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.
Objective of the present analysis is to represent the phenomenon of Heat–mass transfer on MHD micro polar fluids caused by permeable and continuously stretching sheet along with slip impacts fostered in a porous medium. Consequently, the equation of energy includes the term of non-uniform heat source/sink. The equation regarding species concentration in cooperates the terms indicating order of chemical reaction to characterize the chemically reactive species. The application software MATLAB with governing syntax of bvp4c technique are employed to reduce equations of momentum, micro-rations, heat, and concentration into suitable required simplifications to derive necessary arithmetic manipulations of available non-linear equations. Various dimensionless parameters are portrayed in the available graphs with essential consequences. Analysis discovered that micro-polar fluid improves velocity and temperature profile while it suppresses micro-rations profile also magnetic parameter ($$M$$
M
) and porosity parameter ($$K_p$$
K
p
) reduces the momentum boundary layer thickness. The acquired deductions verify remarkable correspondence with already reported in an open literature.
Understanding the mechanisms and kinetics of homogeneous (i.e. water-based ternary-hybrid nanofluid) and heterogeneous (i.e. catalyst) reactions is capable of creating a more effective distribution of species and quality of fluids at the outlet. Thus, the present study focuses on analyzing the quartic type homogeneous-heterogeneous reactions in ternary-hybrid nanofluid of copper, alumina, and titania nanoparticles with water at the surface of a stationary/moving flat plate. The leading non-linear partial differential equations were transformed into a set of ordinary differential equations using local similarity transformations. The resultant non-linear ordinary differential equations were numerically solved using MATLAB's built-in BVP4C tool to explore the impact of pertinent factors. From the design side of view, the Tiwari-Das model for nano-liquid was employed to study the flow-thermal behaviour of the nanofluid. The thermal conductivity formulations were taken from experimental works to incorporate the spherical, platelet and cylindrical-shaped nanoparticles. The proposed concept is comparatively analyzed for Blasius and Sakiadis flows. The homogeneous bulk fluid and heterogeneous catalyst concentrations are observed for small and large nanoparticle volume fractions. The investigation shows that the strength of homogeneous and heterogeneous reactions has the opposite effect on the concentration fields. Strong correlations exist between the heterogeneous catalyst's diffusivity and the homogeneous bulk fluid's viscosity. Mass diffusion became more prevalent at the surface as the Schmidt number surged. Conversely, the bulk fluid concentration was highest in areas far from the surface.
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