Analogue solution of heat conduction problems

THE DIFFERENTIAL EQUATIONS of heat conduction become exceedingly complex for all but the most elementary systems, and in the practical case recourse must be had to numerical or experimental solutions. One such experimental method is to make use of the similarity which exists between the equations of heat flow and the equations of the flow of a unidirectional current in a mesh consisting of resistance and capacitance. In both cases, the quantity of flow depends upon the magnitude of the potential in the direction of flow and upon the conductivity of the medium supporting conduction. In both cases, also, there is a transfer of energy. However, in the thermal system, the thermal conductivity is a function of the magnitude of the applied temperature, while in the electric system, the electrical conductivity is normally independent of the voltage provided, that is, interest is confined to true conductors, and the physical system is ventilated. There is a correspondence too, between the thermal energy stored in the medium and the electrostatic energy stored in a capacitance, for the quantity of heat or electricity stored is simply equal to the product of capacitance (thermal or electrical) and potential.