A rational method for the distribution of nodes in modelling of transient heat conduction in plane slabs

Abstract

In this paper, the thermal response of a homogenous slab to both step and sinusoidal excitations of temperature at one boundary is examined. The distribution of nodes for the purposes of heat balance thermal modelling is discussed. Errors in the heat flux at the external boundary are examined when even and uneven gridding approaches are applied. A denser gridding close to the surface is adopted due to the fact that the curvature of the temperature gradient is greatest near the surface during the early stages of transient heat transfer. Example calculations demonstrate the potential of uneven gridding to obtain a rational compromise between accuracy and computational effort. Rational uneven gridding results in a more accurate solution with a smaller number of thermal nodes compared with even gridding.