Efficient Methodologies for Processing of Fluids by Thermal Convection within Porous Square Cavities

Abstract

Effective use of thermal energy is the key for the energy-efficient processing of materials. A proper understanding of heat flow would be very useful in designing the systems of high energy efficiency with a minimal waste of precious energy resources. In the current study, a distributed heating methodology is proposed for the efficient thermal processing of materials. A detailed investigation on the processing of various fluids of industrial importance (with a Prandtl number of Pr = 0.015, 0.7, 10, and 1000) in differentially and discretely heated porous square cavities is presented. Analysis of laminar convective heat flow within a range of Darcy number, D a = 10−6−10−3 and Rayleigh number, R a = 103−106 has been carried out, based on a heatline visualization approach. The effect of D a and the role of distributed heating in enhancing the convection in the cavities is illustrated via heatline distributions, which represent the paths of the heat flow, the magnitude of heat flow, and zones of high heat transfer. It is observed that distributed heating plays an important role in enhancement of thermal mixing and temperature uniformity. Furthermore, the effect of D a for various Pr values on the variation of local Nusselt number (Nu) is analyzed, based on heatline distributions.

Analysis of efficiency of convection in porous geometries (square vs triangular) with multiple discrete heaters on walls

“…Heatlines and isotherms are found to be perpendicular to each other in the presence of the conduction dominant heat transport. During convection, the heatline and fluid flow cells follow similar sign convention as explained in a few earlier works (Kimura and Bejan, 1983;Basak and Roy, 2008;Kaluri and Basak, 2010b).…”

“…(11) Similar to the earlier works (Basak and Roy, 2008;Kaluri and Basak, 2010b), the nonlinear residual equations for equations 5, 9 and 10 are solved via Galerkin finite element approach at various nodes.…”

“…The Gauss quadrature integration does not use singular points as the integration points do not occur at the element boundaries. In addition, the higher polynomial accuracy with Gauss integration and biquadratic basis functions provides converged solution with less number of grid points (Basak et al , 2006a; Kaluri and Basak, 2010a, 2010b) in contrast to finite difference or finite volume method. Table III provides the grid invariant results for the current solution procedure.…”

“…The presence of multiple heaters can induce complex heat flow inside the geometries and the heat flow from the heaters to the cooler sections can be efficiently seen via the heatlines. The principles of heatfunctions have been implemented to predict the heat flow in square geometries with multiple heaters at the walls (Kaluri and Basak, 2010a, 2010b). An earlier work reported the role of multiple discrete heaters during thermal convection within porous square geometry (Kaluri and Basak, 2010b).…”

Analysis of Entropy Generation during Conjugate Natural Convection within a Square Cavity with Various Location of Wall Thickness

“…The thermal and velocity gradients are evaluated accurately based on the elemental basis set via Galerkin finite element method for the entropy production. Kaluri and Basak 25 analyzed the role of distributed heating in order to enhance the thermal mixing and temperature uniformity during natural convection within square cavities filled with fluid-saturated porous media using heatline approach. Anandalakshmi and Basak 26 also analyzed the entropy generation within the rhombic enclosures of various angles filled with porous media and bounded by adiabatic top wall, cold side walls, and isothermally and nonisothermally heated bottom wall.…”