Implementing the finite element numerical approach to optimize thermosolutal convection (TSC) energy imparted by discrete heat and solute sources in generalized Newtonian fluid flow in square enclosure

Abstract

AbstractMesmerizing utilizations of thermosolutal convection (TSC) have been found in metallurgical and petrochemical procedures, crystal growth, thermal exchangers, nuclear waste disposal, and building environment control. In the current study, we considered three heat and solute sources on the left boundary of the cavity, which raises the significance of studying multiple chemical and civil engineering phenomena. Therefore, the prime motivation to commence this work is to attain the optimization of thermosolutal attributes characterized by non-Newtonian (power–law) liquid in the presence of installed sources. For this purpose, the natural convective flow governed by the nonpersistent impact of buoyancy forces is encompassed in the square enclosure. In addition to the source location, the vertical boundaries are considered to be cold, whereas the horizontal boundaries are kept insulated. Owing to the free convective flow, no compositional and thermal gradients are induced by lid movement, and all walls are prescribed with no-slip constraints. To examine the transport mechanism, structuring of problem is attained in the form of dimensional governing expressions by employing conservation laws. Subsequently, constitutive equations in a dimensionless format are accessed through similar variables. The finite element approach is employed to find the solution using COMSOL Multiphysics software. The deviations in the thermal and solutal fields are examined against the involved physical parameters by illustrating graphs and tables. Quantities of interest, such as the mean Nusselt and Sherwood numbers, are also computed against sundry parameters. The assurance of the computed results is validated by constructing a comparison with published studies. A grid sensitivity test is also executed to ensure the credibility of the built-in software (COMSOL). It is observed that the averaged heat and mass flux coefficient diminishes with an elevation in the magnitude of the power-law index (n), irrespective of the change in other involved parameters. The average Sherwood number tends to increase for a positive magnitude of (N) in contrast to negative values of (N). The average heat flux and average mass flux coefficients increase until the Prandtl number (Pr) reaches a value of 5 in shear thinning case at $$Ra\ge {10}^{5},$$ R a ≥ 10 5 , whereas, for n > 1 there is no substantial effect on either the average heat flux coefficient or average mass flux coefficient.