MIXED CONVECTION JET IMPINGEMENT COOLING OF A RECTANGULAR SOLID HEAT SOURCE IMMERSED IN A POROUS LAYER

Abstract

The jet impingement cooling of a solid rectangular block heated from below and immersed in a fluid-saturated porous medium is considered for investigation numerically. The jet direction is considered to be perpendicular from the top to the solid rectangular block. Therefore the jet flow and the buoyancy-driven flow are in opposite directions. For a fixed block length, the governing parameters in the present Darcy flow problem are: Rayleigh number (Ra), Peclet number (Pe), solid-to-porous thermal conductivity ratio (Kr), the dimensionless thickness (or height) of the solid wall (H), in addition to the dimensionless jet width (D). The results are presented in the mixed convection regime with wide ranges of the governing parameters. At low values of Pe (natural convection cases), it is found that the effect of Pe and the jet width are negligible and the average Nusselt number (Nu) is increasing with the increase of either Rayleigh number or the thermal conductivity ratio, or decreasing the thickness of the solid wall. At high values of Pe (forced convection cases), it is found that the effect of Ra is negligible and Nu increases with either increasing Pe values, the thermal conductivity ratio or jet width, or decreasing the thickness of the solid wall. At moderate values of Pe (opposing mixed convection cases), it is observed that the values of average Nusselt number show minimum values. The value of Pe at which minimum Nu occurs depends on Ra, thermal conductivity ratio, jet width, and the thickness of the solid wall. At low values of either Ra or thermal conductivity ratio, this case where Nu shows a minimum value is not obvious. It is found that the thinner solid walls have higher values of the average Nusselt number with other parameters fixed. Therefore, for cooling applications, the numerical results indicate that the solid wall should be as thin as possible, with high thermal conductivity. The present results show that the cooling rate with the opposing missed convection mode is lower than that with the natural convention mode. The results show that the effect of the jet width D can be incorporated by plotting the average Nusselt number against Pe × D, where the results form a single curve for different values of the jet width.