P.J. Singh

NATURAL CONVECTION HEAT TRANSFER FROM A HORIZONTAL WAVY SURFACE IN A POROUS ENCLOSURE

Abstract The effect of surface undulations on the natural convection heat transfer from an isothermal surface in a Darcian fluid-saturated porous enclosure has been numerically analyzed using the finite element method on a graded nonuniform mesh system. The flow-driving Rayleigh number Ra together with the geometrical parameters of wave amplitude a, wave phase φ, and the number of waves N considered in the horizontal dimension of the cavity are found to influence the flow and heat transfer process in the enclosure. For Ra around 50 and above, the phenomenon of flow separation and reattachment is noticed on the waits of the enclosure. A periodic shift,n the reattachment point from the bottom wall to the adjacent walls in the clockwise direction, leading to the manifestation of cycles of unicellular and bicellular clockwise and counterclockwise flows, is observed, with the phase varying between 0° and 350°. The counterflow in the secondary circulation zone is intensified with the increase in the value of Ra...

FREE CONVECTION HEAT TRANSFER FROM AN ISOTHERMAL WAVY SURFACE IN A POROUS ENCLOSURE

The coupled streamfuction–temperature equations governing the Darcian flow and convection process in a fluid-saturated porous enclosure with an isothermal sinusoidal bottom sun face, has been numerically analyzed using a finite element method (FEM). No restrictions have been imposed on the geometrical non-linearity arising from the parameters like wave amplitude (a), number of waves per unit length (N), wave phase (Φ), aspect ratio (A) and also on the flow driving parameter Rayleigh number (Ra). The numerical simulations for varying values of Ra bring about interesting flow features, like the transformation of a unicellular flow to a multicellular flow. Both with increasing amplitude and increasing number of waves per unit length, owing to the shift in the separation and reattachment points, a row–column pattern of multicellular flow transforms to a simple row of multicellular flow. A cycle of n celluar and n+1 cellular flows, with the flow in adjacent cells in the opposite direction, periodically manifest with phase varying between 0 and 360°. The global heat transfer into the system has been found to decrease with increasing amplitude and increasing number of waves per unit length. Only marginal changes in the global heat flux are observed, either with increasing Ra or varying Φ. Effectively, sinusoidal bottom surface undulations of the isothermal wall of a porous enclosure reduces the heat transfer into the system.

Effect of thermal stratification on free convection in a fluid-saturated porous enclosure

Natural convection heat transfer from an isothermal vertical surface in a fluid-saturated porous medium under the influence of thermal stratification has been numerically analyzed using the finite element method. The combined effect of Rayleigh number and thermal stratification on the global heat flux in porous cavities of varying aspect ratios has been analyzed. It is observed that the global heat flux (1) decreases with increasing values of the thermal stratification b and (2) increases with increasing values of Rayleigh number Ra. However, the cumulative heat flux along the midsegment of the vertical wall increases with increasing b and decreases with Ra. With increasing b, a reduction in the convection zone with a downward drift is noticed. Global heat flux can be boosted by reducing the width L of the cavity by a factor of ∼8 or more. The flow field and the heat transfer results art presented through the streamlines, isotherms, and global heat flux plots.