Novel Method for Estimating Thermal Film Coefficients for Analysis of Thermal Cycling of Microelectronic Packages

A failure analysis on microelectronic packages subjected to temperature cycling between liquid baths required the need for realistic boundary conditions in the thermal analysis portion of the overall thermal stress analysis. Prior arts found in literature for thermal film coefficients in immersion cooling focused only on metallurgical quenching. The results indicated that these data are highly dependant on temperature, thus not applicable since they were derived for quenching of steel at higher initial temperatures. An alternative technique was developed here by assuming that the package could be modeled as a semi-infinite solid for the time interval of interest, and that the fluid is quiescent for the time interval. The effects on the film coefficient of the motion of the package into the liquid bath are neglected. These assumptions enable the use of the available analytical solution for bringing two semi-infinite solids in contact. By being able to model the fluid as a semi-infinite solid, we can then differentiate the solution for transient heat flow in a semi-infinite body subject to a step change in surface temperature to obtain the heat flux from the surface of the package. The temperature difference between the package surface and the bulk fluid temperature then cancel out of the equation for the film coefficient leaving a closed form solution for the effective calculation of a time dependent film coefficient, which can then be applied as a boundary condition in a numerical thermal analysis. The expression for the film coefficient was found to be proportional to the fluid effusivity divided by the square root of the elapsed time.