Impacts of variable viscosity and chemical reaction on Ohmic dissipative fluid flow in a porous medium over a stretching sheet with thermal radiation

This study investigates the chemical reaction influence on heat transfer flow of viscous Newtonian fluid over a moving surface under the intensity of nonuniform heat source/sink. Variable fluid viscosity and ohmic heating effects are considered in the model equation. The uniqueness of the present investigation is to scrutinize the significance of nonuniform heat source/sink and ohmic heating on the heat transfer flow of optically thin radiative fluid in a permeable medium. The flow equations of continuity, momentum, thermal and solutal fields are converted by invoking relevant dimensionless variables. Also, the converted nonlinear equations are analyzed numerically by using the fourth order Runge–Kutta Fehlberg approach. The significance of model parameters are scrutinized and discussed in detail via graphs and tables. The important findings of this study are the effects of Joule heating $J$, viscous dissipation parameter $B_r$, variable fluid property parameter $ϵ$ and radiation parameter $R_a$ on fluid flow, energy profile and solutal field. The results show that the thermal field depreciates as the Prandtl number increases but escalates against higher values of Joule heating parameter and Brinkman number. Also, the outcome of this study reveals that an enhancement in the values of variable viscosity parameter declines velocity distribution. Concentration distributions behave as a growing function of the Soret number and diminishing function of the Schmidt number. Furthermore, contrasting this study with existing results reveals excellent agreement.     

Heat and mass transfer of magnetohydrodynamic Casson fluid flow over a wedge with thermal radiation and chemical reaction

A numerical computation to analyze the heat and mass transfer mechanism of a magnetohydrodynamic radiative Casson fluid flow over a wedge in the presence of Joule heating, viscous dissipation, and chemical reaction is carried out in this study. The flow-governing partial differential equations are transformed as ordinary differential equations by relevant similarity transformations and subsequently resolved by Runge–Kutta numerical approach with a shooting technique. The characteristics of momentum, thermal, and concentration border layers due to various influencing parameters are graphically outlined and numerically computed by MATLAB software. We present comparative solutions to construe the relative outcomes of Casson fluid versus Newtonian fluid. Computational outcomes of friction factor and Nusselt and Sherwood numbers are tabulated with suitable interpretations. An increase in skin friction values is noted due to an increment in the thermal Grashof number, whereas a decrease is observed due to the chemical reaction parameter. The Casson fluid displays a superior heat transfer mechanism than the Newtonian fluid. Obtained outcomes are in good agreement with the prevailing literature in the limiting case.     

Analytical study of heat and mass transfer in unsteady MHD radiant flow of Williamson nanofluid over stretching sheet with heat generation and chemical reaction

This paper presents the analytical study of heat and mass transfer in a two-dimensional time-dependent flow of Williamson nanofluid near a permeable stretching sheet by considering the effects of external magnetic field, viscous dissipation, Joule heating, thermal radiation, heat source, and chemical reaction. Suitable transformations are introduced to reformulate the governing equations and the boundary conditions convenient for computation. The resulting sets of nonlinear differential equations are then solved by the homotopy analysis method. The study on the effects of relevant parameters on fluid velocity, temperature, and concentration profiles is analyzed and presented in graphical and tabular forms. Upon comparison of the present study with respect to some other previous studies, a very good agreement is obtained. The study points out that the transfer of heat can substantially be enhanced by decreasing viscoelasticity of the fluid and the transfer of mass can be facilitated by increasing permeability of the stretching sheet.     

Actions of viscous dissipation and Ohmic heating on bidirectional flow of a magneto-Prandtl nanofluid with prescribed heat and mass fluxes

The present contribution determines the impacts of viscous dissipation and Ohmic heating with magnetic coating on Prandtl nanofluid flow driven by an unsteady bidirectionally moveable surface. Random motion of nanoparticles and thermophoretic diffusion are elaborated through a two-phase nanofluid model. The novelty of the investigation is fortified by prescribed heat flux and prescribed mass flux mechanisms. The appropriate combination of variables leads to a system of strong nonlinear ordinary differential equations. The formulated nonlinear system is then tackled by an efficient numerical scheme, namely, the Keller–Box method. Nanoliquid-temperature and mass-concentration distributions are conferred through various plots with the impacts of miscellaneous-arising parameters. The rates of heat and mass transferences are also discussed through tables. The thermal states of the nanomaterial and mass concentration are reduced for incremental amounts of the unsteady factor, ratio parameter, elastic parameter, and Prandtl fluid parameter. Moreover, escalating amounts of the Brownian parameter, Eckert number, magnetic factor, and thermophoresis parameter enhances the temperature of the nanoliquid. An error analysis is also presented to predict the efficiency of the method used for the computational work.     

