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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Chapter 3, Problem 3.140P
A thin circular disk is subjected to induction heating from a coil, the effect of which is to provide a uniform heat generation within a ring Section as shown. Convection occurs at the upper surface, while the lower surface is well insulated.
(a) Derive the transient, finite-difference equation for node m, which is within the region subjected to induction heating.
(b) On
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8. The shown 2-D plate is in contact with a heat source at its upper edge, which supplies heat
at a constant flux, qo, per unit length.
--
a. Derive a finite-difference relationship to express the steady-state temperature at the
shown boundary point TP, in terms of the temperatures at the surrounding points (TE, Tw,
Ts) and the other quantities in the problem (e.g., k, qo, etc.). Follow the methodology
outlined in the class notes (i.e., use energy balance). Assume Ax = Ay.
y
90
b. Modify the relationship for the case when the upper edge is perfectly insulated (without
heat addition).
3. A thin metallic wire of thermal conductivity k, diameter D, and length 2L is annealed by passing
an electrical current through the wire to induce a uniform volumetric heat generation åg. The
ambient air around the wire is at a temperature To, while the ends of the wire at x
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 3 Solutions
Introduction to Heat Transfer
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