A unified similarity transformation for Darcy and non-Darcy forced-, free- and mixed-convection heat transfer in non-newtonian inelastic fluid-saturated porous media

The Chemical Engineering Journal Pub Date : 1992-10-01 DOI:10.1016/0300-9467(92)80004-T

A. Nakayama, A.V. Shenoy

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引用次数: 32

Abstract

A unified similarity transformation has been proposed which can deduce a class of possible similarity solutions during forced-, free- and mixed-convection flow of non-newtonian inelastic fluids through porous media under Darcy and non-Darcy conditions. The velocity scale using the slip velocity at the wall under mixed-convection flow has been utilized for generating a modified Peclet number which correctly transforms to the appropriate Peclet and Rayleigh numbers under limiting conditions. The unified approach is seen to reveal the existence of three limiting regimes lined by forced convection, Darcy free convection and Forchheimer free convection together with three intermediate regimes of Darcy mixed convection, Darcy-Forchheimer free convection and Forchheimer mixed convection. Exact solutions have been found for each of the regimes and the effects of non-newtonian character on the heat transfer characteristics have been deciphered.

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非牛顿非弹性流体饱和多孔介质中达西和非达西强迫对流、自由对流和混合对流换热的统一相似变换

提出了一种统一的相似变换，可以推导出非牛顿非弹性流体在达西和非达西条件下通过多孔介质的强制对流、自由对流和混合对流过程中可能的相似解。利用混合对流条件下壁面滑移速度的速度尺度，生成了修正的Peclet数，在极限条件下正确地转换为合适的Peclet数和Rayleigh数。统一的方法揭示了强迫对流、Darcy自由对流和Forchheimer自由对流三种极限状态的存在，以及Darcy混合对流、Darcy-Forchheimer自由对流和Forchheimer混合对流三种中间状态的存在。得到了每一种状态的精确解，并破译了非牛顿特性对传热特性的影响。

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The Chemical Engineering Journal

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