Heat and mass transfer characteristics of radiative hybrid nanofluid flow over a stretching sheet with chemical reaction

Unsteady magnetohydrodynamic heat and mass transfer analysis of hybrid nanoliquid flow over a stretching surface with chemical reaction, suction, slip effects, and thermal radiation is analyzed in this study. A combination of alumina (Al₂O₃) and titanium oxide (TiO₂) nanoparticles are taken as hybrid nanoparticles and water is considered as the basefluid. Using the similarity transformation method, the governing equations are changed into a system of ordinary differential equations. These equations together with boundary conditions are numerically evaluated by using the Finite element method. The influence of various pertinent parameters on the profiles of fluids concentration, temperature, and velocity is calculated and the outcomes are plotted through graphs. The values of nondimensional rates of heat transfer, mass transfer, and velocity are also analyzed and the results are depicted in tables. Temperature sketches of hybrid nanoliquid intensified in both the steady and unsteady cases as the volume fraction of both nanoparticles rises.     

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.     

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.     

Heat and mass transfer in MHD stagnation-point flow toward an inclined stretching sheet embedded in a porous medium

The present study elucidates the magnetohydrodynamics boundary layer free convective stagnation-point flow toward an inclined nonlinearly stretching sheet embedded in a porous medium. The recent search explores the consequence of permeability of the medium, thermal as well as mass buoyancy, most importantly obliqueness, and thermal slip at the bounding surface. The solutions of the essential equations are achieved with MATLAB'S inbuilt solver bvp4c. The novelty of the present study is to account for the effect of dissipative heat, nonuniform space-dependent volumetric heat power, and a linear first-order chemical reaction of diffusive species and convective flow phenomena on an inclined plate subjected to thermal slip and space-dependent transverse magnetic field acting at a distance. The important findings are laid down as follows: The oblique-surface reduces the effect of body forces, low permeability of the medium causes instability in the flow due to sudden fall in velocity, Biot number contributes to the Newtonian cooling of the surface, these may be of use in a design requirement of the heat exchanger.     

Heat and mass transfer of water-based copper and alumina hybrid nanofluid over a stretching sheet

Hybrid nanofluids (HNFs) are vital in engineering and industrial applications due to significant effective thermal conductivity as compared with regular fluid and nanofluid (NF). The HNF is a process of the conglomeration of two or more nanoparticles of different thermophysical properties to affect the thermal transport characteristics of base fluid, particularly in gearing up heat switch charge. Further, the impact of HNF combined with stretching and squeezing of bounding surface has direct application in thinning/thickening of polymeric sheets in the chemical industry. The current study analyzes the flow of HNF over a stretching sheet under the influence of chemical reaction as well as suction/injection. We have considered water $\left({\mathrm{H}}_2\mathrm{O}\right)$ as the base fluid and copper $\left(\mathrm{Cu}\right)$, and aluminum oxide $\left({\mathrm{Al}}_2{\mathrm{O}}_3\right)$ as nanoparticles. The consequences of the magnetic field, viscous dissipation, and Joule heating are also to be investigated. The resulting partial differential equations are transformed into nonlinear ordinary differential equations using suitable similarity transformations. The numerical solutions to governing equations are obtained with the help of MATLAB software using the bvp4c solver. The important finding is: the rate of heat transfer of HNF is higher than that of NF as well as base fluid. Moreover, contributions of higher Eckert number and radiation parameter are to increase the temperature in the flow domain, whereas the Prandtl number reduces it. It is further noticed that heavier species as well as viscous dissipation decline the level of concentration across the flow field.     

Characteristics of MHD three-dimensional flow of nanofluid over a permeable stretching porous sheet

The aim of the present work is to focus on heat and mass transfer characteristics of the magnetohydrodynamic three-dimensional flow of nanofluid over a permeable stretching porous sheet. The significance of this study is the consideration of copper-based and aluminum oxide-based nanofluids. The physical parameters like a chemical reaction, Soret effect, radiation, and heat generation, and radiation absorption being involved in this examination are novel. The nonlinear partial differential equations are transformed into ordinary differential equations by adopting suitable similarity transformations. The numerical solutions are obtained by applying the Runge–Kutta method of fourth-order with the Shooting technique using MATLAB. The results obtained are presented through graphs and tables for various parameters. A comparison with published results has been done to validate the methodology and found good coincidence. It is claimed that the increase in heat generation parameters results in increasing the temperature. With an increase in the Soret effect, the skin friction coefficient along x-axis increases and skin friction coefficient along the y-axis, Nusselt number and Sherwood number decrease.     

