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An electrically conducting three-dimensional non-Newtonian Carreau fluid induced by bidirectional movement of sheet is demonstrated in this work. The aspects of viscous heating, radiation and first-order chemical reactions are executed in energy transport and mass species expressions. The new variables are defined to restructure the mathematical problem into single independent variable equations (ordinary differential equations, ODE’s). The re-framed ODE’s are exploited numerically through the utilization of MATLAB bvp4c package. The derived results of velocities, temperature and species distributions are executed graphically and interpreted physically for both shear-thinning and shear-thickening cases. Also, the numerical results for coefficients of skin friction, rate of mass transfer in terms of Sherwood number and rate of heat transfer in terms of Nusselt number are presented in tables. The influence of local Weissenberg numbers on Sherwood and Nusselt numbers for shear-thinning fluids is reversed to shear-thickening fluids. The thermal radiation parameter enhances the fluid temperature, and chemical reaction parameter decelerates the fluid concentration.

In this paper, we propose a mathematical model to analyze the effect of a non-uniform heat source or sink on chemically reacting magnetohydrodynamic Casson fluid flowing across a slendering sheet. A chemically reacting fluid with multiple slips has various applications in controlling heating and mass transport phenomena such as biological reactants being converted to products, biomedical signal processing and image processing to establish a dynamic area of specialization in research aspects of biomedical engineering. For these reasons multiple slips (diffusion, thermal and momentum slips) are applied in modeling the heat and mass transfer process. The non-linear ordinary differential equations (ODEs) are solved using the Runge-Kutta-Fehlberg integration method. The characteristics of the velocity, temperature and concentration boundary layers are presented for different physical parameters such as space and temperature-dependent heat source or sink parameter, porosity parameter, chemical reaction parameter, velocity slip parameter, and temperature and concentration jump parameters. Moreover, the skin friction coefficient, and the local Nusselt and Sherwood numbers have been estimated for different parameters are discussed from an engineering point of view. We found a significant increase in thickness of the thermal and concentration boundary layer when the strength of the thermophoresis parameter is increased. In contrast, the thermal boundary layer increases with increasing the Brownian motion parameter while the reverse trend holds true for the concentration field.

Numerical study of three dimensional Carreau liquid flow with heat and mass transport features over a variable thickness sheet filled with microorganisms is analyzed. We considered the non-uniform heat sink or source and multiple slip effects. The governing non-linear partially differential expressions are developed into ordinary differential systems by using variable transformations. These expressions are solved numerically by using Runge-Kutta fourth order method connected with shooting methodology. A Parametric study is implemented to demonstrate the effects of Hartmann number, Prandtl number, Weissenberg number, Peclet number, chemical reaction and heat sink/source parameters on liquid velocity, temperature and concentration profiles. The quantities of physical interest are described within the boundary layer. From this analysis, we found that the magnetic parameter decrease the local Sherwood and local Nusselt numbers for both and cases. The constraint of chemical reaction enhances the mass transfer rate and decelerates the density of motile mass transfer rate. The space dependent and temperature dependent heat source/sink suppress the local Nusselt number.

The present study emphases on the three-dimensional (3D) Casson nanofluid flow across a slendering sheet in porous layers by considering the thermophoresis and Brownian motion effect. The proposed mathematical model has a tendency to characterise the effect of the non-uniform heat source/sink. In the present simulation, the graphene–water-based nanoparticles have been used at two different temperatures namely 10 and 50 °C. The nonlinear ordinary differential equations are solved using the Runge–Kutta Feldberg integration method. The characteristics of velocity, temperature and concentration boundary layers in the presence of graphene–water nanoparticles are presented for different physical parameters such as heat source/sink parameter, thermophoresis parameter, Brownian motion parameter, Casson fluid parameter, porosity parameter, volume fraction and velocity power index parameter. Moreover, the friction factor coefficients, Nusselt number and Sherwood number are also estimated and discussed for aforesaid physical parameters. It is found that there is a significant increase in the thermal and concentration boundary layer thickness when the strength of the thermophoresis parameter is increased. In contrast, thermal boundary layer increases with the rise in the Brownian motion parameter, while the reverse trend holds true for concentration field. In addition, the rate of heat and mass transfer rate are higher in case of graphene–water nanoparticle at 50 °C compared to 10 °C temperature.

A theoretical analysis is performed for investigating the flow and heat transfer characteristics of Maxwell fluid over a stretching cylinder with Cattaneo–Christov, heat source or sink, and suction/injection. The solution to the transformed similarity equations is derived using Runge–Kutta fourth-order method along shooting technique. The present result for both the surface shear stress and the local Nusselt number is validated with the previously published results, while a very sound agreement is attained. The impacts of the distinct parameters related to this study are presented in graph and tabular form, respectively. Moreover, the local Nusselt number and surface shear stress have been computed for both the suction and injection cases. It is found that strengthening the thermal relaxation parameter value increases the heat transfer rate. The dimensional heat transfer rate is observed being rising in the injection case when compared with the suction case.

