ψ - v Computation of steady-state conjugate heat transfer in backward-facing step flow

In this paper, we study steady-state conjugate heat transfer over a backward-facing step flow using a combination of a compact finite difference scheme for the $\psi$-$v$ form of the Navier–Stokes equations and a higher-order compact scheme for the temperature equations on nonuniform grids. We investigate the effect of Reynolds number ($200\le Re\le 800$), conductivity ratio ($1\le k\le 1000$), Prandtl number ($0.1\le Pr\le 15$), and slab thickness ($h\le b\le 6h$) on the heat transfer characteristics. Isotherms remain clustered near the reattachment point in the fluid, while the temperature in the solid decreases vertically, with the minima at the reattachment point. Heat transfer rate (HTR) increases with Re, the maximum at the reattachment point. The HTR increases with $k$ till $k=100$ after, which it becomes invariant as $k\to \infty$. Isotherms at the inlet become more disorderly with increasing Pr, and progressively clustered near the interface, indicating an increase in HTR, while the temperature in the solid region decreases with Pr. Increasing b decreases the HTR. In addition to obtaining an excellent match with results previously reported in the literature, we offer more comprehensive and previously unreported insights on flow physics.     

A mathematical simulation of unsteady MHD Casson nanofluid flow subject to the influence of chemical reaction over a stretching surface: Buongiorno's model

In this study, unsteady boundary layer flow with Casson nanofluid within the sight of chemical reaction toward a stretching sheet has been analyzed mathematically. The fundamental motivation behind the present examination is to research the influence of different fluid parameters, in particular, Casson fluid $\beta (0.2\le \beta \le 0.4)$, thermophoresis $Nt(0.5\le Nt\le 1.5)$, magnetohydrodynamic $M(3.0\le M\le 5.0)$, Brownian movement $Nb(0.5\le Nb\le 2.0)$, Prandtl numberty, unsteadiness parameter $A(0.10\le A\le 0.25)$, chemical reaction parameter $\gamma (0.1\le \gamma \le 0.8)$, and Schmidt number $Sc(1.0\le Sc\le 3.0)$ on nanoparticle concentration, temperature, and velocity distribution. The shooting procedure has been adopted to solve transformed equations with the assistance of Runge–Kutta Fehlberg technique. The impact of different controlling fluid parameters on flow, heat, and mass transportation are depicted in tabular form and are shown graphically. Additionally, values of skin friction coefficient, Nusselt number, and Sherwood number are depicted via tables. Present consequences of the investigation for Nusselt number are related with existing results in writing by taking $Nb=0$ and $Nt=0$ where results are finding by utilization of MATLAB programming. Findings of current research help in controlling the rate of heat and mass aspects to make the desired quality of final product aiding manufacturing companies and industrial areas.     

Boundary layer flow and stability analysis of forced convection over a diverging channel with variable properties of fluids

The objective of the current study is to investigate the forced convection laminar boundary layer flow over a flat plate in a diverging channel with variable viscosity. The physical governing equations are converted to nondimensional partial differential equations (PDEs) using similarity transformation. The coupled PDEs with boundary constrains are solved numerically using quasilinearization technique. Computational results are given in terms of flow parameter $ϵ\left(0<ϵ<1\right)$, suction or injection A, and viscous dissipation parameter Ec. Stability analysis was conducted and the solutions were found to be stable for real values of $\gamma$. We found that variable Prandtl number with quasilinearization technique method gives smoothness of solution compared to fixed Prandtl number. This is shown graphically for different fluids in Section 5. Also, the significant effect of the suction/injection parameter $\left(A\right)$ on velocity, temperature profiles, skin friction, and heat transfer is observed.     

Heat generation/absorption on MHD flow of a micropolar fluid over a heated stretching surface in the presence of the boundary parameter

A model study is reported to examine the effect of magnetic hydrodynamics polar fluid over a semistretched infinite vertical porous surface in the presence of heat source, temperature, magnetic field, and thermal radiation. The governing dimensional partial differential equations are transformed into an ordinary differential equation set by introducing the similarity variables. The reduced model is numerically solved via Runge–Kutta fourth order along with the shooting technique. The effects of various physical parameters on coefficient of skin friction, microrotation coefficient, and Nusselt number are studied whereas the outcomes are explained through a set of graphs. The results obtained are explained in tabular form and graphs. Prandtl and Hartman's numbers enhance the velocity profile while the opposite behavior is noticed for $\phi ,\delta$. Higher values of Pr enlarge the angular velocity near the surface. Improved temperature distribution is noticed for higher values of Ha and ϕ, However, a declined behaviour is observed for $\text{Pr},\delta$, and $fo$.     

MHD slip flow and heat transfer of UCM fluid with the effect of suction/injection due to stretching sheet: OHAM solution

In this study, the optimal homotopy analysis (OHAM) technique has been examined to solve the laminar magnetohydrodynamic flow (MHD flow) on the upper-convected Maxwell fluid on an isothermal porous stretch surface. A study on the effects of parameters like the relaxation time, suction/injection velocity, as well as the magnetic number on velocity over a sheet was conducted and these results are compared to the corresponding previously available results. It was observed that the thickness of the boundary layer is lowered by enhancing $s$, $\beta$, and $M$ values. Opposing this, it was observed that large $\beta$ values increase the $f″\left(0\right)$ magnituIIde. It is found that OHAM is an efficient method capable of giving a greater degree of accuracy in numerical values of flow parameters even after fewer approximations.     

Computations of mixed convection slip flow around the surface of a sphere: Effects of thermophoretic transportation and viscous dissipation

The effects of thermophoretic motion and viscous dissipation on the two-dimensional fluid flowing along different positions of a sphere are inspected by considering slip flow. The leading set of partial differential equations is altered as a set of nonlinear primitive partial differential equations utilizing primitive variable transformation. The finite difference method is used to solve the governing equations numerically. The impacts of appropriate parameters, such as Eckert number slip flow parameters, mixed convection parameter, and thermophoresis parameter on unknown variables, such as velocity profile, mass concentration, and temperature profile are analyzed and displayed with the help of graphs by using the highly technical software, Tecplot 360. And also, we have observed the effects of the identical parameters on skin friction coefficient, rate of heat, and rate of mass transfers by means of graphs. From the outcomes, we noted that (a) the velocity profile is dominant at position $X=1.5$ rad and the temperature distribution and mass concentration are dominant at position $X=\pi$ rad for increasing values of Eckert number. (b) Slip parameter boosts the velocity at position $X=2.095$ rad but temperature and mass concentration are maximum at position $X=\pi$ rad. (c) The thermophoretic parameter is also having a very strong impact on heat and fluid flow mechanics. The slip flow provides benefits in improving heat and mass transfer mechanisms along with skin friction. It is also predicted that the concentration boundary layer will be thinner during thermophoresis around the different positions. The novelty of the predicted work is holding slip flow with the inclusion of mechanical energy and thermophoretic motion around different positions of the sphere. It is worth mentioning that the obtained results predicted in graphs are satisfied by the prescribed boundary conditions, which yield the corrected skin friction, rate of heat transfer, and rate of mass transfer.