Effects of the viscous dissipation and chemical reaction on Casson nanofluid flow over the permeable stretching/shrinking sheet

A steady two‐dimensional Casson nanofluid flow over the permeable stretching/shrinking sheet along the viscous dissipation and the chemical reaction is studied in this article. The convective boundary condition is incorporated in energy equation. Similarity variables are applied to convert the governing partial differential equations into ordinary differential equations. The numerical solutions of the equations are obtained by using the shooting method with Maple implementation. The numerical findings indicate occurrence of the dual solutions for a certain range of stretching/shrinking and suction parameters. Therefore, a stability analysis is done to find the solution that is stable and physically realizable. The effects of the pertinent physical parameters on velocity, temperature, and concentration profiles are investigated graphically. Numerical results of various parameters involved for skin friction coefficient, the local Nusselt as well as Sherwood numbers are determined and also discussed in detail. The Casson and suction parameters decrease the velocity in the first solution, whereas they increase it in the second solution. The rate of heat transfer increases in both solutions with an increment in Eckert number, Biot number, thermophoresis, and Brownian motion parameters. Thermophoresis and Brownian motion parameters show opposite behavior in the nanoparticle's concentration. The nanoparticle concentration decreases in both solutions with increment in Schmidt number, Brownian motion, and chemical reaction parameters.     

Steady magnetohydrodynamic Poiseuille flow of two immiscible non-Newtonian and Newtonian fluids in a horizontal channel with Ohmic heating

In this paper, an analytical study has been carried out on a steady magnetohydrodynamics (MHD) Poiseuille flow of two immiscible fluids in a horizontal channel with ohmic heating in the presence of an applied magnetic field. The channel is divided into two sections, Region I and Region II, respectively. Region I contains an electrically conducting, third grade, non-Newtonian fluid while Region II is a Newtonian fluid. The regular Perturbation series method is used to transform the coupled nonlinear differential equations governing the flow into a system of linear ordinary differential equations in both fluid regions. Suitable interface matching conditions were chosen to obtain separate solutions for each fluid in both regions and the results were displayed graphically for various values of physical parameters, such as pressure gradient, suction parameter, Hartmann number, Prandtl number, viscosity, and conductivity ratios to show their effects on the flow. The effect of skin friction and Nusselt number was shown with the aid of tables. The results obtained among other findings clearly shows that as the value of the magnetic parameter increases, the velocity and temperature of the fluid decrease.     

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.     

Transient natural convective flow of a radiative viscous incompressible fluid past an exponentially accelerated porous plate with chemical reaction species

The present study deals with an unsteady magnetohydrodynamic natural convective flow of a viscous, incompressible fluid past an exponentially accelerated porous plate surrounded by a porous medium with suction or injection. The novelty of the current research is to analyze the behavior of the flow due to mass transfer with first-order chemical reaction in the presence of a heat source in the energy equation. The existence of suction/injection and radiation parameters in the flow enhances the utility of the research as they are an integral part of nuclear reactors, thermal and chemical engineering processes, and many more. The Laplace transform technique (via Bromwich contour) is applied to solve exactly the governing equations. The nature of the flow velocity, temperature, and concentration profiles due to the impact of pertinent flow parameters are presented graphically. The numerical outcomes of coefficient of skin friction, rate of heat transfer, and mass transfer are obtained in tabular form. The results indicate that the skin friction increases slowly with the reaction parameter and largely with the suction parameter, whereas the concentration gradient increases at a much higher rate with the reaction parameter. The fluid injection has a negative impact on the velocity gradient. It is seen that the heat source enhances both velocity and temperature profiles throughout the flow field, whereas the first-order chemical reaction acts reversely on the velocity and mass transfer process. The current research can be applied to identify the cause behind the drag force produced in seepage flow due to the heated or cooled accelerated plate.     

Heat and mass transfer for Soret and Dufour's consequences on unsteady MHD free convection flow over a porous media with heat absorption

The significance of this article lies in explaining the influence of Soret and Dufour numbers on an unsteady MHD free convection of flow of heat and mass transfer through porous media. The substances and radiation along the viscous, incompressible, and conductive compounds respond to the unstable convection of the liquid. Using physical quantities, the dimensional governing equations are converted to non-dimensional equations. Finite element Galerkin method is applied to numerically solve the resulting partial differential equations. Flow parameters on velocity, temperature, and concentration are studied and explained graphically to reflect their effects. Similarly, the skin friction number and Nusselt number are also observed and recorded in tables.     

