Fluid flow and heat transfer in capillary tubes (Stokes’ boundary-layer thickness nearly equal to the tube radius), subject to oscillatory flow from two reservoirs maintained at different temperatures, has been analyzed. Extension of existing analysis has been made by allowing for finite wall thickness and estimating the viscous dissipation. For a bundle of tubes connected to reservoirs of finite volume, analysis is also made of the oscillatory motion in the reservoirs (assuming a piston-type displacement within the reservoirs). The effects of various fluid and tube parameters on the heat transfer in a single tube are examined. The pathlines followed by fluid particles show that the extent of interaction between the fluid exiting the bundle and the fluid in the reservoirs (or the heat transfer surfaces in the reservoirs) depends strongly on the radial position of the exiting fluid particles. In a follow-up paper, these predictions are compared with some experimental results.

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