The simultaneous interaction of viscous dissipative and thermal radiation in MHD two dimensional flows of ferro-liquid over a nonlinear moving surface is analyzed here. The slip on velocity and convective boundary condition on temperature are imposed on stretching surface. We used water as conventional base liquid which have magnetite (Fe3O4) and alumina (Al2O3) as nanoparticles. The governing mathematical expressions are converted into non-dimensional form via nonlinear type similarity variables. The resulting mathematical model is numerically solved with the help of MATLAB solver bvp4c. The roles of non-dimensional constraints on velocity and temperature are elaborated through plots. The numerical data of skin-friction coefficient and Nusselt number is presented and visualized. The validity of computed results is analyzed through comparative benchmark. Keywords: Ferro fluid, Velocity slip condition, Convective boundary condition, Viscous dissipation, Radiation

Purpose The purpose of this paper is to present an analytical study for a problem of unsteady free convection boundary layer flow past a periodically accelerated vertical plate with Newtonian heating (NH). Design/methodology/approach The equations governing the flow are studied in the closed form by using the Laplace transform technique. The effects of various physical parameters are studied through graphs and the expressions for skin friction, Nusselt number and Sherwood number are also derived and discussed numerically. Findings It is observed that velocity, concentration and skin friction decrease with the increasing values of Sc whereas temperature distribution decreases in the increase in Pr in the presence of NH. Research limitations/implications This study is limited to a Newtonian fluid. This can be extended for non-Newtonian fluids. Practical implications Heat and mass transfer frequently occurs in chemically processed industries, distribution of temperature and moisture over agricultural fields, dispersion of fog and environment pollution and polymer production. Social implications Free convection flow of coupled heat and mass transfer occurs due to the temperature and concentration differences in the fluid as a result of driving forces. For example, in atmospheric flows, thermal convection resulting from heating of the earth by sunlight is affected differences in water vapor concentration. Originality/value The authors have studied heat and mass transfer effects on unsteady free convection boundary layer flow past a periodically accelerated vertical surface with NH, where the heat transfer rate from the bounding surface with a finite heat capacity is proportional to the local surface temperature, and which is usually termed as conjugate convective flow. The equations governing the flow are studied in the closed form by using the Laplace transform technique. The effects of various physical parameters are studied through graphs and the expression for skin friction also derived and discussed.

In this paper, an exact analysis is carried out for the Laplace transform solution of unsteady MHD chemically reacting elasto-viscous fluid past an infinite vertical plate through porous medium in the presence of radiation absorption and transverse applied magnetic field. The governing equations describing the flow pattern are transformed to a system of linear partial differential equations using appropriate non-dimensional quantities. The resulting transformed equations are solved analytically by using Laplace transform technique and exact solutions for velocity, temperature and concentration as well as Nusselt number and Sherwood number are obtained in terms of exponential and complementary error functions. Behaviour of emerging parameters like elasto-viscous, heat absorption, radiation absorption, magnetic field, Schmidt number, chemical reaction, thermal Grashof number, mass Grashof number, Prandtl number and time is presented graphically and discussed in detail. It was found that increasing radiation absorption parameter, velocity is decreasing for elasto-viscous fluid, but the reverse effect is found for viscous fluid in case of cooling of the plate. An increase in heat absorption, Schmidt number and chemical reaction lead to rise in the Sherwood number and Nusselt number while a reverse effect is noticed in the flow transport.

A numerical investigation is carried out on an unsteady MHD free convection flow of a well-known non-Newtonian visco elastic second order Rivlin-Erickson fluid past an impulsively started semi-infinite vertical plate in the presence of homogeneous chemical reaction, thermal radiation, thermal diffusion, radiation absorption and heat absorption with constant mass flux. The presence of viscous dissipation is also considered at the plate under the influence of uniform transverse magnetic field. The flow is governed by a coupled nonlinear system of partial differential equations which are solved numerically by using finite difference method. The effects of various physical parameters on the flow quantities viz. velocity, temperature, concentration, Skin friction, Nusselt number and Sherwood number are studied numerically. The results are discussed with the help of graphs. We observed that the velocity decreases with an increase in magnetic field parameter, Schmidt number, and Prandtl number while it increases with an increase in Grashof number, modified Grashof number, visco-elastic parameter and Soret number. Temperature increases with an increase in radiation absorption parameter, Eckert number and visco-elastic parameter while it decreases with increasing values of radiation parameter, Prandtl number and heat absorption parameter. Concentration increases with increase in Soret number while it decreases with an increase in Schmidt number and chemical reaction parameter.

