Comprehensive analysis of radiation impact on the transfer of heat and mass micropolar MHD free convective fluid flow across a stretching permeability sheet with suction/injection

As part of our research, we investigate the analysis influence of radiation on heat and mass transfer free convection of micropolar MHD fluids over a stretched porosity sheet involving suction and injection. The governing energy, rotational momentum, and concentration and momentum partial differential equations are transformed into ordinary differential equation ones via a similarity transformation. This system of equations is then solved by using MATLAB's built-in solver. The Sherwood numbers, Nusselt, friction factor, wall couple shear stress, and dimensionless profiles are all influenced by the various physical parameters of the flow. When the material parameter is increased, velocity rises but decreases when the magnetic parameter and surface condition factor are increased.     

Magnetohydrodynamic bio‐nanoconvective Naiver slip flow of micropolar fluid in a stretchable horizontal channel

The purpose of this paper is to formulate and analyze a nano‐bio transport model for magnetohydrodynamic convective flow, heat, and mass diffusion of micropolar fluid containing gyrotactic microorganisms through a horizontal channel. Both the walls are considered to be stretched, and the Navier slip boundary condition is taken into account. The governing bio‐nano transport partial differential equations are rendered to ordinary differential equations using similarity variables. The resulting normalized self‐similar boundary value problem is solved computationally with the Matlab bvp4c function. The effect of the controlling parameters on the nondimensional velocity, temperature, nanoparticle concentration, and motile microorganism density functions, and their gradients at the wall are visualized graphically and in a tabular form and expounded at length. Validation with a previous simpler model is included. All physical quantities, except the local Nusselt number, increases with an increase in the velocity slip and magnetic parameters. The present problem finds applications in industries related to pharmaceutical, nanofluidic devices, microbial enhanced oil recovery, modeling oil, and gas‐bearing sedimentary basins.     

Magnetohydrodynamic micropolar slip flow due to an exponentially stretching sheet with chemical reaction and nonuniform heat generation

The main focus of the current study is to examine the impact of melting heat transfer and chemical reaction on magnetohydrodynamic micropolar fluid flow over a sheet that is exponentially stretching and immersed in a porous medium. A nonuniform heat source is placed within this flow system. Other impacts like slip phenomena and thermal radiation are also taken into consideration. The governing partial differential equations are converted to a system of ordinary differential equations (ODEs) via similarity transformation and we also get the corresponding necessary boundary conditions. These nonlinear ODEs are resolved with the help of shooting technique and an Runge-Kutta fourth order (RK-4) iterative strategy. Also, we solve this problem using the Bvp4c approach for validating the results of the RK-4 method. Both outcomes are consistent with previously published data. With the help of tables and graphs, we examine the influence of multiple physical parameters on velocity, thermal, microrotation, concentration, Nusselt number, Sherwood number, coefficient of skin friction, and wall couple stress. We see that the temperature distribution and velocity profiles decrease when the melting parameter increases. The temperature profile boosts when the heat source parameter is increased.     

Heat and mass transfer in a MHD non‐Darcian micropolar fluid over an unsteady stretching sheet with non‐uniform heat source/sink and thermophoresis

The effect of heat and mass transfer in a MHD non‐Darcian flow of a micropolar fluid over an unsteady stretching sheet with thermophoresis and non‐uniform heat source/sink is discussed. The fluid is electrically conducting in the presence of a uniform applied magnetic field. The arising nonlinear problem is solved by the Keller box method. The effects of various physical parameters on skin friction, local Nusselt number, and Sherwood number are presented graphically and in tabular form. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21018     

A non‐Fourier heat flux model for magnetohydrodynamic micropolar liquid flow across a coagulated sheet

In this analysis, a heat transfer extrusion system was made by using a modified heat flux model, namely, the Cattaneo‐Christov heat flux. In the present study, we examined the effect of Arrhenius activation energy on magnetohydrodynamic mixed convection stagnation point flow of a micropolar fluid over a variable thickened surface in the attendance of Brownian motion. The fluid motion is assumed to be steady and laminar. The combined influence of heat and mass transfer aspects are scrutinized. First, suitable transformations are considered to modify the governing partial differential equations as ordinary differential equations and revealed by the consecutive application of numerical procedures like shooting and Runge‐Kutta‐Fehlberg. Graphs are delineated to scrutinize the effects of sundry dimensionless parameters on the flow fields. We found that, the present results made a good agreement with the existing results. We observed that there is an enhancement in the fields of concentration with thermophoresis and activation energy parameters but an opposite trend is noticed for the Brownian motion parameter. Also, it is interesting to note that the buoyancy and the primary slip parameters are increasing functions of velocity fields.     

