EFFECT OF HEAT AND MASS TRANSFER AND THERMAL RADIATION ON A STEADY MHD CONVECTIVE FLOW WITH VISCOUS DISSIPATION AND SUCTION/INJECTION

Our motive is to examine the impact of thermal radiation and suction or injection with viscous dissipation on an MHD boundary layer flow past a vertical porous stretched sheet immersed in a porous medium. The set of the flow equations is converted into a set of non-linear ordinary differential equations by using similarity transformation. We use Runge Kutta method and shooting technique in MATLAB Package to solve the set of equations. The impact of non-dimensional physical parameters on flow profiles is analysed and depicted in graphs. We observe the influence of non-dimensional physical quantities on the Nusselt number, the Sherwood number, and skin friction and presented in tables. A comparison of the obtained numerical results with existing results in a limiting sense is also presented. We enhance radiation to observe the deceleration of fluid velocity and temperature profile for both suction and injection. While enhancing porosity parameter accelerates velocity whereas decelerates temperature profile. As the heat source parameter increases, the temperature of the fluid decreases for both suction and injection, it has been found. With the increasing values of the radiation parameter, the skin friction and heat transfer rate decreases. Increasing magnetic parameter decelerates the skin friction, Nusselt number, and Sherwood number.

Prediction Method for Condensation Heat Transfer in the Presence of Non-condensable Gas for CFD Applications

The objective of this study was to present a prediction method for condensation heat transfer in the presence of non-condensable gas (air or nitrogen) for CFD (computational fluid dynamics) analyses, where physical quantities in the computational cells in contact with the structural wall are generally used. First by using existing temperature distributions T(y) in the turbulent boundary layer along a flat plate as functions of the distance y from the condensation surface, we evaluated the distribution of condensation heat flux qc,pre(y) from the gradient of steam concentration, we derived a modification factor η(y+) as a function of the dimensionless distance y+ to obtain a good agreement with qc,cal calculated by the qc correlation defined by using the bulk quantities; and we obtained qc,mod(y)/qc,cal = 0.90-1.10 for the region of y+ > 17. Second we modified the local Sherwood number Sh(x) for flat plates for the boundary layer thickness d and obtained the function Sh(d). An existing qc correlation for flat plates as a function of Sh(d) was applied to predict the distribution of the local value qc,pre(y), and qc,pre(y)/qc,cal = 0.95-1.15 in the best case was obtained for the region of y+ > 30. Finally a correlation of the local Sherwood number Sh(y) was derived from the temperature distributions T(y) as a function of the local Reynolds number Re(y).

MHD Free Convection Flow Across an Inclined Porous Plate in the Presence of Heat Source, ISoret Effect, and Chemical Reaction Affected by Viscous Dissipation Ohmic Heating

This work studies the steady two-dimensional MHD free convection flow past an inclined porous plate embedded in the porous medium in the presence of heat source, iSoret effect, and chemical reaction. The non-dimensional governing equations are solved by the perturbation technique. The Rosseland approximation is utilized to describe the radiative heat flux in the energy equation. The effect of magnetic parameter, heat source parameter, radiation parameter, Grashofi number, modified Grashofi number, Schmidt number, Prandtl number, porosity parameter, Soreti number, and chemical reaction on velocity, temperature, concentration profiles, skin friction, Nusselt number, and Sherwood number are mainly focussed in discussion with the help of graphs. It is seen that velocity, concentration, and skin friction fall with the increasing value of chemical reaction. Further, temperature, Nusselt number, and Sherwood number increase with the increasing value of chemical reaction.

An Enhanced Sherwood Number to Model the Hydrogen Transport in Membrane Steam Reformers

It is well known that membrane reactors are inherently two-dimensional systems in which species concentrations vary as a consequence of both the reaction and permeation across the membrane, which occurs in the direction perpendicular to that of the main gas flow. Recently, an expression for an enhanced Sherwood number was developed to describe the hydrogen concentration gradients arising in methane steam-reforming membrane reactors as a consequence of the combined effect of hydrogen production, dispersion, and permeation. Here, the analysis is developed in further detail with the aim of (i) assessing the validity of the simplifying assumptions made when developing the 1D model and (ii) identifying the operating conditions under which it is possible to employ the 1D model with the enhanced Sherwood number.

Numerical Simulations of Magnetic Dipole over a Nonlinear Radiative Eyring–Powell Nanofluid considering Viscous and Ohmic Dissipation Effects

This research work interprets the influences of magnetic dipole over a radiative Eyring–Powell fluid flow past a stretching sheet while considering the impacts of viscous and ohmic dissipation that produce a quite illustrious effect due to the generated magnetic dipole. This whole analysis is characterized by the effects of steady, laminar, and incompressible flow. The highly nonlinear and coupled partial differential equations (PDEs) are remodeled into a system of nonlinear ordinary differential equations (ODEs) by utilizing reliable and nondimensional parameters leading to the momentum, thermal, and concentration equations, that are computationally solved using b v p 4 c on MATLAB, and “dsolve” command on MAPLE software, in the companionship of boundary conditions. The physical constraints such as viscous and ohmic dissipation and many other sundry parametric effects are sketched with their ultimate effects on fluid flow. For the sustenance of this research with the prior work and in collaboration with the below mentioned literature review, a comprehensive differentiation is given, which defines the sustainability of the current work. The Buongiorno nanoliquid model elaborates the thermophoresis and Brownian features that are deliberately scrutinized within the influence of activation energy. Also, the skin friction coefficient, Nusselt number, and Sherwood number are illustrated in tables. The skin friction coefficient decreases with a rise in the ferromagnetic interaction parameter as well as the Hartmann number, whereas the Nusselt number and Sherwood number show variation for varying parameters. It can be observed that Eyring–Powell fluid intensifies the rate of heat and mass transfer.

