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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Textbook Question
Chapter 2, Problem 2.46P
A steam pipe is wrapped with insulation of inner and outer radii
Are conditions steady-state or transient? How do the heat flux and heat rate vary with radius?
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Shown in the figure below is an insulated copper block that receives energy at a rate of 200 W from an
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PROBLEM 3
In the given schematic of heat transfer for a wall, there is heat conduction through the wall
and the outer surface of the wall is subject to both convection and radiation.
T₁ = 308 K
k = 0.3 W/m-K
L = 3 mm
-T₁
-ε = 0.95
111
Air
Tsur = 297 K
T = 297 K
h = 2 W/m² K (Air)
(a) Write the energy conservation equation for the system in terms of the three heat
transfer modes.
(b) Find the surface temperature Ts in °C.
A plane wall of thickness 2L=40 mm and thermal conductivity k=5 W/m·K experiences
uniform volumetric heat generation at a rate q, while convection heat transfer occurs at both of
its surfaces (x=-L, +L), each of which is exposed to a fluid of temperature T=20 °C. Under
steady-state conditions, the temperature distribution in the wall is of the form T(x) = a+bx+cx²
where a = 82.0 °C, b=-210 °C/m, c = -2x10 °C/m², and x is in meters. The origin of the x-
coordinate is at the midplane of the wall.
-L x
-L
(a) Determine the surface heat fluxes, qx(-L) and qx(+L).
(b) What is the volumetric rate of heat generation & in the wall?
(c) What is the convection heat transfer coefficient for the surfaces at x = +L?
(d) Obtain an expression for the heat flux distribution q (as a function of x). Is the heat flux
zero at any location?
(e) If the source of the heat generation is suddenly deactivated (i. e. q = 0), what temperature
will the wall eventually reach with q = 0?
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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