A model for transverse heat transfer in thermoacoustics

A model for transverse heat transfer in parallel thermoacoustic pores is developed. The model is one-dimensional, in the sense that the temperatures in the gas, Tg, and in the solid walls, Tw, are assumed to be fully represented by their dependences on the pore’s axial coordinate, z. All effects of transverse variation across the cross section of the pore are subsumed into a transverse heat-transfer coefficient, h1, that couples the temperatures according to q(z)=h1[Tg(z)−Tw(z)], where q is the transverse heat transfer per unit area. First the model is applied to thermally isolated pores, and results are compared to a recent three-dimensional analysis of this case [G. Mozurkewich, J. Acoust. Soc. Am. 103, 380–388 (1998)]. Then it is extended to the case of heat-exchanger pores immediately adjacent to the end of a long stack. The heat-transfer results are cast in nondimensional form as the product of two factors. One factor depends on gas properties and the geometry of the heat exchanger, the other on the length of the stack and on a parameter related to the relative total heat pumping capacity of heat exchanger and stack. Plots of both factors are given for the special case of planar pores. The results may be applied to the design of heat exchangers for practical thermoacoustic devices.