Influence of heat source on viscous dissipative hydromagnetic fluid flow in a permeable vertical channel subjected to time-periodic boundary conditions

Unsteady heat-generating natural convective viscous dissipative fluid flow through a permeable steady-periodic vertical channel in the presence of heat source is studied. The coupled partial differential governing equations of the problem are simplified to obtain second-order nonlinear ordinary differential equations. The resulting differential equations are solved using differential transform method to obtain approximate solutions for the momentum and energy equations. The impacts of pertinent parameters, such as heat source/sink ($\delta$), Prandtl number ($\mathit{Pr}$), viscous heating ($\lambda$), suction/injection (S), and Strouhal number ($\mathit{St}$), on the velocity and temperature distributions in the periodic regime are illustrated using graphs and discussed. From the computational results, it is observed that an increase in the values of heat source/sink parameter ($\delta$) in the presence of viscous dissipation has significant influence on the flow and heat transfer. This study provides useful information in handling and processing the extraction of crude-oil-based slurries.     

Hydromagnetic boundary layer flow with heat transfer past a rotating disc embedded in a porous medium

In this study, the effect of Coriolis force along with the Darcy parameter has been analyzed on time-dependent forced convective boundary layer flow of conducting fluids over a rotating disc embedded in a porous medium. The modeled system is solved by power series approximations in the Mathematica environment shooted values. The significant impact of the rheological properties, such as Darcy parameter $\beta$ and Prandtl number $\mathit{Pr}$, of water, hydrocarbon, and kerosene-based conducting fluids for the deviation of parameter $\xi$ (Karman) has been noted and then analyzed qualitatively and quantitatively with graphs and tables.     

FHD flow and heat transfer over a porous rotating disk accounting for Coriolis force along with viscous dissipation and thermal radiation

The prime concern of the current findings includes the effect of viscous dissipation and nonlinear thermal radiation on the study of ferrofluid flow and heat transfer past a porous rotating disk. The time-independent flow of incompressible ferrofluid is modeled for the considered geometry, and via similarity transformations, the given system is converted to a dimensionless system of the nonlinear ordinary differential equations. Here, the findings are explored computationally with help of Maple software. The study exhibits the effect of the involved emerging parameters: the interaction parameter $B$, Prandtl number $Pr$, rotation parameter $R$, radiation parameter $Qr$, Eckert number $Ec$, and these are discussed graphically. Moreover, the numerical values of heat transfer rate and skin frictions are also presented in tabular form. From the perspective of numerical findings, it is perceived that the radial flow is dominant when we increase the rotation of the disk. Furthermore, the magnitude of magnetic-fluid temperature is enhanced with the surge in the magnetic field, viscous dissipation, and thermal radiation mechanism. Finally, the current research can successfully fill a gap in the existing literature.     

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 $fo$.     

Influence of peristalsis on the convective flow of two immiscible fluids in a vertical channel

This article explores the flow characteristics of peristaltic transport of two immiscible fluids in a vertical channel with heat transfer are studied. The flow domain is divided into the core region and a peripheral region, respectively. The solution is derived analytically in the form of temperature from which the stream function and axial velocity corresponding to each region are found. The two regions are separated by an interface, which is determined by using nonlinear algebraic equation. In peristaltic transport, the importance of physical quantities like pumping, axial velocity, temperature distribution, and interface are discussed for different considerations of interest governing the flow parameters. It is noticed that the increase in $Gr$ enhances the pressure change at a given flow rate. It shows that increasing $Gr$ enhances the displacement of fluid particles, which yields to increase in axial velocity. The increase in heat source/sink parameter yields the increase in temperature of the fluid, which, in turn, results in an increase in temperature distribution.     

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.     

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.