Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 3, Problem 3.80P
To determine
Radial distribution of the temperature, heat flux and heat rate
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Consider a solid sphere of radius R with a fixed surface temperature, TR. Heat is generated within
the solid at a rate per unit volume given by q = ₁ + ₂r; where ₁ and ₂ are constants.
(a) Assuming constant thermal conductivity, use the conduction equation to derive an expression
for the steady-state temperature profile, T(r), in the sphere.
(b) Calculate the temperature at the center of the sphere for the following parameter values:
R=3 m 1₁-20 W/m³ TR-20 °C k-0.5 W/(m K) ₂-10 W/m³
Derive a heat rate expression for the following geometry. Assume there is a poor contact at the
junction of walls Y and Z and consider one-dimensional steady-state heat transfer with constant
thermal conductivities of the walls.
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Chapter 3 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 3 - Consider the plane wall of Figure 3.1, separating...Ch. 3 - A new building to be located in a cold climate is...Ch. 3 - The rear window of an automobile is defogged by...Ch. 3 - The rear window of an automobile is defogged by...Ch. 3 - A dormitory at a large university, built 50 years...Ch. 3 - In a manufacturing process, a transparent film is...Ch. 3 - The walls of a refrigerator are typically...Ch. 3 - A t=10-mm -thick horizontal layer of water has a...Ch. 3 - A technique for measuring convection heat transfer...Ch. 3 - The wind chill, which is experienced on a cold,...
Ch. 3 - Determine the thermal conductivity of the carbon...Ch. 3 - A thermopane window consists of two pieces of...Ch. 3 - A house has a composite wall of wood, fiberglass...Ch. 3 - Consider the composite wall of Problem 3.13 under...Ch. 3 - Consider a composite wall that includes an...Ch. 3 - Work Problem 3.15 assuming surfaces parallel to...Ch. 3 - Consider the oven of Problem 1.54. 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The...Ch. 3 - Consider a rod of diameter D, thermal conductivity...Ch. 3 - A carbon nanotube is suspended across a trench of...Ch. 3 - A probe of overall length L=200mm and diameter...Ch. 3 - A metal rod of length 2L diameter D, and thermal...Ch. 3 - A very long rod of 5-mm diameter and uniform...Ch. 3 - From Problem 1.71, consider the wire leads...Ch. 3 - Turbine blades mounted to a rotating disc in a...Ch. 3 - Prob. 3.127PCh. 3 - Prob. 3.128PCh. 3 - Prob. 3.129PCh. 3 - A brass rod 100 mm long and 5 mm in diameter...Ch. 3 - The extent to which the tip condition affects the...Ch. 3 - A pin fin of uniform. cross-sectional area is...Ch. 3 - The extent to which the tip condition affects the...Ch. 3 - A straight tin fabricated from 2024 aluminum alloy...Ch. 3 - Triangular and parabolic straight tins are...Ch. 3 - Two long copper rods of diameter D=10mm are...Ch. 3 - Circular copper rods of diameter D=1mm and length...Ch. 3 - During the initial stages of the growth of the...Ch. 3 - Consider two long, slender rods of the same...Ch. 3 - A 40-mm-long, 2-mm-diameter pin fin is fabricated...Ch. 3 - An experimental arrangement for measuring the...Ch. 3 - Finned passages are frequently formed between...Ch. 3 - The fin array of Problem 3.142 is commonly found...Ch. 3 - An isothermal silicon chip of width W=20mm on a...Ch. 3 - As seen in Problem 3.109, silicon carbide...Ch. 3 - A homeowner's wood stove is equipped with a top...Ch. 3 - Water is heated by submerging 50-mm-diameter,...Ch. 3 - As a means of enhancing heat transfer from...Ch. 3 - Consider design B of Problem 3.151. Over time....Ch. 3 - Determine the percentage increase in heat transfer...Ch. 3 - Aluminum fins of triangular profile are attached...Ch. 3 - An annular aluminum fin of rectangular profile is...Ch. 3 - Annular aluminum fins of rectangular profile are...Ch. 3 - It is proposed to air-cool the cylinders of a...Ch. 3 - Prob. 3.165PCh. 3 - Prob. 3.166PCh. 3 - Prob. 3.168PCh. 3 - Prob. 3.173PCh. 3 - Prob. 3.174PCh. 3 - Prob. 3.175PCh. 3 - A nanolaminated material is fabricated with an...
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