Transient 3D heat flow analysis for microchannel heat sinks using the transmission line matrix method

This paper presents the implementation of the transmission line matrix (TLM) method for the modelling of the heat transfer in microchannel heat sinks. The convective heat transfer is accounted for by using Newton's law of cooling, and the heat transport in the channels is modelled in terms of the bulk properties. An additional TLM link line is introduced to account for the enthalpy variation in the fluid. The incorporation of an electrical diode, in the new enthalpy link line as described in this paper, is shown to be an excellent way to account for the enthalpy convection without altering classical TLM algorithm arrangements. The results are applied to a ducted water flow under heat source constraints and compared to those obtained by an upwind FDM model. Good agreement is found for Reynolds numbers higher than 12, with axial conduction neglected, for typical microchannel geometries used in this work. The method is applied afterwards to solve a 3D transient heat flow in a water cooled microchannel heat sink subjected to uniform heat constraints. The results are compared with those obtained by the standard FDM method based on the same assumptions. The maximum relative error is found to be less than 1.5% between the two methods. The TLM CPU time was much lower than the minimum time required by the FDM routine. A comparison of the steady-state results to experimental results obtained by Tuckerman showed a relative error between 6 and 8% depending on the temperature used to evaluate the water thermophysical properties and on the Nusselt number value used to evaluate the convective heat transfer coefficient.