Free convective heat transmission under LTNE in nanofluids within a trapezoidal permeable crater in view of three energy equations: influences of variable permeability and porosity

Authors: Sheikha M. Al-Waheibi, M. M. Rahman, M. Ziad Saghir

Volume 8, Issue 2, Paper No. 080204


  Current research examines the effects of variable permeability and porosity through the free convective heat transmission flow of copper-water, aluminum oxide-water, and cobalt-water nanofluids via a glass bead permeable matrix within a trapezoidal crater in view of thermal non-equilibrium conditions amongst the permeable medium, nanoparticles, and the base fluid (three energy equations model). We employed the weighted residual Galerkin finite element strategy to simulate the non-dimensional model equations. We compared our results with the existing data from the open literature for a special case, and we get an excellent agreement with nominal relative error. We analyzed the influences of varying penetrability and porosity factors for different Nusselt numbers of fluid, nanoparticles, as well as the porous matrix in detail. The acquired numerical outcomes affirm that the critical Rayleigh number value to begin the thermal non-equilibrium situation diminished by expanding the glass bead diameter and the porosity parameter.  Moreover, the expansion of variable porosity substantially amplifies the amount of heat transmission in a base fluid (approx. 120%) and nanoparticles (approx. 30%). The corresponding intensifications in Nusselt number of the base fluid, nanoparticles, and permeable medium are 100.7%, 6.3%, and 32.6%, respectively, when beads diameter increases from 0.1 to 0.4 for the Rayleigh number equal to 105.  The interface heat transmission parameters (or Nield numbers) have an active part in controlling the heat transmission in different phases. Comparing with the other two nanofluids, we noticed that the base fluid, nanoparticles, and permeable matrix heat transmission coefficients are the highest in a copper-water nanofluid.

Keywords: Free convection; Nanofluids; permeability; Thermal non-equilibrium condition; Trapezoidal crater.

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