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Heat Transfer Handbook part 14

Heat Transfer Handbook part 14. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | 120 THERMOPHYSICAL PROPERTIES OF FLUIDS AND MATERIALS 9mcp x v2r 2.58 Grouping the material properties the thermal diffusivity is defined as aD X pmcp. Thus the important thermophysical properties are aD X pm and cp. In general these properties can be functions of direction deformation and temperature. Some crystalline elements such as carbon bismuth and tin have anisotropic thermal conductivities. Some polymers develop anisotropy after finite deformation Choy et al. 1978 Broerman et al. 1999 Ortt et al. 2000 . The temperature dependence of a is sometimes less strong than that of X which can simplify analytical solutions of conduction problems Ozisik 1980 . For analyses of l.ransieni heat transfer aD is the important parameter while for analyses of steady heat transfer and boundary conditions of us e nt analyses X is required. Equation 2.58 is nonphysical because it predicts an infinite speed of propagation oftemperature change that is a temperature change in one part ofthe body causes an immediate change in temperature throughout the body. Substituting the Maxwell-Cattaneo equation for Fourier s equation yields 1 dT 1 dT 2 aD dt c2 dt2 2.59 where c has dimensions of velocity. If c is approximated as the speed of sound in the body then for good conductors the ratio of the coefficients is aD c 10 11 s Parrott and Stuckes 1975 . Thus except in rare circumstances finite propagation speeds are important only for very short times. Joseph and Preziosi 1989 1990 provide an extensive review of studies examlnîng Maxwell-Cattaneo conduction. In general analyses of thermal conduttion astimae fiiat maeerials .ire rigid and incompressible. This is not strictly so. Relaxing this assumption requires the addition ofthe simultaneous solution ofthe balance oflinear momentum and the addition of the stress work term see e.g. Day 1985 . The linear coefficient of thermal expansion may be defined as p L L0 L0 T T0 where L is the length of flee soiid at its new temperature T and L0 is its