surrounding medium,
which is held at a constant temperature of 0°.
In each part below, determine which of the above conditions corresponds to the
given initial or boundary condition for the heat equation.
(a) u(x, 0) = 0
(b) u(0, 1) = 0
(c) du
(d) ou
x=L
ox|x=0
= -hu(L, 1)
= hu(0, 1)
Chapter 2 Solutions
Introduction to Heat Transfer
Ch. 2 - Assume steady-state, one-dimensional heat...Ch. 2 - Assume steady-state, one-dimensional conduction in...Ch. 2 - A hot water pipe with outside radius r1 has a...Ch. 2 - A spherical shell with inner radius r1 and outer...Ch. 2 - Assume steady-state, one-dimensional heat...Ch. 2 - A composite rod consists of two different...Ch. 2 - A solid, truncated cone serves as a support for a...Ch. 2 - To determine the effect of the temperature...Ch. 2 - Prob. 2.9PCh. 2 - A one-dimensional plane wall of thickness 2L=100mm...
Ch. 2 - Consider steady-state conditions for...Ch. 2 - Consider a plane wall 100 mm thick and of thermal...Ch. 2 - Prob. 2.13PCh. 2 - In the two-dimensional body illustrated, the...Ch. 2 - Consider the geometry of Problem 2.14 for the case...Ch. 2 - Steady-state, one-dimensional conduction occurs in...Ch. 2 - Prob. 2.17PCh. 2 - Prob. 2.18PCh. 2 - Consider a 300mm300mm window in an aircraft. For a...Ch. 2 - Prob. 2.20PCh. 2 - Use IHT to perform the following tasks. Graph the...Ch. 2 - Calculate the thermal conductivity of air,...Ch. 2 - A method for determining the thermal conductivity...Ch. 2 - Prob. 2.24PCh. 2 - Prob. 2.25PCh. 2 - At a given instant of time, the temperature...Ch. 2 - Prob. 2.27PCh. 2 - Uniform internal heat generation at q.=5107W/m3 is...Ch. 2 - Prob. 2.29PCh. 2 - The steady-state temperature distribution in a...Ch. 2 - The temperature distribution across a wall 0.3 m...Ch. 2 - Prob. 2.32PCh. 2 - Prob. 2.33PCh. 2 - Prob. 2.34PCh. 2 - Prob. 2.35PCh. 2 - Prob. 2.36PCh. 2 - Prob. 2.37PCh. 2 - One-dimensional, steady-state conduction with no...Ch. 2 - One-dimensional, steady-state conduction with no...Ch. 2 - The steady-state temperature distribution in a...Ch. 2 - One-dimensional, steady-state conduction with no...Ch. 2 - Prob. 2.42PCh. 2 - Prob. 2.43PCh. 2 - Prob. 2.44PCh. 2 - Beginning with a differential control volume in...Ch. 2 - A steam pipe is wrapped with insulation of inner...Ch. 2 - Prob. 2.47PCh. 2 - Prob. 2.48PCh. 2 - Two-dimensional, steady-state conduction occurs in...Ch. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - A chemically reacting mixture is stored in a...Ch. 2 - A thin electrical heater dissipating 4000W/m2 is...Ch. 2 - The one-dimensional system of mass M with constant...Ch. 2 - Consider a one-dimensional plane wall of thickness...Ch. 2 - A large plate of thickness 2L is at a uniform...Ch. 2 - Prob. 2.57PCh. 2 - Prob. 2.58PCh. 2 - A plane wall has constant properties, no internal...Ch. 2 - A plane wall with constant properties is initially...Ch. 2 - Consider the conditions associated with Problem...Ch. 2 - Prob. 2.62PCh. 2 - A spherical particle of radius r1 experiences...Ch. 2 - Prob. 2.64PCh. 2 - A plane wall of thickness L=0.1m experiences...Ch. 2 - Prob. 2.66PCh. 2 - A composite one-dimensional plane wall is of...Ch. 2 - Prob. 2.68PCh. 2 - The steady-state temperature distribution in a...
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