Heat and Mass Transfer: Fundamentals and Applications
5th Edition
ISBN: 9780073398181
Author: Yunus A. Cengel Dr., Afshin J. Ghajar
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 2, Problem 153P
Consider a cylindrical sheel of length L, inner radius r1, and outer radius r2 whose thermal conductivity varies in a specified temperature range as
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1- A solid infinitely long cylinder, radius 2 cm, has uniform internal heat generation. The
temperature distribution in the cylinder is
T(r) =
= 256 – 8.6 x 104 r²
where r is in meters, T in °C and the thermal conductivity of the cylinder material is 16 W/ m °C.
Determine:
(a) The temperature at the centerline.
(b) The surface temperature.
(c) The heat flux at the surface.
(d) The rate of heat transfer to the surrounding per unit meter of cylinder length.
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?
Q1: In a nuclear reactor, heat is generated uniformly in the 5-cm-diameter cylindrical uranium rods at a rate of 7
x 10' W/m. If the length of the rods is 1 m, determine the rate of heat generation in each rod.
Answer: Q=137.4 kW
Q2: Write down the one-dimensional transient heat conduction equation for a plane wall with constant thermal
conductivity and heat generation in its simplest form, and indicate what each term represents. Also, what is
the units of every term?
Q3: Consider a spherical container of inner radius r1, outer radius r2, and thermal conductivity k. Express the
boundary condition on the inner surface of the container for steady one dimensional conduction for the
following cases: (a) specified temperature of 50°C, (b) specified heat flux of 30 W/m² toward the center, (c)
convection to a medium at T with a heat transfer coefficient of h.
Q4: Heat is generated in a long wire of radius ro at a constant rate of go per unit volume. The wire is covered
with a plastic…
Chapter 2 Solutions
Heat and Mass Transfer: Fundamentals and Applications
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Ch. 2 - Prob. 11CPCh. 2 - Consider the cooking process of a roast beef in an...Ch. 2 - Consider heat loss from a 200-L cylindrical hot...Ch. 2 - Consider a cold canned drink left on a dinner...Ch. 2 - Heat flux meters use a very sensitive device know...Ch. 2 - Consider a large 3-cm-thick stainless steel plate...Ch. 2 - In a nuclear reactor, heat is generated uniformly...Ch. 2 - Prob. 18PCh. 2 - Prob. 19EPCh. 2 - Writer down the one-dimensional transient heat...Ch. 2 - Writer down the one-dimensional transient heat...Ch. 2 - Starting with an energy balance on rectangular...Ch. 2 - Prob. 23PCh. 2 - Prob. 24PCh. 2 - Consider a medium in which the heat conduction...Ch. 2 - Consider a medium in which the heat conduction...Ch. 2 - Consider a medium in which the heat conduction...Ch. 2 - Consider a medium in which the heat conduction...Ch. 2 - Consider a medium in which the heat conduction...Ch. 2 - Consider a medium in which the heat conduction...Ch. 2 - Consider a medium in which the heat conduction...Ch. 2 - Starting with an energy balance on a volume...Ch. 2 - Prob. 33PCh. 2 - Prob. 34PCh. 2 - What is a boundary condition? 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