A macroscopic two-length-scale model for natural convection in porous media driven by a species-concentration gradient

The modelling of natural convection in porous media is receiving increased interest due to its significance in environmental and engineering problems. State-of-the-art simulations are based on the classic macroscopic Darcy–Oberbeck–Boussinesq (DOB) equations, which are widely accepted to capture the underlying physics of convection in porous media provided the Darcy number, $Da$ , is small. In this paper we analyse and extend the recent pore-resolved direct numerical simulations (DNS) of Gasow et al. (J. Fluid Mech, vol. 891, 2020, p. A25) and show that the macroscopic diffusion, which is neglected in DOB, is of the same order (with respect to $Da$ ) as the buoyancy force and the Darcy drag. Consequently, the macroscopic diffusion must be modelled even if the value of $Da$ is small. We propose a ‘two-length-scale diffusion’ model, in which the effect of the pore scale on the momentum transport is approximated with a macroscopic diffusion term. This term is determined by both the macroscopic length scale and the pore scale. It includes a transport coefficient that solely depends on the pore-scale geometry. Simulations of our model render a more accurate Sherwood number, root mean square (r.m.s.) of the mass concentration and r.m.s. of the velocity than simulations that employ the DOB equations. In particular, we find that the Sherwood number $Sh$ increases with decreasing porosity and with increasing Schmidt number $(Sc)$ . In addition, for high values of $Ra$ and high porosities, $Sh$ scales nonlinearly. These trends agree with the DNS, but are not captured in the DOB simulations.

Fluid Flow and Heat Transfer Analysis of a Nanofluid Containing Motile Gyrotactic Micro-Organisms Passing a Nonlinear Stretching Vertical Sheet in the Presence of a Non-Uniform Magnetic Field; Numerical Approach

The behavior of a water-based nanofluid containing motile gyrotactic micro-organisms passing an isothermal nonlinear stretching sheet in the presence of a non-uniform magnetic field is studied numerically. The governing partial differential equations including continuity, momentums, energy, concentration of the nanoparticles, and density of motile micro-organisms are converted into a system of the ordinary differential equations via a set of similarity transformations. New set of equations are discretized using the finite difference method and have been linearized by employing the Newton’s linearization technique. The tri-diagonal system of algebraic equations from discretization is solved using the well-known Thomas algorithm. The numerical results for profiles of velocity, temperature, nanoparticles concentration and density of motile micro-organisms as well as the local skin friction coefficient Cfx, the local Nusselt number Nux, the local Sherwood number Shx and the local density number of the motile microorganism Nnx are expressed graphically and described in detail. This investigation shows the density number of the motile micro-organisms enhances with rise of M, Gr/Re2, Pe and Ω but it decreases with augment of Rb and n. Also, Sherwood number augments with an increase of M and Gr/Re2, while decreases with n, Rb, Nb and Nr. To show the validity of the current results, a comparison between the present results and the existing literature has been carried out.

Fluid Flow and Heat Transfer Analysis of a Nanofluid Containing Motile Gyrotactic Micro-Organisms Passing a Nonlinear Stretching Vertical Sheet in the Presence of a Non-Uniform Magnetic Field; Numerical Approach

The behavior of a water-based nanofluid containing motile gyrotactic micro-organisms passing an isothermal nonlinear stretching sheet in the presence of a non-uniform magnetic field is studied numerically. The governing partial differential equations including continuity, momentums, energy, concentration of the nanoparticles, and density of motile micro-organisms are converted into a system of the ordinary differential equations via a set of similarity transformations. New set of equations are discretized using the finite difference method and have been linearized by employing the Newton’s linearization technique. The tri-diagonal system of algebraic equations from discretization is solved using the well-known Thomas algorithm. The numerical results for profiles of velocity, temperature, nanoparticles concentration and density of motile micro-organisms as well as the local skin friction coefficient Cfx, the local Nusselt number Nux, the local Sherwood number Shx and the local density number of the motile microorganism Nnx are expressed graphically and described in detail. This investigation shows the density number of the motile micro-organisms enhances with rise of M, Gr/Re2, Pe and Ω but it decreases with augment of Rb and n. Also, Sherwood number augments with an increase of M and Gr/Re2, while decreases with n, Rb, Nb and Nr. To show the validity of the current results, a comparison between the present results and the existing literature has been carried out.