Impact of Lorentz force on forced convective MHD Jeffrey fluid flow through annular sector duct

Abstract

Present numerical simulation is to investigate the Lorentz force and constant axial pressure gradient effects on flow and heat transfer of electrically conducting magneto-hydrodynamic, $\left(\mathrm{MHD}\right)$ Jeffrey fluid at fully developed region of annular sector duct. The law of conservation of energy is simulated by taking two thermally boundary conditions, known as $\left(a\right)H$ 1 thermally boundary condition (i.e. constant axial heat flux with uniform peripherally temperature in the annular sector duct’s cross section) and $\left(b\right)T$ thermally boundary condition (i.e. constant temperature axially and peripherally). The numerical results are simulated in the following range of parameters: the ratio of radii, $R_i/R_o=0.25,0.50$ , an apex angle of duct $2\beta =2\pi /N$ by using $N=6,12,18,24$ number of fins, Hartman number, $M=0,2,4,6,8,10,12$ and the ratio of relaxation time to retardation time, $\lambda =0,0.5,1.0,1.5,2.0,2.5,3.0$ . During the simulation, it has been concluded that the other parameter corresponding to Jeffrey fluid (i.e. the retardation time, ${\lambda }_1$ ), has ignored due to minor attribution on flow and heat transfer by increasing the value from $0.2$ to $0.5$ . Hartman number, $M$ , upgrades the $\mathrm{fRe}$ up to 18.76% and 14.60%, while $N{u}_{H1}$ / $N{u}_T$ up to 1.82% and 1.47%/1.55% and 1.29% for $\hat{R}=0.25$ and $0.50$ respectively at $N=6$ and $\lambda =1.5$ by increasing its value from 0 to 2. At higher $N=24$ , the difference becomes ignored in the case of $\mathrm{fRe}$ when we change the annular region along radial direction.