Governing Principle of Dissipative Processes proposed by Gyarmati for non-equilibrium thermodynamics has been employed to obtain the variational solution of steady, laminar, magnetohydrodynamic stagnation flow of a nanofluid over a non-isothermal stretching sheet with Brownian motion and thermophoresis effects when the flow is controlled by suction/injection. The velocity, temperature and concentration fields inside their boundary layers are approximated by polynomial functions which are satisfied by the boundary conditions. The variational principle is formulated, and Euler-Lagrange equations of the principle are reduced to simple polynomial equations in terms of momentum, thermal and concentration boundary layer thicknesses. The temperature, concentration profiles, skin friction, heat and mass transfer effects are analyzed for various values of velocity ratio parameter e, suction/injection parameter H, magnetic parameter x, Prandtl number Pr, wall temperature parameter n, Lewis number Le, Brownian motion parameter Nb and thermophoresis parameter Nt. The obtained results are compared with numerical solutions, and the order of accuracy is remarkable.
Gyarmati's variational principle, nanofluid, stagnation flow, stretching sheet, suction / injection.
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