Fluid properties of an unsteady MHD free stream flow over a stretching sheet in presence of radiation

Variable fluid properties with thermal radiation in an unsteady magnetohydrodynamics free stream incompressible flow over a stretching sheet has been considered. The thermal diffusivity and viscosity of the fluid varies linearly with temperature. The governing partial differential equations are moulded to ordinary differential equations using time-dependent similarity variables and the stream function. RKF technique with shooting method has been implement to find the solution numerically. In the current analysis the impact of unsteadiness, magnetic field, radiative parameter, variable fluid viscosity and thermal diffusivity parameter on heat and flow behavior with the free stream parameter have been studied. Transition point observed in the velocity profiles with an change in unsteadiness parameter and the effect of magnetic field is reduced in the presence of free stram velocity. The velocity and the temperature gradient are computed on the surface and their outcomes with different parameters have been analyzed in the results shown graphically and in tabular form.     

MHD stagnation point flow of Casson fluid over a convective stretching sheet considering thermal radiation,slip condition,and viscous dissipation

This study presents the problem of MHD stagnation point flow of Casson fluid over a convective stretching sheet considering thermal radiation, slip condition, and viscous dissipation. The partial differential equations with the corresponding boundary conditions that govern the fluid flow are reduced to a system of highly nonlinear ordinary differential equations using scaling group transformations. The fourth-order method along shooting technique is applied to solve this system of boundary value problems numerically. The effects of flow parameters on the velocity, temperature, and concentration profiles are presented via graphs. The impact of the physical parameters on the skin friction coefficient reduced Nusselt numbers and reduced Sherwood numbers are investigated through tables. Comparison of the present findings with the previously published results in the literature shows an excellent agreement. It is also noted that a rise in the Eckert number results in a drop in the temperature of the fluid in the thermal boundary layer region of the fluid flow.     

Entropy generation on MHD flow of a Casson fluid over a curved stretching surface with exponential space-dependent heat source and nonlinear thermal radiation

The present model concentrates on entropy generation on a steady incompressible flow of a Casson liquid past a permeable stretching curve surface through chemical reaction and magnetic field effects. The exponential space-dependent heat source cum heat and mass convective boundary conditions are accounted for. The resulting nonlinear boundary layer model is simplified by the transformation of similarity. Chebyshev spectral technique is involved for obtaining numerical results of the converted system of the mathematical models. Behavior of the determining thermo-physical parameters on the profiles of velocity, temperature, concentration, skin friction, heat, mass transfer rate, rate of entropy generation, and finally the Bejan number are presented. The major point of the present investigation show that the curvature term weakens the mass transfer profile as the fluid temperature reduces all over the diffusion regime. A decrease in heat generation strengthens the species molecular bond, which prevents free Casson particle diffusion. Furthermore, the mass transfer field diminishes in suction and injection flow medium.     

Unsteady boundary layer flow of a Casson fluid due to an impulsively started moving flat plate

This paper discusses the unsteady flow and heat transfer of a Casson fluid over a moving flat plate with a parallel free stream. The analytic solutions of the system of nonlinear partial differential equations valid for all times in the whole spatial domain are constructed in the series form by a homotopic approach. The influences of the governing parameters on the velocity, temperature, skin friction coefficient, and local Nusselt number are thoroughly investigated. It is revealed that an increase in the dimensionless time decreases the velocity and enhances the temperature. The surface shear stress and surface heat transfer are enhanced by increasing the Casson fluid parameter (β) and Eckert number (Ec), respectively. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20358     

Velocity slip,chemical reaction,and suction/injection effects on two-dimensional unsteady MHD mass transfer flow over a stretching surface in the presence of thermal radiation and viscous dissipation

The purpose of this study is to analyze the impact of velocity slip, chemical reaction, and suction/injection on two-dimensional mass transfer effects on unsteady MHD flow over a stretching surface in the presence of thermal radiation and viscous dissipation. The governing time-dependent nonlinear partial differential equations are transformed into nonlinear ordinary differential equations by using similarity transformations. The converted equations are solved using the numerical technique with the help of Keller-Box method. The effect of nondimensional variables is studied and graphically illustrated on velocity, temperature, concentration, friction factor, Nusselt number, and Sherwood number. Concentration and temperature profiles are enhanced and the contrasting pattern for velocity profiles as increasing the velocity slip and magnetic parameter. The concentration profile is diminished as the Schmidt number (Sc) and chemical reaction (C_r) increase. The concentration, velocity, and temperature profiles display a reversal pattern, as the suction and unsteady parameter (A) increase. The findings of this study are very well-acknowledged with current research.     

