Eur. Phys. J. Plus (2021) 136: 1034
https://doi.org/10.1140/epjp/s13360-021-02040-4

Regular Article

Heat and mass transfer in a two-sided lid-driven square cavity with non-uniform sinusoidal heating on horizontal walls

¹ Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, 110007, Delhi, India
² Cluster Innovation Centre, University of Delhi, 3rd Floor University Stadium, G C Narang Road, 110007, Delhi, India

^b manojransiwal@gmail.com

Received: 7 August 2021
Accepted: 4 October 2021
Published online: 15 October 2021

Abstract

The present study investigated the characterization of heat and mass transfer in a two-sided lid-driven square cavity subjected to non-uniform sinusoidal heating on its horizontal walls. The amplitude ratio ($\epsilon$) and phase deviation ($\varphi$) of sinusoidal temperature at the bottom wall are assumed to be constant, while it behaves as a variable on the cavity’s top boundary. The cavity’s adiabatic and impermeable vertical walls are kept in motion at a uniform speed in the opposite directions, while the horizontal walls are stationary. An unsteady, laminar, and compressible fluid flow under Boussinesq approximation has admitted in the cavity. The considered problem is taken into account due to its great importance in various thermal engineering applications. The stream function–vorticity formulation with the alternating-direction-implicit method is used to solve the non-dimensional governing equations. Also, the stability and consistency of the numerical scheme have been proved using the matrix method. A MATLAB code is written, executed to do the numerical simulations for various non-dimensional parameters, such as Richardson number $(0.01\le \text{Ri}\le 100)$, amplitude ratio ($\epsilon =0$, 0.25, 0.5, 1), phase deviation ($\varphi =0$, $\pi /4$, $\pi /2$, $3\pi /4$, $\pi$), and buoyancy ratio $(-5\le N\le 5)$. The MATLAB code is validated with some of the available literature and found a good agreement with them. The streamline, isotherm, and concentration contours are examined graphically for the different values of the non-dimensional parameter. It is found that the distribution of the contours within the square cavity depends on the relative contributions of the parameters. The heat and mass transfer inside the square cavity are analyzed in terms of the average Nusselt number and the average Sherwood number. The rate of heat and mass transfer in the cavity is found almost constant in forced convection but increases significantly in natural convection. It is also found that the buoyancy ratio, amplitude ratio, and phase deviation contribute significantly only under natural convection.