An Approximate Analytical Solution to Heat Transfer Problem in Laminar Forced Flow between Parallel Plates

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  • 平行平板間の層流強制対流熱伝達問題の近似解析解

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Forced convection heat transfer in a non-Newtonian fluid flow between parallel plates subjected to heat convection on the external surfaces is investigated analytically. Fully developed laminar velocity distributions obtained by a power law fluid rheology model are used, and viscous dissipation is taken into account. The effect of heat conduction in the direction of fluid flow is considered to be negligble. The physical properties are assumed to be constant. The theoretical analysis of the heat transfer is performed using an integral transform technique-Vodicka's method on the assumption that the velocity distribution is piecewise constant in the channel cross section. An important feature of the approach is that an arbitrary variation of surrounding medium temperatures in the direction of fluid flow and an arbitrary velocity distribution can be permitted. A comparison with the existing results provides a verification of this technique. The effects of the Brinkman number, outside heat transfer coefficients and rheological property on the distributions of the fluid temperature and the local Nusselt number are illustrated. Moreover, the effects of the parameters on the length of freeze-free zone are discussed in the case where the surrounding medium temperatures are below the solidification temperature of the fluid.

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