Heat transfer in dusty fluid with suspended hybrid nanoparticles over a melting surface

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 M_E 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.     

Solar radiative heat-driven Sakiadis flow of a dusty nanoliquid with Brownian motion and an exponential space-based heat source: Koo–Kleinstreuer–Li (KKL) model

The advancement of heat transportation is a significant phenomenon in nuclear reactors, solar collectors, heat exchangers, and electronic coolers; and it can be accomplished by choosing a nanofluid as the functional fluid. Nanofluids have improved thermophysical properties, due to their great progress in engineering and industrial applications. Therefore here, the significance of exponential space-related heat source (ESHS) on radiative heat motivated Sakiadis two-phase flow over a moving plate is analyzed for a particulate nanoliquid (CuO–H₂O). The impact of the haphazard motion of nanoparticles is analyzed through the Koo–Kleinstreuer–Li model. On applying a similarity transformation to the governing equations, a set of ordinary differential equations is obtained and numerically solved. Through the perception of graphs, the behavior of the velocity and temperature constraints for diverse values of effective parameters is decoded. The results show that the temperature of both phases (dust and fluid) improves with the ESHS aspect. Also, the heat transport rate/friction factor enhances/declines with the concentration of dust particles.     

Two-phase Sakiadis flow of a nanoliquid with nonlinear Boussinesq approximation and Brownian motion past a vertical plate: Koo-Kleinstreuer-Li model

This paper investigates the Sakiadis flow of a Al₂O₃-H₂O nanoliquid with consistently scattered dust particles over a vertical plate. To account for the effect of the Brownian movement, the Koo-Kleinstreuer-Li model is considered. In some thermal systems such as reactor safety areas, and solar collectors, combustion works from moderate to high temperature, making the relationship between the temperature and density nonlinear. To consider this temperature-dependent density, the nonlinear Boussinesq estimation is utilized. The present physical structure, which includes energy and momentum equations, is converted into a system of ordinary, coupled, and nonlinear differential conditions through the help of similarity transformations. By using the finite difference code, the subsequent equations have been numerically solved. The impact on the velocity and the thermal profiles of the nondimensional parameters is visualized through graphs. Both the Nusselt number and friction factor strengthen with a higher nonlinear thermal parameter in the case of nonlinear Boussinesq approximation compared to the linear Boussinesq case. Growing estimations of nonlinear thermal parameter deteriorate the thermal profile but it boosts the velocity profile of both liquid and dust phases.     

A study on entropy generation and heat transfer in a magnetohydrodynamic flow of a couple-stress fluid through a thermal nonequilibrium vertical porous channel

The effect of local thermal nonequilibrium (LTNE) on the entropy generation and heat transfer characteristics in the magnetohydrodynamic flow of a couple-stress fluid through a high-porosity vertical channel is studied numerically using the higher-order Galerkin technique. The Boussinesq approximation is assumed to be valid and the porous medium is considered to be isotropic and homogeneous. Two energy equations are considered one each for solid and fluid phases. The term involving the heat transfer coefficient in both equations renders them mutually coupled. Thermal radiation and an internal heat source are considered only in the fluid phase. The influence of inverse Darcy number, Hartmann number, couple-stress fluid parameter, Grashof number, thermal radiation parameter, and interphase heat transfer coefficient on velocity and temperature profiles is depicted graphically and discussed. The entropy generation, friction factor, and Nusselt number are determined, and outcomes are presented via plots. The effect of LTNE on the temperature profile is found to cease when the value of the interphase heat transfer coefficient is high, and in this case, we get the temperature profiles of fluid and solid phases are uniform. The physical significance of LTNE is discussed in detail for different parameters' values. It is found that heat transport and friction drag are maximum in the case of LTNE and minimum in the case of local thermal equilibrium. We observe that LTNE opposes the irreversibility of the system. The corresponding results of a fluid-saturated densely packed porous medium can be obtained as a limiting case of the current study.     

A numerical study on heat transfer and MHD flow of a Newtonian through a porous channel—Local thermal nonequilibrium model

 Vast numbers of studies concentrate on the thermal equilibrium state whereas in many real-world applications the model exists in the nonequilibrium state. Also, local thermal non-equilibrium precisely represents the thermohydroflow characteristics. Therefore, the current study examines the heat transfer and fluid flow characteristics of the magnetohydrodynamic flow of a Newtonian fluid through a local thermal non-equilibrium (LTNE) porous channel in the presence of the induced magnetic field. The mathematical model of the prescribed flow encloses the coupled nonlinear equations which are difficult to approach analytically. Hence, they are solved numerically using the shooting method with the Newton–Raphson method. The implications of various physical parameters of the problem on fluid flow, induced magnetic field, current density, temperature profiles, and heat transfer are elucidated with the aid of plots and tables. From the examination, it is clear that the porous medium significantly influences the characteristics of the fluid flow. That is, the least value of the Darcy number is related to a higher momentum field. Another interesting phenomenon is that the induced magnetic field remarkably enhances when the Darcy number is high, whereas the process is contrary to the current density. The effect of LTNE on the flow characteristics and heat transfer ceases for higher values of inter-phase heat transfer coefficient and the ratio of thermal conductivities, which gives rise to the local thermal equilibrium (LTE) situation. Furthermore, the amount of heat transport is maximum in the LTE case compared to that of the LTNE case.