Analysis of unsteady non-axisymmetric Homann stagnation point flow of nanofluid and possible existence of multiple solutions

Abstract

This study examines the unsteady 3D non-axisymmetric Homann flow of an electrically conducting nanofluid in the presence of buoyancy forces. We consider the uniform external magnetic field B0, by neglecting induced magnetic field and examine the three possible directions of magnetic field which coincides with the direction of axes. A similarity solution is derived which involves the important physical dimensionless parameters like the nanoparticles volume fraction φ, the unsteadiness parameter ω, the buoyancy parameter λ,Hartmann numberMandshear to strain ratioγ. We have treated the case for forced convection when λ=0 which arise from the singularity γ=∓1. We found that, for large γ and λ, the leading terms of the solutions are independent of M and ω, and the effects of φ in that solutions are negligible. Numerical results are found for illustrative values of all the flow parameters by using bvp4c scheme in MATLAB. The critical values λc of λ are seen in opposing flow for small rate of deceleration parameter ω while it changes to assisting flow for large value of ω.