Heat and mass transport on MHD flow over semi-infinite moving porous plate with chemical reaction effect

The consequences of chemical reaction, on unsteady magnetohydrodynamic heat and mass transport laminar flows of a viscous, electrically conducting with heat-generating or absorbing fluid enclosed through a semi-infinite absorbent plate has been premeditated. The plate is assumed to be in motion with a constant velocity within the path of fluid flow. A homogeneous magnetic field performs at right angles to the absorbent surface; it is absorbing the fluid with a suction velocity varying with a certain instant of time. The nondimensional governing equations for the present configuration are solved systematically utilizing harmonic and nonharmonic terms. Graphical consequences for the velocity, temperature, and concentration profiles together supported by the investigative solutions are displayed and discussed computationally. The resulting velocity is reducing by an augment in the strength of the magnetic field and Prandtl number, whereas it is enhancing by growing in the permeability of the porous medium. The temperature delivery is reduces by an escalating heat source parameter and occurrence of fluctuation. It is significant to note that the temperature increases notably with growing the radiation absorption parameter. The influences of the chemical reaction and Schmidt number reduced the concentration in the entire fluid medium.     

MHD non-Darcian mixed convection heat and mass transfer over a non-linear stretching sheet with Soret-Dufour effects and chemical reaction

A study has been carried out to analyze the effects of variable thermal conductivity, Soret (thermal-diffusion) and Dufour (diffusion-thermo) on MHD non-Darcy mixed convection heat and mass transfer over a non-linear stretching sheet embedded in a saturated porous medium in the presence of thermal radiation, viscous dissipation, non-uniform heat source/sink and first-order chemical reaction. The governing differential equations transform into a set of non-linear coupled ordinary differential equations using similarity analysis. Similarity equations are then solved numerically using shooting algorithm with Runge-Kutta Fehlberg integration scheme over the entire range of physical parameters. A comparison with previously published work has been carried out and the results are found to be in good agreement. Graphical presentation of the local skin-friction coefficient, the local Nusselt number and the local Sherwood number as well as the temperature profiles show interesting features of the physical parameters.     

Mass transfer of viscous gas flow over porous stretching/shrinking sheet in the presence of slip and mass transpiration

The effect of the mass transpiration parameter on the viscous gas flow past a porous stretching/shrinking sheet in the presence of Navier's slip is investigated, and also, the mass transfer characteristics are examined. The physical flow problem executes the Navier–Stokes and the mass equation, which forms the system of nonlinear partial differential equations. These are transformed via similarity variables into a system of ordinary differential equations. The slip flow model of the total mass transfer on the moving sheet is modeled by introducing gas slip velocity. The total mass transfer on the moving sheet is modeled by inducing slip models of first and second order. Further, the suction which induces the slip velocity as opposed to the surface movement is examined. The mass suction-induced slip forces the adjacent gases to flow in the reverse direction to sheet movement. Thus, the solution space expands with the slip-induced suction and sheet movement. In the mass injection case, the induced slip increases the effect of the fluid flow for sheet movement. Upon all previous flow models, the present investigation is significant due as it investigates the mass transfer of viscous gasses flow past a porous medium in the presence of slip and mass transpiration.     

Viscous dissipation effect on mixed convective heat transfer of MHD flow of Williamson nanofluid over a stretching cylinder in the presence of variable thermal conductivity and chemical reaction

The effect of viscous dissipation and thermal radiation on mixed convective heat transfer of an MHD Williamson nanofluid past a stretching cylinder in the existence of chemical reaction is analyzed in this study. When energy equation is formulated, the variable thermal conductivity is deliberated. By proposing applicable similarity transformations, nonlinear ordinary differential equations (ODEs) are attained from partial differential equations. These nondimensional ODEs are computed through Runge-Kutta method integrated with shooting method using MATLAB software. The results found numerically are in agreement with that of the published works of similar nature in a limiting case. The results of the local Nusselt number, skin friction coefficient, and Sherwood numbers are organized in tables. The influence of protuberant parameters on temperature, velocity, and concentration is presented by graphs. From the results, it is seen that for higher values of variable thermal conductivity parameter, the local Sherwood number and skin friction coefficient upsurge, whereas the local Nusselt number diminishes.