The variational approach to study the mixed convection boundary layer flow over a permeable Riga plate

The physical problem of steady state, laminar, mixed convection (Ri) with double-diffusive (N) in an electrically low conducting fluid past a semi-infinite electromagnetic ($Q_H$) influenced flat plate with internal uniform heat generation (Q) in the presence of suction/injection (H) by considering viscous dissipation (Ec), thermophoresis (Nt) and thermal diffusion effects (Sr) is mathematically modeled as a simultaneous system of nonlinear partial differential equations. To achieve the solution of the problem numerically, Gyarmati's variational principle known as the “Governing Principle of Dissipative Processes” on the basis of nonequilibrium thermodynamic processes in the theory of continua, is adopted. This research work correlates the phenomenon of fluid around submersibles/space vehicles and provides related insights. To estimate the transportation fluid fields within the boundary layer, the appropriate trial polynomials have been employed, and functionals for the integral variational principle are determined. Next, the Euler–Lagrange equations of the functionals are obtained as a system of polynomial equations involving boundary layer thicknesses of momentum, temperature, and concentration. The expressions of local shear stress, local Nusselt, and local Sherwood numbers have been derived and the effects of various physical factors involved in the problem are explored. A comparison with the previously published results in the literature is provided to confirm the validity of the solution procedure. The results depict that injection ($H>0$) and opposing buoyancy ($N<0$) decrease the skin friction about 38% in sea water and 11% in ionized air when compared to impermeable plate for $Ri=0.5$. The aiding buoyancy ($N>0$) plays a dominant role in heat and mass transfers, respectively, with the massive gradients of 340% and 763% in magnitude for the heavier fluid sea water flow while 47% and 3% for the lighter fluid ionized air flow when $Ri=0.5$. The buoyancy parameters (Ri, N) decrease the heat transfer, but increase the mass transfer.