Buoyancy effects on nanofluid past a continuous stretching Riga plate: variational approach

Purpose The purpose of this reserach work aims to study the steady state laminar mixed convection flow of electro magnetohydrodynamic (EMHD) nanofluid over a continuously moving plate is considered to evaluate the irreversible transportation fields inside the boundary layer by a traditional non-equilibrium thermodynamics variational approach. Design/methodology/approach The Lagrangian forms of the variational principle are determined using the trial polynomials of the flow fields inside and on the boundary layer including the governing balance equations by dual field method. Then, Euler–Lagrangian equations of integral principle produce the boundary layer thicknesses of momentum, temperature and concentration. The integration of governing boundary layer equations provides the transportation fields, skin friction, heat and mass transfer rates as non-linear polynomials in terms of dimensionless sources EMHD (QH), Joule heating (Ec), Brownian motion (NB), thermophoresis (NT), buoyancy force (Ri) and nanoparticle concentration flux (NR) considered in this study. Findings For asymptotic behavior of the results, the appropriate ranges of parameters, −0.3 ≤ Ri ≤ 0.3, 0 ≤ NR ≤ 0.1, −0.3 ≤ QH ≤ 0.3 and, fixed values such as Pr = 6.2, Sc = 5, NB = NT = 0.1, Ec = 0.2 and X = 1, are considered. Some of the main findings in shear, heat and mass transfer rates are as follows: the aiding Lorentz force (QH > 0) increases the skin friction and heat transfer, but decreases the mass transfer; the aiding buoyancy force (Ri > 0) increases the skin friction and mass transfer, but decreases the heat transfer; and the nano particle concentration flux parameter (NR) decreases all the skin friction, heat and mass transfers but not at significant level. Originality/value In this problem, the significance of buoyancy effects such as Richardson number (Ri) and concentration flux parameter (NR) on nanofluid past a continuously stretching Riga plate are focused and discussed. This analysis can be applicable to study industrial extrusion, continuously moving submerged bodies such as submarine hulls and aerofoils.