Impact of the electromagnetic flow of an MHD Casson fluid over an oscillating porous plate

This study deals with the effect of electric force and magnetohydrodynamics (MHD) of the transient state on natural convection flow past an oscillating vertical plate. In addition to this, thermal radiation and porous media are also examined in the Casson fluid flow. The Poisson-Boltzmann equation is employed to show the electric potential character within the fluid region, which is put into a linear form by the implementation of Debye–Hückel linearization. It is possible to compute the precise solution to the governing equations using the Laplace transform approach. The expression of fluid velocity, fluid concentration, and temperature are exposed graphically, and numerical results for Nusselt and Sherwood numbers are also derived for vital pertinent flow constraints. Increasing electroosmosis parameters strongly boosts fluid velocity. The nonnegative values of the Helmholtz–Smoluchowski velocity highly induce the axial velocity and the negative value decelerates. With increasing radiation strength and Prandtl number, the fluid's temperature distribution diminishes. These more intricate electrokinetic rheological flows associated with electroosmotic separators, such as biomedical absorbers, are illuminated by these models.     

Thermal radiation and diffusion effects in MHD Williamson and Casson fluid flows past a slendering stretching surface

The article is presented to analyze the magnetohydrodynamic Casson and Williamson fluids flow over a stretched surface of variable thickness by including the conditions of thermal radiation, velocity slip, temperature, and concentration slip. The equations governing the flow characteristics are transformed to ordinary differential equations by applying similarity transformations. The solution of the simplified equations is obtained by the numerical bvp5c Matlab package. The behavior for Williamson and Casson fluid cases is explored and discussed with the impact of sundry parameters on the flowing fluid, thermal, and diffusion fields. The profiles under the impact of parameters are depicted through graphs. Also, we evaluated the performance of local Nusselt and Sherwood numbers along with the friction of the wall and are displayed through tables. We found that the temperature and mass transfer distribution is low in Williamson fluid when compared to Casson fluid flow. The computed results indicate that the flow, thermal and concentration boundary layer characteristics of Williamson and Casson fluids are not unique.     

Influence of nonlinear radiation on MHD micropolar fluid flow with viscous dissipation

This study takes account of the impact of the convective boundary conditions. The energy equation consists of Joule heating and thermal nonlinear radiation impacts. Contact between the solid and the fluid is also susceptible to a velocity slip. The resultant differential equations system is solved using homotopy analysis method. To find all numerical computations, Mathematica is utilized. The behavior, with graphical results, of pertinent parameters in micropolar fluid flow characteristics is studied. We look at the impact of the material parameter, magnetic parameter, slip parameter, and electrical parameter to grasp the physics of the problem better. Different values of skin friction, wall couple stress, and Nusselt and Sherwood numbers are discussed.     

Stability analysis on dual solutions of MHD Casson fluid flow with thermal and chemical reaction over a permeable elongating sheet

The endeavor of this study is to explore the nature of dual solutions (steady and unsteady) for the Casson fluid flow with the simultaneous consequences of both thermal and mass transmissions. The flow passes above an absorbent elongating sheet in the existence of a constant magnetic field. The supported leading equations are remodeled into a set of solvable forms with the assist of suitable similarity variables and hence deciphered utilizing the “MATLAB routine bvp4c scheme.” Due to the sudden changes in the surface with time, the temperature and flow behavior over the sheet also change, and hence dual-type flow solutions exist. Stability scrutiny is implemented to examine the less (more) stable and visually achievable solutions. From this study, we have achieved many interesting facts, among them, we can use magnetic and Casson fluid parameters to control the motion of the fluid and to enlarge of thermal transmission of the fluid. This flow model has many important applications in different physical fields, such as engineering sciences, medical sciences, and different industrial processes. One of the most important results, which has been achieved from this investigation, is that the Prandtl number enriches the heat transfer rate of the fluid at the surface during the time-independent case under the suction environment. Also, the chemical reaction parameter helps to enhance the mass accumulation rate of the fluid in both cases.     

