Three problems involving heat transfer from a protein crystal to a cooling agent are analyzed: flash-cooling in a cold nitrogen- or helium-gas stream, plunge-cooling into liquid nitrogen, propane or ethane and crystal heating in a cold gas stream owing to X-ray absorption. Heat transfer occurs by conduction inside the crystal and by convection from the crystal's outer surface to the cooling fluid. For flash-cooling in cold gas streams, heat transfer is limited by the rate of external convection; internal temperature gradients and crystal strains during cooling are very small. Helium gas provides only a threefold improvement in cooling rates relative to nitrogen because its much larger thermal conductivity is offset by its larger kinematic viscosity. Characteristic cooling times vary with crystal size L as L(3/2) and theoretical estimates of these times are consistent with experiments. Plunge-cooling into liquid cryogens, which can give much smaller convective thermal resistances provided that surface boiling is eliminated, can increase cooling rates by more than an order of magnitude. However, the internal conduction resistance is no longer negligible, producing much larger internal temperature gradients and strains that may damage larger crystals. Based on this analysis, factors affecting the success of flash-cooling experiments can be ordered from most to least important as follows: (1) crystal solvent content and solvent composition, (2) crystal size and shape, (3) amount of residual liquid around the crystal, (4) cooling method (liquid plunge versus gas stream), (5) choice of gas/liquid and (6) relative speed between cooling fluid and crystal. Crystal heating by X-ray absorption on present high-flux beamlines should be small. For a fixed flux and illuminated area, heating can be reduced by using crystals with areas normal to the beam that are much larger than the beam area.
This paper presents a theoretical study of fully developed forced convection in a channel partially filled with a porous matrix. The matrix is attached at the channel wall and extends inward, toward the centerline. Two channel configurations are investigated, namely, parallel plates and circular pipe. For each channel configuration, both the case of constant wall heat flux and constant wall temperature were studied. The main novel feature of this study is that it takes into account the flow inside the porous region and determines the effect of this flow on the heat exchange between the wall and the fluid in the channel. The Brinkman flow model which has been proven appropriate for flows in sparsely packed porous media and for flows near solid boundaries was used to model the flow inside the porous region. Important results of engineering interest were obtained and are reported in this paper. These results thoroughly document the dependence of the Nusselt number on several parameters of the problem. Of particular importance is the finding that the dependence of Nu on the thickness of the porous layer is not monotonic. A critical thickness exists at which the value of Nu reaches a minimum.
Third-generation synchrotron sources generate strong X-ray beams. The beam's interaction with biomaterials gives rise to concerns related to thermal damage and radiation damage. Of the two issues, the thermal interaction is conducive to rigorous analysis from first principles, although this has not been performed to date in a comprehensive manner. In this study, the interaction of the X-ray beam emanating from a third-generation synchrotron with a typical frozen biocrystal is theoretically studied, focusing specifically on the resulting unsteady (time-dependent) and steady heat-transfer phenomena. A unique regime map is developed to explain and to identify, on the basis of Fourier and Biot numbers as governing parameters, the applicable mathematical models that predict the subsequent thermal behavior. Depending on the values of these parameters, some simplified but realistic 'generic' solutions are generated that are suitable for that particular domain of applicability. Classical heat-transfer theory was used to describe the third-generation X-ray beam and biomaterial thermal interaction. Besides the generalized approach presented, numerous illustrative cases were solved and the resulting temperature levels are explicitly presented. Overall, the resulting thermal behavior of the system, i.e. peak and local temperature distribution, during both early transient development and for sustained long-time steady-state conditions, depends on a number of factors including the amount of energy absorbed, convective heat-transfer film coefficient and gas temperature, the sample size and shape, and the thermophysical properties of the sample and cooling gas. Results of the analysis revealed the strong influence that convection has on the transient and final steady-state temperature of the sample and the impact of internal heat conduction. The characteristic timescales of the important and dominant thermal processes with respect to the two types of thermal models are clearly identified.
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