Shifted legendre collocation method for the solution of unsteady viscous-ohmic dissipative hybrid ferrofluid flow over a cylinder

A numerical treatment for the unsteady viscous-Ohmic dissipative flow of hybrid ferrofluid over a contracting cylinder is provided in this study. The hybrid ferrofluid was prepared by mixing a 50% water (H₂O) + 50% ethylene glycol (EG) base fluid with a hybrid combination of magnetite (Fe₃O₄ ) and cobalt ferrite (CoFe₂O₄ ) ferroparticles. Suitable parameters were considered for the conversion of partial differential equations (PDEs) into ordinary differential equations (ODEs). The numerical solutions were established by expanding the unknowns and employing the truncated series of shifted Legendre polynomials. We begin by collocating the transformed ODEs by setting the collocation points. These collocated equations yield a system of algebraic equations containing shifted Legendre coefficients, which can be obtained by solving this system of equations. The effect of the various influencing parameters on the velocity and temperature flow profiles were plotted graphically and discussed in detail. The effects of the parameters on the skin friction coefficient and heat transfer rates were further presented. From the discussion, we come to the understanding that Eckert number considerably decreases both the skin friction coefficient and the heat transfer rate.