The melting effect with the magnetic field performs a significant role in various manufacturing and industrial applications, such as welding, casting, magma‐solidification, nuclear engineering, and so forth. The present study focuses on the impact of the melting effect and magnetic field with inhomogeneous heat origination and sink. The formulation of the mathematical model is done by considering fluid with hybrid nanoparticles and dust particles in two different phases. We have considered Fe2SO4 and Cu as nanoparticles dispersed in the base fluid water along with suspended dust particles. The set of partial differential equations is reduced by using apt similarity variables and boundary conditions to obtain ordinary differential equations. The numerical solution is approximated using MATLAB‐bvp4c adopting the shooting technique. The impact of numerous pertinent physical parameters on the velocity and thermal profiles is plotted and deliberated. Furthermore, the rate of heat flow and friction factor is also tabulated and visualized through the graphs. Streamlines are also drawn to know the behavior of the fluid flow. The rise in values of ME quickly increases the velocity of the fluid motion but declines the thermal gradient and thickness of its related boundary layer. Also, inclining values of Pr enhance the thermal profile due to the impact of melting.
A mathematical model is proposed to describe the flow, heat, and mass transfer behaviour of a non-Newtonian (Jeffrey and Oldroyd-B) fluid over a stretching sheet. Moreover, a similarity solution is given for steady two-dimensional flow subjected to Buongiorno’s theory to investigate the nature of magnetohydrodynamics (MHD) in a porous medium, utilizing the local thermal non-equilibrium conditions (LTNE). The LTNE model is based on the energy equations and defines distinctive temperature profiles for both solid and fluid phases. Hence, distinctive temperature profiles for both the fluid and solid phases are employed in this study. Numerical solution for the nonlinear ordinary differential equations is obtained by employing fourth fifth order Runge–Kutta–Fehlberg numerical methodology with shooting technique. Results reveal that, the velocity of the Oldroyd-B fluid declines faster and high heat transfer is seen for lower values of magnetic parameter when compared to Jeffry fluid. However, for higher values of magnetic parameter velocity of the Jeffery fluid declines faster and shows high heat transfer when compared to Oldroyd-B fluid. The Jeffery liquid shows a higher fluid phase heat transfer than Oldroyd-B liquid for increasing values of Brownian motion and thermophoresis parameters. The increasing values of thermophoresis parameter decline the liquid and solid phase heat transfer rate of both liquids.
The fluid flow through inclined plates has several applications in magneto-aerodynamics, materials processing and magnetohydrodynamic propulsion thermo-fluid dynamics. Inspired by these applications, the rate of entropy production in a bio-convective flow of a magnetohydrodynamic Williamson nanoliquid over an inclined convectively heated stretchy plate with the influence of thermal radiation, porous materials and chemical reaction has been deliberated in this paper. The presence of microorganisms aids in stabilizing the suspended nanoparticles through a bioconvection process. Also, the thermal radiation assumed an optically thick limit approximation. With the help of similarity transformations, the coupled partial differential equations are converted to nonlinear ordinary differential equations and the resulting model is numerically tackled using the shooting method. The influences of the determining thermo-physical parameters on the flow field are incorporated and extensively discussed. The major relevant outcomes of the present analysis are that the upsurge in values of Schmidt number decays the mass transfer characteristics, but the converse trend is depicted for boost up values of the thermophoresis parameter. Enhancement in bioconvection Peclet and Schmidt numbers deteriorates the microorganism density characteristics. Further, the upsurge in the Williamson parameter declines the Bejan number and irreversibility ratio.
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