E0047

Numerical Analysis of Three-Dimensional Convective and Conduction Heat Transfer from Protein Crystals with Localized X-Ray Beam Heating and Variable Beam Size. A. Mhaisekar, M. Kazmierczak, and R. Banerjee, Dept. of Mechanical, Industrial and Nuclear Engineering, Univ. of Cincinnati, Cincinnati, Ohio, 45221-0072.

A review of all previous x-ray beam heating studies of protein crystals in 3rd generation sources are presented both with regards to the predicted temperature increases and in terms of modeling considerations. Thermal transport of the energy deposited in the crystal samples involves coupled internal heat conduction and external convective heat transfer. Previous modeling attempts to date range from the very simple to the more advanced. Analyzing the heat conduction in the crystal interior is relatively straightforward, but, on the other hand, dealing with the external convection problem (i.e., the rate of energy leaving the crystal surface to the cooling gas stream) is a much more difficult to treat. Thermal model studies in the past have dealt with the rate of convection in various ways with differing level of accuracy, from assuming very simple estimates of the average outer heat transfer coefficient, h, to more refined estimates of h based on boundary layer theory, and to those models that utilize empirically derived heat transfer correlations for h developed for related shapes.

Here we present the next, and significantly more refined, level of thermal modeling of a biocrystal exposed to intense x-rays beam, where the convection phenomenon is much more accurately determined based on first principles, by solving the differential momentum and differential thermal energy equations for fluid flow and convective heat transfer around the sample via advanced numerical CFD modeling techniques. Local as well as average value of the convective heat transfer coefficients h are reported (and quantitatively compared to earlier reported values). The results of these numerical solution also show, for the first time, the 3-D fluid flow field around the crystal and provide the detailed internal temperature distribution inside the crystal now taking into account the spatial variation in the convective heat transfer caused by the complex external fluid flow that includes flow separation and recirculation. Finally, a detailed comparison is provided that shows the internal temperature distribution within the crystal when exposed to different beam sizes (but assuming constant incident power, i.e., same, but focused x-ray source beam) clearly showing the effect of beam size on maximum crystal temperature. The effect of localized beam heating and thermal spreading is discussed.