Fast local transient solution of micro-channel heat sink using asymptotic waveform evaluation.

摘要

Thermal analyses of one-, two- and three-layered micro-channels have been carried out. Seven types of micro-channels have been identified based on all the possible types of flow directions. Finite element method (FEM) is used to discretise the domain into nodes and elements, and then Galerkin's weighted residual method is used to reduce the equation from a second order partial differential equation to a first order ordinary differential equation. Asymptotic waveform evaluation (AWE) then takes over the formulation steps, by obtaining the transient response equation of one node per calculation. The verification of AWE results is done by comparing the transient response equation with FEM, and the steady state results have also been verified by comparing the thermal resistance from other literatures.;Steady state and transient parametric studies have been performed, including the effect of initial conditions, dimensionless parameters like Reynolds number, thermal conductivity ratio between wall and fluid materials, Prandtl number, Nusselt number, and non-uniform heat flux boundary conditions. When the transient response graph is smooth and monotonic towards steady state temperature, AWE approximates this graph well even at small number of moments. However, if the transient response graph shows irregular pattern towards steady state temperature, higher number of moments are required to obtain a good approximation.;Comparisons of results among all micro-channels have also been made in several aspects: CPU time, flow rate, non-uniform heat flux and channel geometry. The CPU time using AWE are compared with results generated using FEM. The effect of flow rate is analysed using two methods: same the flow rate for each layer and for the whole channel. The fluid stream and wall centreline temperature profiles for all micro-channels using non-uniform heat flux are also compared. The channel geometry is analysed using a constant total channel height. Results indicate that three-layered micro-channels give the most reduction in thermal resistance.