Dynamic thermal networks: a methodology to account for time-dependent heat conduction

摘要

Thermal networks provide a handy and instructive way to represent steady-state heat flow processes. Time-dependent thermal flow is much more difficult to handle. The paper outlines a general methodology and theory for time-dependent thermal processes. The method requires that the heat flows through the boundary surfaces are calculated for a unit step change at one surface and zero temperature at the other surfaces. The relations between surface temperatures and heat flows for any time-dependent process are obtained by superposition of the step responses. The theory provides nice insight into the memory effects for time-dependent heat flow. The mathematically exact temperature-flow relations between the surfaces are represented graphically as a dynamic thermal network. The heat flow between two nodes is given by the steady-state conductance times a suitable mean value of the difference of preceding node temperatures. A new conductance has to be added for each surface. This part involves the difference between the actual node temperature and a mean value of preceding temperatures. There are transmittive heat fluxes between all pairs of nodes, and an absorptive flow component at each node.