Magnetohydrodynamics double-diffusive natural convection and entropy generation in novel E-shaped enclosure

Abstract

A CFD interpretation is presented to analyze the double-diffusive natural convection along with the entropy generation inside inclined E-shaped enclosure with wavy wall under the influence of magnetic field. The existence of inner heated circular body had been included in this study that it solved numerically using finite element formulation. The enclosure wavy wall is kept at the same hot temperature of the inner heated body while the vertical wall of the enclosure is kept at cold temperature and the rest of the horizontal walls are thermally insulated. The enclosure had been filled by electrically conducting fluid with Prandtl number of $\left(Pr=0.024\right)$. Additionally, Hartmann number and Darcy number kept constant at as $\left(\mathrm{Ha}=20,\mathrm{Da}={10}^{-5}\right).$ The studied parameters are the inclination of the magnetic field that varied as $\left(\gamma =0^{°},{15}^{°},{30}^{°},{45}^{°},{60}^{°},{75}^{°}\text{and}{90}^{°}\right)$. Additionally, the enclosure its self is orientated as $\left(\lambda =0^{°},{45}^{°},{90}^{°},{135}^{°},{180}^{°},{225}^{°},{270}^{°},{315}^{°}\text{and}{360}^{°}\right)$. The Rayleigh number are varied as $\left(\mathrm{Ra}={10}^3-{10}^6\right)$. The buoyancy ratio had been varied as $\left(N=0,2,4,6,8,10\right)$and Lewis number is varied as $\left(\mathrm{Le}=1-10\right)$. Additionally, the inner circular body is varied $\left(-0.3\le \delta \le +0.3\right)$. The results show that applied the magnetic field in the vertical direction $\left(\gamma ={90}^{°}\right)$ helped in enhancing the heat transfer and lower entropy generation while at $\left(\gamma =0^{°}\right)$ helped in better mass transfer. Additionally, in spite inclining the enclosure at $\left(\lambda ={270}^{°}\right)$ contributed in lower entropy generation but it led to lower heat and mass transfer rate. At zero buoyancy ratio number $\left(N=0\right)$, there is no impact of Lewis number on heat transfer rate. However, when buoyancy ratio number into $\left(N=10\right)$, it is noted that increasing Lewis number from $\left(\mathrm{Le}=1\right)$ into $\left(\mathrm{Le}=10\right)$, leads to decreases Nu by 52.17 %. Similar behavior is noted for the entropy generation while Sherwood number increases with the increasing of Lewis number regardless the value of buoyancy ratio number. Lastly, the position of the inner body and its role in heat and mass transfer is highly impacted by the Rayleigh number. It is obtained that at low Ra, the best position for heat transfer is at $\delta =-0.2$ while at high Ra, the best position is at $\delta =-0.3$. Additionally, at high Ra, the entropy generation decreases as the inner body moved in the positive direction.