Hybrid nanofluid magnetohydrodynamic mixed convection in a novel W-shaped porous system
Authors: Mandal Dipak Kumar , Biswas Nirmalendu , Manna Nirmal K. , Gorla Rama Subba Reddy , Chamkha Ali J. 
Published: August 2022

Purpose
This study aims to numerically examine the influence of various geometric parameters of a novel W-shaped porous cavity undergoing hybrid nanofluid-based magnetohydrodynamic mixed convection. The W-shaped cavity is modified from the classical trapezoidal cavity by constructing a triangular shape at its bottom. This cavity is isothermally active at the bottom, with different numbers and heights of the triangular peak (or undulation). The heated hybrid nanofluid (Cu–Al2O3–H2O) flow is cooled through the translating top wall. Inclined sidewalls are thermally insulated. To compare the impacts of change in geometric parameters, a square cavity under similar boundary conditions is also simulated. This study is carried out systematically addressing the various influences from a range of parameters like side angles (γ), number (m) and height (λ) of the bottom undulation, Reynolds number (Re), Richardson number (Ri), Darcy number (Da), Hartmann number (Ha), hybrid nanoparticles volume fraction (φ) on the overall thermal performance of the cavity.

Design/methodology/approach
Applying the finite volume approach, the transport equations involving multiphysical conditions like porous substance, hybrid nanofluid, magnetic field and shearing force are solved numerically by using a written FORTRAN-based code following the SIMPLE algorithm. The algebraic equations are solved over all the control volumes in an iterative process using the alternate direction implicit scheme and the tri-diagonal matrix algorithm. The converged solution of the iterative process is obtained when the relative error levels satisfy the convergence criterion of 10–8 and 10–10 for the maximum residuals and the mass defect, respectively.

Findings
It is revealed that an increase in the bottom undulation height always improves the thermal energy transfer despite the reduction of fluid volume. Thermal energy transfer significantly depends on the heating and cooling surface lengths, fluid volume in the cavity and the magnitude of the bottom undulation height of the W-shaped cavity. With the increase in bottom undulation height, effective heating length increases by ∼28%, which leads to a ∼15% reduction in the effective volume of the working fluid and a gain in heat transfer by ∼56.48%. In general, the overall thermal energy transport is improved by increasing Re, Ri and Da; whereas it is suppressed by increasing Ha.

Research limitations/implications
There are many opportunities for future research experimentally or numerically, considering different curvature effects, orientations of the geometry, working fluids, boundary conditions, etc. Furthermore, this study could be extended by considering unsteady flow or turbulent flow.

Practical implications
In many modern systems/processes pertaining to materials processing, continuous casting, food processing, chemical reactors, biomedical applications, etc. fine control in the transport process is a major concern. The findings of this analysis can effectively be useful for other applications for getting more control features in terms of achieving the operational objectives. The approach of the system analysis (considering geometrical size parameters to delve into the underlying transport physics) and the obtained simulated results presented in the work can usefully be applicable to similar thermal systems/devices such as materials processing, thermal mixing, chemical reactors, heat exchangers, etc.

Originality/value
From the well-documented and vast pool of literature survey, it is understood that there exists no such investigation on the considered geometry and study. This study contributes a lot to understanding magnetic field moderated thermofluid flow of a hybrid nanofluid in a porous medium filled W-shaped cavity, in consideration of different geometrical shape parameters (undulation peak numbers at bottom wall, peak heights, side angles and heating and cooling length). Findings brought by this study provide great insights into the design and operation under various ranges of multiphysical thermofluid-flow processing phenomena.