Heat and mass transfer effect on an unsteady MHD radiative chemically reactive Casson fluid over a stretching sheet in porous medium

The objective of the present study is to investigate the effects of the variable magnetic field, chemical reaction, thermal radiation, Soret effect, and variable heat absorption on the fluid flow and heat and mass transfer of an unsteady Casson fluid past a stretching surface in a saturated porous medium. Velocity slip near the plate and conjugate heating boundary conditions in heat and mass transfer have been considered in this study. Due to the complexities in boundary conditions, the analytic solution of the governing equations of the present model is not possible. Thus, to overcome these issues, the coupled partial differential equations of the model are converted into a set of ordinary differential equations using similarity transformation. These equations have then been solved numerically using the fourth-order Runge-Kutta technique via the shooting method. The effects of various pertinent flow parameters on the velocity, concentration, and temperature field have been studied graphically. For the field of engineering, to get an insight into the physical quantities, especially Nusselt number, Sherwood number, and skin friction, their numerical values have been estimated against various parameters and presented in tables. From the tabulated values, it has been perceived that the shear stress increases with an increase in magnetic parameter, unsteadiness parameter, Casson parameter, and heat source parameter, whereas the Biot number shows the reverse trend. The mixture of porous media has justified that the heat transport process over a stretching sheet results in averting heat loss and accelerating the process of cooling, which is a significant outcome of the study. Furthermore, it has also been revealed that with the increase in the Soret effect and magnetic field, there is a reduction in the fluid velocity and temperature near the plate, whereas there is an increase in the species concentration. It has also been mentioned that the effects of the variable magnetic field have been widely applied in various engineering applications like magnetohydrodynamic (MHD) propulsion forces, rate of cooling, MHD power generation, and so on.     

Interaction between turbulence and thermal radiation in combined heat transfer channel flows

The aim of the present work is to examine the effects of interaction between turbulence and thermal radiation on the fully developed turbulent channel flow with variable properties in the presence of combined mixed convection‐radiation heat transfer. The vertical and horizontal channels under study are formed by differentially heated flat parallel plates. Large eddy simulation and the low Mach number approach are used to solve the governing equations. Also, the radiative transfer equation is solved using the method. The results are achieved by developing a solver in an open‐source computational fluid dynamics toolbox. The main focus is to find out whether neglecting turbulence‐radiation interaction (TRI) is a valid assumption for such flows under consideration. The present results show that, in both configurations, the maximum values of emission TRI and incident TRI are 2% and 3%, respectively. These results are consistent with the previous findings suggesting that in the nonreactive flows, these two terms are negligible.     

Influence of radiation and viscous dissipation on MHD heat transfer Casson nanofluid flow along a nonlinear stretching surface with chemical reaction

The present article investigates the influence of Joule heating and chemical reaction on magneto Casson nanofluid phenomena in the occurrence of thermal radiation through a porous inclined stretching sheet. Consideration is extended to heat absorption/generation and viscous dissipation. The governing partial differential equations were transformed into nonlinear ordinary differential equations and numerically solved using the Implicit Finite Difference technique. The article analyses the effect of various physical flow parameters on velocity, heat, and mass transfer distributions. For the various involved parameters, the graphical and numerical outcomes are established. The analysis reveals that the enhancement of the radiation parameter increases the temperature and the chemical reaction parameter decreases the concentration profile. The empirical data presented were compared with previously published findings.     

Radiation and Hall effects on a 3D flow of MHD Williamson fluid over a stretchable surface

Magnetohydrodynamics (MHD) three-dimensional flow of an unsteady Williamson fluid on an enlarging surface with Hall current, radiation, heat source/sink, and chemical reaction is investigated in this article. The basic governing equations are transformed into a system of ordinary differential equations by using an appropriate similarity transformation. The system is deciphered using the shooting method. The properties of influential parameters such as parameters of magnetic field, Hall current, radiation, and so forth, on the flow are discussed with the help of graphs and tables. We noticed that the increase in the magnetic field reduces the velocity in x-direction and the rate of heat and mass transfer. We also acknowledged that the growing values of Hall current parameter boost the velocity in z-direction but it reduce the temperature and concentration distributions, respectively. The results of this study represent many applications in biomedical engineering and these results are helpful for further study of non-Newtonian fluids in various circumstances.     

