Abstract
A complete analytical study is presented for the determination of the three-dimensional unsteady temperature distributions in a finite hollow circular cylinder under the influence of a variable internal heat source and an arbitrary initial temperature distribution when the entire surface is subjected to variable heat flux rates. The volume heat source as well as the surface flux rates are prescribed in terms of arbitrary functions of space and time. General expressions are derived and their various alternative forms are noted. Corresponding general expressions for the two-dimensional and the one-dimensional heat flow problems are systematically deduced as limiting cases.
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