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 $fo$.     

Analysis of MHD micropolar nanofluid flow and heat transfer between a porous plate and a nonporous plate filled with porous medium

This article presents an analytical study on magnetohydrodynamic micropolar nanofluid flow through parallel, coaxial discs filled with a porous medium with uniform blowing from the upper plate. Three different types of nanoparticles, namely copper, aluminum oxide, and titanium dioxide are considered with water and used as base fluids. The governing equations are solved via Differential Transformation Method. The validity of this method has been verified with the results of numerical solution (fourth‐order Runge‐Kutta scheme). The analytical investigation is carried out for different governing parameters. The results indicate that skin friction coefficient has a direct relationship with Hartmann number and the micropolar parameter. It is also found that Nusselt number is increased with increment in Prandtl number and Eckert number. Additionally, this analysis concluded that an increase in volume fraction of nanofluid increases the Nusselt number on the top plate and decreases it on the lower plate.     

Unsteady MHD mixed convection flow of a micropolar fluid along an inclined stretching plate

In this research, the unsteady magnetohydrodynamic mixed convection flow of a micropolar fluid over an inclined plate has been investigated. The problem is reduced to a system of non‐dimensional partial differential equations, which are solved numerically using the implicit finite‐difference scheme. Velocity profiles, temperature profiles, concentration profiles, the skin friction coefficient, the rate of heat transfer, and the rate of mass transfer are computed numerically for various values of different physical parameters. In this study, we consider both assisting and opposing flow. It is found that in the assisting flow case, a solution could be obtained for all positive values of the buoyancy parameter λ, while in the opposing flow case the solution terminated at $\lambda = {\lambda _c}(\lambda < 0)$ . © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21034     

Exploration of heat transfer effect in a magnetohydrodynamics flow of a micropolar fluid between a porous and a nonporous disk

An analysis is carried out for the flow characteristics of a conducting micropolar fluid. The fluid was passed in between two parallel disks of infinite radii. The novelty of the study is to consider one of the disks as porous and the other one as nonporous, and the external magnetic field is applied along the transverse direction of the flow. The flow phenomena for the polar fluid characterized by the magnetic effect in conjunction with the temperature equation reduce to a set of coupled nonlinear ordinary differential equations using the requisite transformations and nondimensionalization. An analytical approach such as the variation parameter method is employed to tackle the system efficiently. To emphasize the effect of various physical parameters contributing to the flow phenomena, that is, non-zero tangential slip, Reynolds number, Prandtl number, magnetic parameter, and material parameter on the flow profiles of axial and radial velocities, the microrotation and temperature profiles are presented graphically. To validate the simulated results, a comparison with established results is made, and it is concluded that both are in good correlation.     

Dual solutions for flow and radiative heat transfer of a micropolar fluid over stretching/shrinking sheet

A boundary layer analysis is presented for the flow and radiative heat transfer of an incompressible micropolar fluid over stretching/shrinking sheet with power-law surface velocity and temperature distributions. Dual solutions are analytically obtained firstly by homotopy analysis method (HAM). It is found that dual solutions not only exist for the shrinking flow as reported in the previous literatures, but also exist for the stretching flow. The special case of the first branch (K = 0, classical Newtonian fluid) is compared with the existing numerical results of stretching flow in good agreement. Our results show that both solutions are physically meaningful (two solutions are closely related to each other), unlike the results previously reported that only one solution is acceptable. Moreover, the effects of the material parameter K, the radiative Prandtl number Pr_n, the velocity exponent parameter m and the temperature exponent parameter λ on the flow and heat transfer characteristics are analyzed in detail.     

