Optimization of double diffusive mixed convection in a BFS channel filled with Alumina nanoparticle using Taguchi method and utility concept

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Abstract
This research work focuses on the implementation of Taguchi method and utility concept for optimization of flow, geometrical and thermo-physical parameters for mixed convective heat and mass transfer in a backward facing step (BFS) channel filled with Alumina nanoparticle doped in water-ethylene glycol mixture. Mass, momentum, energy and solutal conservation equations for the flow field are cast in velocity-vorticity form of Navier-Stokes equations, which are solved using Galerkin’s weighted residual finite element method through isoparametric formulation. The following six parameters, expansion ratio of the BFS channel (H/h), Reynolds number (Re), buoyancy ratio (N), nanoparticle volume fraction (χ), shape of nanoparticles and thermal Grashof number (GrT) at three levels are considered as controlling parameters for optimization using Taguchi method. An L27 orthogonal array has been chosen to get the levels of the six parameters for the 27 trial runs. Simulation results were obtained for 27 trial runs from which three different sets of optimum levels of the control parameters were obtained for maximum Nu and Sh and minimum wall shear stress during double diffusive mixed convection in the channel. Then, in order to obtain a single set of optimum levels of the control parameters to achieve maximum heat and mass transfer and minimum wall shear stress concurrently, utility concept has been implemented. Taguchi results indicate that expansion ratio and volume fraction of nanoparticles are the significant contributing parameters to achieve maximum heat and mass transfer and minimum wall shear stress. Utility concept predicts the average Nusselt number less by 2% and Sherwood number less by 3% compared to the Taguchi method with equal weightage of 40% assumed for Nusselt and Sherwood numbers and 20% for wall shear stress.

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