Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 2, Problem 2.3P
A hot water pipe with outside radius r, has a temperature
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Consider a single cylindrical fin of a uniform cross-sectional area (D = 5 mm, L = 70 mm,k = 400 W/m.K) that is attached to a wall with a base temperature of Tb = 180 C. Ambientconditions are T∞ = 50 °C and h = 210 W/m2.K.a. What is the heat transfer rate of a single fin?b. Plot the temperature distribution within the fin (Excel, MATLAB, … etc.)c. What is the material of the fin?
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
A solid cylinder of radius R and length L is made from material with thermal conductivity 2.
Heat is generated inside the cylinder at a rate S (energy per unit volume per unit time).
(a) Neglecting conduction along the axis of the cylinder, find the steady-state temperature
distribution in the cylinder, given that the surface temperature is Ts.
(b) Consider a crude approximation of a mouse modeled as a cylinder of radius 1 cm and
length 5 cm. If the ambient air temperature is 10°C and the internal rate of heat
generation in the animal is 10-³ W/cm³, find the skin temperature (Ts) for the mouse. The
external heat-transfer coefficient is h = 0.2 W/m².K. (You can neglect conduction along
the axis of the mouse, as in part a.)
Chapter 2 Solutions
Fundamentals of Heat and Mass 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 r, 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 - A young engineer is asked to design a thermal...Ch. 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 - A cylinder of radius ro, length L, and thermal...Ch. 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 - An apparatus for measuring thermal conductivity...Ch. 2 - An engineer desires to measure the thermal...Ch. 2 - Consider a 300mm300mm window in an aircraft. For a...Ch. 2 - Consider a small but known volume of metal that...Ch. 2 - Use INT 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 - Compare and contrast the heat capacity cp of...Ch. 2 - A cylindrical rod of stainless steel is insulated...Ch. 2 - At a given instant of time, the temperature...Ch. 2 - A pan is used to boil water by placing it on a...Ch. 2 - Uniform internal heat generation at q=5107W/m3 is...Ch. 2 - Consider a one-dimensional plane wall with...Ch. 2 - The steady-state temperature distribution in a...Ch. 2 - The temperature distribution across a wall 0.3 m...Ch. 2 - Prob. 2.33PCh. 2 - One-dimensional, steady-state conduction with...Ch. 2 - Derive the heat diffusion equation, Equation 2.26,...Ch. 2 - Derive the heat diffusion equation, Equation 2.29....Ch. 2 - The steady-state temperature distribution in a...Ch. 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 - Prob. 2.41PCh. 2 - Prob. 2.42PCh. 2 - cylindrical system illustrated has negligible...Ch. 2 - Beginning with a differential control volume in...Ch. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - For a long circular tube of inner and outer radii...Ch. 2 - Passage of an electric current through a long...Ch. 2 - Two-dimensional. steady-state conduction occurs in...Ch. 2 - An electric cable of radius r1 and thermal...Ch. 2 - A spherical shell of inner and outer radii ri and...Ch. 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 - The plane wall with constant properties and no...Ch. 2 - Consider the steady-state temperature...Ch. 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 - Consider the steady-state temperature distribution...Ch. 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 - Typically, air is heated in a hair dryer by...Ch. 2 - Prob. 2.69P
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