THERMAL OPTIMIZATION OF A COMPOSITE HEAT SPREADER: FINITE VOLUME FRACTION FOR HIGHCONDUCTIVITY BLADE
DOI: 10.1615/IHTC13.p22.40 page 12
Gerard F. Jones Villanova University, Villanova, Pennsylvania, USA
P. Chanda Villanova University, Villanova, Pennsylvania, USA
S. Ghassemi Villanova University, Villanova, Pennsylvania, USA
AbstractA theoretical study is undertaken to determine the optimal geometry of a composite heat spreader subjected to cooling by convection. Optimal geometry is obtained when heat transfer from the spreader is maximized. Constructal theory is employed, where the fundamental construct for the composite consists of a highthermal conductivity blade in contact with a matrix of lesser conductivity. Following a systematic procedure, a treelike geometry is built up from this fundamental unit, which increases in surface area with each successive construct and possesses optimal geometry at each construct level. Numerical results are presented for a carbon fiber in an epoxy matrix. Among the salient results from this study are the following:
 Three regions having different characteristics exist for the solution for the aspect ratio for the fundamental construct. With increasing values of construct area, A_{0}*, these are a growth of the blade length relative to the matrix height, a reduction in the rate of growth of blade length relative to the matrix height culminating in thermal choking of the matrix, and growth in the blade length for a constant matrix height.
 The optimal aspect ratio (construct height to length) is less than unity, and in the limit of large A_{0}* and for nominal values of blade heat flux, the ratio of blade length to construct height is of the order of 10. Further increases in A_{0}* will cause thermal choking for a dimensionless blade length of approximately 1.33.
 Growth of the lowconductivity matrix occurs before the final growth of the highconductivity blade as A_{0}* increases, an effect due to the very small surface area for convection from the blade compared with that for the matrix. Interestingly, for A_{0}* < 0.001, nearly all of the heat transfer from the blade is to the matrix.
 Peak power dissipation for the optimized system occurs for dimensionless blade heat fluxes in the range of 1.6 to 2.2.