Nonlinear radiation and cross-diffusion effects on the micropolar nanoliquid flow past a stretching sheet with an exponential heat source

Metallurgy, polymer and processing engineering, and petrochemical enterprises frequently encounter polar nanoliquid flows due to stretchable surfaces with radiative heat energy. Therefore, the radiative flow of a polar nanoliquid over a stretchable sheet is analyzed considering cross-diffusion and magnetic heat flux effects. The heat transport phenomenon is explored, including the characteristics of nonlinear radiation and exponential space-based heat generation. The highly nonlinear governing equations are converted to ordinary differential equations using apt transformations. These are, in turn, solved employing the finite difference method. The behavior of contributing parameters is presented using graphical visualizations. The interactive impacts of the pertinent constraints on the rate of heat transfer and skin friction are analyzed using three-dimensional surface plots. The enhancement of the temperature profile is observed by incrementing the radiation and exponential heat generation parameters. The magnetic field can be used to regulate the fluid flow as it decreases the flow field. Also, the heat generation factor has a predominant decreasing effect on the Nusselt number.     

Numerical simulation of natural convection heat transfer from a heated square cylinder in a square cavity filled with micropolar fluid

A numerical investigation has been performed to visualize the magnetohydrodynamic natural convective heat transfer from a heated square cylinder situated within a square enclosure subjected to nonuniform temperature distributions on the left wall. The flow inside the enclosure is unsteady, incompressible, and laminar and the working fluid is micropolar fluid with constant Prandtl number (Pr = 7). The governing equations of the flow problem are the conservation of mass, energy, and linear momentum, as well as the angular momentum equations. Governing equations formulated in dimensionless velocity and pressure form has been solved by Marker and Cell method with second-order accuracy finite difference scheme. Comprehensive verification of the utilized numerical method and mathematical model has shown a good agreement with numerical data of other authors. The results are discussed in terms of the distribution of streamlines and isotherms and surface-averaged Nusselt number, for combinations of Rayleigh number, Ra (10³–10⁶), Vortex viscosity parameter, K (0–5), and Ha parameter (0–50). It has been shown that an increase in the vortex viscosity parameter leads to attenuation of the convective flow and heat transfer inside the cavity.     

Multiple slip impacts on unsteady MHD micropolar fluid past a stretching sheet with non-Darcy porous medium and uneven heat source/sink

The major scope of this research is to scrutinize the effects of multiple slips on unstable magnetohydrodynamic micropolar fluid past a stretched sheet with a non-Darcy porous medium. In the momentum equation, the non-Darcy porous medium effect is also taken into consideration. The effects of uneven heat source/sink and thermal radiation in the energy equation are also analyzed. By implementing the similarity transmission, the mathematical modeling of the set of managing partial differential equations is reframed into nonlinear ordinary differential equations. These equations are numerically solved by applying Matlab built-in solver bvp5c. The implications of foremost parameters such as micropolar parameter, magnetic parameter, permeability parameter, Prandtl, Eckert, and Schmidt numbers, Chemical reaction, slip parameters on velocity, microrotation, temperature as well as concentration profiles are displayed pictorially and explained. It is worthwhile to mention that the improving values of micropolar parameter $K$ escalate the velocity as well as microrotation profiles. However, the upsurge in non-Darcy porous medium $F_s$ will cause a declining nature in the velocity profile. Also, an enhancement in the unsteadiness parameter $A$ brings about a lessening in all the profiles. Increment in all the three usual slip parameters will bring a declining nature in the respective profiles. An increase in Schmidt number will give a deduction nature in velocity as well as concentration profile. Moreover, the physical quantities are defined and Nusselt numbers are formulated in the table, and it enlarges while boosting up $Pr$ and $R$, whilst a reverse nature is noticed for others. This present study compared with the earlier studies in special cases holds a better agreement.     

Investigation of Oldroyd-B fluid flow and heat transfer over a stretching sheet with nonlinear radiation and heat source

The given investigation concerns the study of non-Newtonian Oldroyd-B fluid flow across a permeable surface along with nonlinear thermal radiation, chemical reactions, and heat sources. Equations modified are thus numerically evaluated by employing bvp4c-technique. Obtained outcomes are exhibited graphically. Pictorial notations are used to investigate the consequences of necessary parameters of velocity, energy, and mass. Acquired outcomes provide promising agreement with already established consequences provided in the open literature. The obtained results guided that magnetic field parameter ($M$), porosity parameter ($Kp$), Deborah number ${\beta }_1$ reduce momentum boundary layer thickness, furthermore, growth in the relevant Deborah number ${\beta }_2$ improves the corresponding momentum boundary layer.     

