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.