Work Problem 5.47 for a cylinder of radius r o and length L = 20 r o

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Work Problem 5.47 for a cylinder of radius ro and length L = 20 ro.


Data From Problem 5.47

A constant-property, one-dimensional plane slab of width 2L, initially at a uniform temperature, is heated convectively with B= 1.

(a) At a dimensionless time of Fo1, heating is suddenly stopped, and the slab of material is quickly covered with insulation. Sketch the dimensionless surface and midplane temperatures of the slab as a function of dimensionless time over the range 0 < Fo < ∞. By changing the duration of heating to Fo2, the steady-state midplane temperature can be set equal to the midplane temperature at Fo1. Is the value of Fo2 equal to, greater than, or less than Fo1?
(b) Letting FoFo1 + ΔFo, derive an analytical expression for ΔFo, and evaluate ΔFo for the conditions of part (a).
(c) Evaluate ΔFo for Bi = 0.01, 0.1, 10, 100, and ∞ when Foand Fo2 are both greater than 0.2.

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Fundamentals Of Heat And Mass Transfer

ISBN: 9780470501979

7th Edition

Authors: Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera, David P. DeWitt

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