Based on the one-term Fourier series solution, a simple equation is derived for low Biot number transient conduction in plates, cylinders, and spheres. In the range, the solution gives approximately three times less error than the lumped capacity solution. For asymptotically low values of Bi, it approaches the lumped capacity solution. A set of equations valid for is developed next. These equations are more involved but give approximately ten times lower error than the lumped capacity solution. Finally, a set of broad-range correlations is presented, covering the range with less than 1% error.
Keywords:Fourier series, heat conduction, transient, conduction, diffusion, Fourier series, eigenvalues
J. B. J., 2003, “
Theorie analytic da la chaleur,”
The Analytical Theory of Heat,
M. P., 1947, “
Temperature Charts for Induction and Constant-Temperature Heating,”
S. W., and
R., 1972, “
A General Expression for the Correlation of Rates of Transfer and Other Phenomena,”
A. V., 1968,
Analytical Heat Diffusion Theory,
Heat Conduction Using Green’s Functions,
Washington, DC, p.
M. M., 1996, National Heat Transfer Conference, Houston, TX, Aug. 3–6, Paper No. AIAA-96–3968.
A. G., and
B. B., 2008,
J. Cryst. Growth0022-0248,
F. P., and
D. P., 1990,
Introduction to Heat Transfer, 2nd ed.,
B. B., 2007/2008, private communication.
Conduction Heat Transfer,
Heat Conduction, 3rd ed.,
Taylor & Fancis,
W. M., and
H. Y., 1961,
Heat Mass and Momentum Transfer,
Englewood Cliffs, NJ.
Copyright © 2009
by American Society of Mechanical Engineers