The RC Analogy Provides a Versatile Computational Tool for Unsteady, Unidirectional Heat Conduction in Regular Solid Bodies Cooled by Adjoining Fluids

Abstract

Evaluation of spatio-temporal temperatures and total heat transfer rates in simple bodies (large plate, long cylinder and sphere) has been traditionally explained in undergraduate courses of heat transfer by the Heisler/Gröber or by the Boelter/Gröber charts. These three charts pose some restrictions with respect to the applicable times. Additionally, the charts do not provide information about the time-dependent heat fluxes at the surface. Conversely, evaluation of spatio-temporal temperatures, time-dependent heat fluxes at the surface and total heat transfer rates can be easily done for the entire time domain with the network simulation method (NSM) in conjunction with the commercial code PSPICE. NSM relies on the existing physical analogy between the unsteady transport of electric current and the unsteady transport of unidirectional heat by conduction. This analogy has been named the RC analogy in the specialized literature. The code PSPICE simulates the electric circuits for a specific body together with the imposed boundary and initial conditions, and produces numerical results for the quantities of interest, such as: the spatio-temporal temperature distributions; the time-dependent heat flux distributions at the surface; and the total heat transfer.