A novel analytical solution of heat transfer of a micropolar fluid through a porous medium with radiation by DTM‐Padé

In this paper, the differential transform method (DTM) was applied to heat transfer of a micropolar fluid through a porous medium with radiation. The governing equations can be written as a system of nonlinear ordinary differential equations. The approximate solutions of these equations were obtained in the form of series with easily computable terms. Then, Padé approximant was applied to increase the convergence rate of the series. The results obtained in this study were compared with the numerical results (fourth‐order Runge–Kutta method). © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res, 39(8), 575–589, 2010; Published online 26 July 2010 in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20317     

Effects of nonlinear thermal radiation over magnetized stagnation point flow of Williamson fluid in porous media driven by stretching sheet

In this study, the stagnation point flow of a magnetized Williamson fluid past a stretching sheet in the presence of nonlinear thermal radiation and buoyancy effect is studied. The present situation is remodeled using similarity transformation that transforms the flow model of partial differential equations into the set of nonlinear ordinary differential equations. The fourth-order Runge-Kutta scheme and shooting method are employed to solve these reduced equations. The effects of various associated parameters over the velocity and temperature profiles are plotted and the outcome of each associated parameter is discussed through graphs. The key findings are noted as follows: the velocity profile declines with an increase in the magnetic force number, and an increment in buoyancy parameter leads to the increase in the boundary layer thickness and decrease in the thickness of the thermal boundary layer.     

Approximate analytical approach to unsteady conducting micropolar fluid flow in the presence of buoyant forces and reactive species

The present analysis studied the significance of free convective flow of an unsteady non‐Newtonian fluid through a semi‐infinite vertical porous plate embedded in a porous medium. The thermal transport equation is enhanced by incorporating the heat source/sink and mass transfer in the chemical reaction parameters. The plate moves at a constant velocity and the velocity near the free stream varies exponentially, which allows perturbation laws. Such a model has relevance to a few industrial and engineering applications. In particular, a micropolar fluid is used as a lubricant in various gadgets, also, in polymeric suspensions as well as in animal blood, the phenomena are used to define the local structure and micromotion of the particles. Transformed nondimensional governing equations are solved analytically employing the perturbation method. Influences of the characterizing parameters are presented via graphs and computations for the coefficients of quantities of interest obtained and shown in a table. Also, validation of the present results in a particular case such as the case of Newtonian fluid is obtained with an earlier study and found to be in good agreement. The major findings are laid down here; an increase in plate velocity enhances the velocity profile near the plate and a destructive chemical reaction restrains the fluid concentration in the entire flow domain.     

Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet

The article examines the hydromagnetic laminar boundary layer flow and heat transfer in a power law fluid over a stretching surface. The flow is influenced by linear stretching of the sheet. Also the energy equation with temperature-dependent thermal conductivity, thermal radiation, work done by stress, viscous dissipation and internal heat generation is considered. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then the equations are solved by Keller–Box method. The effects of various physical parameters on the flow and heat transfer characteristics are presented graphically and discussed.     

Flow and heat transfer in a porous medium saturated with a Sisko nanofluid over a nonlinearly stretching sheet with heat generation/absorption

This work is focused on steady flow and heat transfer in a porous medium saturated with a Sisko nanofluid (non‐Newtonian power‐law) over a nonlinearly stretching sheet in the presence of heat generation/absorption. Nonlinear PDEs are transformed into a system of coupled nonlinear ODEs with related boundary conditions using similarity transformation. The reduced equations are then solved numerically using the Runge–Kutta–Fehlberg fourth–fifth order method (RKF45) with Maple 14.0 software. The solutions depend on the power‐law index n and the effect of pertinent parameter such as the Brownian motion parameter, thermophoresis parameter, Lewis number, the permeability, and the heat generation/absorption on the dimensionless velocity, temperature, and nanoparticles volume fraction and also on the skin friction, local Nusselt, and Sherwood numbers are produced for values of the influence parameter. A rapprochement of the numerical results of the actual study with formerly published data detected an excellent agreement.     

Stagnation point flow and heat transfer over a stretching/shrinking sheet in a porous medium

The steady stagnation point flow and heat transfer over a shrinking sheet in a porous medium is studied. A similarity transformation is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using the Keller-box method. The behavior of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. The results indicate that dual solutions exist for the shrinking case.