Effects of chemical reaction and thermal radiation on MHD free convective flow of micro polar fluid past an infinite moving vertical porous plate with viscous dissipation

This article discusses the impact of chemical reaction and radiation on an unstable two-dimensional laminar flow around a viscous fluid over a semi-infinite, vertical absorbent surface that moves progressively. The governing classification of partial differentiation was converted into an ordinary differentiation system in this case. To get numerical solutions, the Galerkin finite element technique is applied to nondimensional velocity, micro-rotation, temperature, and concentration profiles. The consequences of skin friction, the combined pressure quantity, the mass, and heat assignments at the boundary are formed using different fluid properties and flow conditions. Physical quantities and their effects Graphs depict the radiation parameter R, thermal conductivity k, Eckert number Ec, and other velocities, micro-rotation, temperature, and concentration factors. The main findings of this current problem is showing the chemical reaction effects on velocity and concentration. It is observed that both the velocity and concentration of the fluid decrease when Kr increases.     

Irreversibility Analysis of MHD Flow over an Exponentially Stretching Sheet

This laminar fluid study investigates the effects of a magnetic field on the entropy generation during fluid flow and heat transfer due to an exponentially stretching sheet. Using the suitable transformations we have obtained the analytical solutions for momentum and energy equation in terms of Kummer's function. The velocity and temperature profiles are obtained for various physical parameters which are utilized to find the entropy generation number N_s and the Bejan number Be. The effects of various parameters on entropy production number and the Bejan number are studied through graphs using velocity and temperature profiles. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21112     

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 $fo$.     

The effect of combined viscous dissipation and Joule heating on unsteady mixed convection MHD flow on a rotating cone in a rotating fluid with variable properties in the presence of Hall and ion-slip currents

This paper is concerned with the effect of combined viscous dissipation and Joule heating on unsteady mixed convention magnetohydrodynamics (MHD) flow on a rotating cone in an electrically conducting rotating fluid in the presence of Hall and ion-slip currents. The fluid properties (density, (ρ), viscosity, (μ) and thermal conductivity, (κ)) are taken to be dependent on temperature and a strong uniform magnetic field is applied in the z-direction. It has been shown that a self-similar solution is possible when the free stream angular velocity and the angular velocity of the cone vary inversely as a linear functions of time. The unsteady Navier–Stokes equations along with the energy equation are reduced to a system of ordinary differential equations by using similarity transformations and the resulting equation system is solved numerically by using a shooting method. Results for the details of the velocity as well as temperature are shown graphically and the numerical values of the skin friction and the rate of heat transfer are entered in tables.     

Analytical study of heat and mass transfer effects on unsteady Casson fluid flow over an oscillating plate with thermal and solutal boundary conditions

In this study, the impacts of heat and mass transfer characteristics on an isotropic incompressible Casson fluid flow over an oscillatory plate with the incidences of solutal and thermal boundary conditions have been investigated. Exact solutions of the fundamental equations governing the fluid flow are determined by using the Laplace transform technique. Numerical results based on analytical solutions are presented in graphical and tabular illustrations to clarify the behaviors of the fluid. Most interestingly, both fluid velocity and species concentration increase with an increment of mass transfer coefficient, whereas the fluid velocity diminishes as oscillating frequency increases near the surface of the plate. This happens due to the presence of high fluctuation of the plate in the flow system. Finally, this investigation is helpful to the scientific community, and the obtained results can be used as benchmark solutions for solving nonlinear flow governing problems fully via various numerical methods.     

Free convective MHD micropolar fluid flow with thermal radiation and radiation absorption: A numerical study

An analysis is carried out for the free convective flow of an electrically conducting micropolar fluid through permeable stretching sheet in the presence of porous medium. Inclusion of thermal radiation to the energy equation enhances the thermal properties of polar fluid. In addition to that the radiation absorption parameter occurs due to the interaction of solutal concentration difference also considered in the heat transfer equation. Suitable similar transformation is used to convert the governing partial differential equations to ordinary differential equations. Furthermore, though analytical solutions of these complex nonlinear coupled equations are more complicated therefore, numerical solution such as Runge‐Kutta fourth order method associated with shooting technique is adopted. Behavior of characterizing parameters for the flow phenomena are presented via graphs and computed values of physical quantities of interest are obtained and shown in tabular form. Present result validates with that of earlier results in particular case which confirms the existence of present solution methodology. However, the main findings of contributing parameters are laid down as; angular velocity profile contributes a dual character from the point of contact at the middle of the channel. Fluid temperature is affected by the inclusion of absorption coefficient.