Three-dimensional numerical analysis of convection and conduction cooling of spherical biocrystals with localized heating from synchrotron X-ray beams.

The differential momentum and thermal energy equations for fluid flow and convective heat-transfer around the sample biocrystal, with coupled internal heat conduction, are solved using advanced computational fluid dynamics techniques. Average \bar{h} as well as local h(theta) values of the convective heat-transfer coefficients are obtained from the fundamental equations. The results of these numerical solutions show the three-dimensional fluid flow field around the sample in conjunction with the detailed internal temperature distribution inside the crystal. The external temperature rise and maximum internal temperature increase are reported for various cases. The effect of the important system parameters, such as gas velocity and properties, crystal size and thermal conductivity and incident beam conditions (intensity and beam size), are all illustrated with comparative examples. For the reference case, an external temperature rise of 7 K and internal temperature increase of 0.5 K are calculated for a 200 microm-diameter cryocooled spherical biocrystal subjected to a 13 keV X-ray beam of 4 x 10(14) photons s(-1) mm(-2) flux density striking half the sample. For all the cases investigated, numerical analysis shows that the controlling thermal resistance is the rate of convective heat-transfer and not internal conduction. Thermal diffusion results in efficient thermal spreading of the deposited energy and this results in almost uniform internal crystal temperatures (DeltaT(internal) approximately 0.5 K), in spite of the non-uniform h(theta) with no more than 1.3 K internal temperature difference for the worst case of localized and focused beam heating. Rather, the major temperature variation occurs between the outer surface of the crystal/loop system and the gas stream, T(s) - T(gas), which itself is only about DeltaT(external) approximately 5-10 K, and depends on the thermal loading imposed by the X-ray beam, the rate of convection and the size of the loop/crystal system.