Simple Explicit Equations for Transient Heat Conduction in Finite Solids

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 $0<Bi<0.3$ 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 $0<Bi<1$ 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 $0<Bi<∞$ range with less than 1% error.