Lie group analysis for bioconvection MHD slip flow and heat transfer of nanofluid over an inclined sheet: Multiple solutions

•The parametric critical values for mass transfer (sc), shrinking (χc) are determined.•Gyrotactic density {−w′(0)}{−w′(0)} at the plate enhances with an increasing value of Scb.•First solution is physically stable while second solution is physically unstable.•The rate of heat transfer decreases with thermal slip parameter δ and thermophoresis parameter Nt.

This paper considers numerical analysis of bioconvection boundary layer flow and heat transfer of electrically conducting nanofluid containing nanoparticles and gyrotactic microorganism over an inclined permeable sheet. Lie symmetry group transformations are used to convert the governing non-linear partial differential equations for continuity, momentum, energy, nanoparticles and microorganisms conservation into non-linear ordinary differential equations. The influences of important physical parameters such as mass transfer parameter s, Richardson number Ri, Buoyancy ratio Nr, bioconvection Rayleigh number Rb, velocity and thermal slip parameters, Brownian motion parameter Nb, thermophoresis parameter Nt, the bioconvection Schmidt number Scb and the bioconvection Peclet number Pe, on the skin friction, the rate of heat transfer and microorganisms flux are discussed numerically in this study. The dual solutions are obtained for some critical range of mass transfer parameter s and stretching/shrinking parameter χ.

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