Thermal management in three-dimensional packaging

An analytical model of steady state heat conduction in a multilayered rectangular stack is presented and discussed. N layers are considered in the present study. The thermal conductivities and thickness may be different for each layer but the width and the length of each layer is the same. For the entire geometry consisting of N layers, different boundary conditions such as convection or adiabatic are applied on the top and bottom. All other lateral surfaces are subjected to natural convection, and the convection coefficient for each layer may be different. A special case this analytical solution is also discussed by varying the boundary conditions on top and bottom layers. The results are discussed by considering different examples and comparing them with the results from Desai dissertation [8]. Analytical and numerical results are plotted, considering the same number of layers as in experimental setup [8]. Results are plotted and compared by considering different cases such as varying the boundary conditions on top and bottom layers and by varying the power inputted to top and bottom dies. Analytical results without convection on lateral sides are in agreement with Desai [8] analytical results and analytical results with convection on lateral sides are in good agreement with Desai [8] experimental results.