THE EFFECT OF LOCAL THERMAL NONEQUILIBRIUM ON THE ONSET OF CONVECTION IN A POROUS MEDIUM LAYER SATURATED BY A NANOFLUID: BRINKMAN MODEL

The onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. For the porous medium the Brinkman model is employed. Three cases of free free, rigid rigid, and rigid free boundaries are considered. The effect of local thermal nonequilibrium between the particle, fluid, and solid-matrix phases is investigated using a three-temperature model. The analysis reveals that in some circumstances the effect of local thermal nonequilibrium (LTNE) can be significant, but for a typical dilute nanofluid (with large Lewis number and with small particle-to-fluid heat capacity ratio) the effect is small.