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The problem of fully developed forced convection in a parallel-plates channel filled with a saturated porous medium (involving a Brinkman model for the momentum equation), with the effect of viscous dissipation (involving a Brinkman number), is discussed. Some general matters relating to the possibility of fully developed convection are also discussed.

A two-velocity two-temperature model for bi-dispersed porous media is formulated. Using the model, an analytic solution is obtained for the problem of forced convection in a channel between parallel plane walls that are held either at uniform temperature or uniform heat flux. In each case, Nusselt number values are given as functions of a conductivity ratio, a velocity ratio, a volume fraction, and an internal heat exchange parameter.

Fully developed forced convection in a parallel plate channel filled by a saturated porous medium, with walls held either at uniform temperature or at uniform heat flux, with the effects of viscous dissipation and flow work included, is treated analytically. The Brinkman model is employed. The analysis leads to expressions for the Nusselt number, as a function of the Darcy number and Brinkman number.

The modelling of viscous dissipation in a porous medium saturated by an incompressible fluid is discussed, for the case of Darcy, Forchheimer and Brinkman models. An apparent paradox relating to the effect of inertial effects on viscous dissipation is resolved, and some wider aspects of resistance to flow (concerning quadratic drag and cubic drag) in a porous medium are discussed. Criteria are given for the importance or otherwise of viscous dissipation in various situations.

Comments are made about limitations of the model proposed by Hennenberg et al. for convection in a porous medium layer driven by the Marangoni effect, and an alternative model for this problem is presented. The predictions of the two models are significantly different.