The present study investigated the variable viscosity and multiple slips on two-dimensional magnetohydrodynamic Carreau fluids due to slendering sheet filled with microorganisms. The Carreau model is used to characterize the behavior of the fluids with shearing thickening properties using the various values of exponent of power law. The diffusion-thermo and thermos diffusion effects are taken into account. The nonlinear sets of ordinary differential equations are treated numerically by shooting technique with Runge–Kutta Fehlberg method. Different parameters like magnetic interaction parameter $$ M $$ , Weissenberg number $$ We $$ , the index of power law $$ m $$ , various multiple slip parameters like the velocity slip parameter $$ \tau_{1} $$ , the temperature jump parameter $$ \tau_{2} $$ , the concentration $$ \tau_{3} $$ , and the concentration jump parameter $$ \tau_{4} $$ are analyzed. The velocity, the skin friction, the rate of heat transport namely Nusselt number and rate of mass transport as Sherwood number are elaborated graphically and computed in tabular benchmark. The analysis found that the density of motile organism grows with the growing magnetic field parameter, diffusion-thermo number, thermo-diffusion number and Weissenberg number.

In this article we have investigated the Soret effect due to mixed convection on unsteady magneto hydrodynamic flow past a semi-infinite vertical permeable moving plate in presence of thermal radiation, heat absorption and homogenous chemical reaction, subjected to variable suction. The plate is assumed to be embedded in a uniform porous medium and moves with a constant velocity in the flow direction in the presence of a transverse magnetic field. The equations governing the flow are transformed into a system of nonlinear ordinary differential equations by using perturbation technique. Graphical results for the velocity distribution, temperature distribution and concentration distribution based on the numerical solutions are presented and discussed. We also discuss the effects of various parameters on the skin-friction coefficient and the rate of heat transfer in the form of Nusselt number and rate of mass transfer in the form of Sherwood number at the surface. Velocity distribution is observed to increase with an increase in Soret number and in the presence of permeability, where as it shows reverse effects in the case of heat absorption coefficient, magnetic parameter, radiation parameter and chemical reaction parameter.

An analytical solution is presented for the case of time dependent variable temperature and variable concentration boundary layer on unsteady MHD free convection flow past a vertical porous plate in the presence of thermal radiation, thermal diffusion and first order chemical reaction. The dimension less governing equations are solved analytically and the expressions for temperature, concentration and velocity fields are determined using the Laplace transform technique. Finally, the influence of various physical parameters on the temperature, concentration and velocity fields is graphically studied and discussed. The expressions for local skin friction, Nusselt number and Sherwood number are derived and discussed with the help of tables. It noticed that Skin friction increase with an increase in magnetic parameter, Prandtl number, radiation parameter and chemical reaction parameter while it decrease with an increase in Grashof number, modified Grashof number, permeability parameter, heat source and Schmidt number. The rate of heat transfer increase with increasing values of Prandtl number and radiation parameter while it decreases with increasing value of heat source. The rate of mass transfer increases with increasing values of Schmidt number and chemical reaction parameter.

In this manuscript, we have investigated the influence of radiation absorption on an unsteady MHD convective heat and mass transfer flow of a Newtonian fluid past a vertical porous plate in the presence of thermal radiation and chemical reaction. The non dimensional governing equations have been solved by using a multiple perturbation method, subject to the corresponding boundary conditions. The effects of various physical parameters such as velocity, temperature and concentration are studied through graphs. The expressions for local skin friction, Nusselt number and Sherwood number are derived and discussed with the help of a table. It is noticed that velocity increases when an increase in modified Grashof number Gm, radiation absorption parameter χ, Sorret number S0, time t whereas it decreases when an increase in Schmidt number Sc, chemical reaction parameter Kr and radiation parameter F. Temperature increases with an increase in radiation parameter χ and Sorret number S0whereas it decreases with an increase in chemical reaction parameter Kr, F and ϕ. Concentration is observed to be decreased when chemical reaction parameter Kr and Schmidt number Sc increase whereas it increases with an increase in Sorret number S0. Skin friction increases with an increase modified Grashof number Gm, radiation parameter χ and Sorret number S0whereas it has reverse effect in the case of Schmidt number Sc, chemical reaction parameter Kr. Nusselt number increases with an increase in Sc, S0, χ whereas it has reverse effect in the case of Kr. Sherwood number gets decreased when Sc, χ and Kr both are increased whereas it has shown revere effect in the case of S0.

The present study investigates the thermal diffusion and radiation effects on magneto hydro dynamic mixed convection flow of a micro polar fluid past an infinite, steadily moving porous plate with variable suction and constant viscosity. The equations of continuity, linear momentum, angular momentum, energy and diffusion, which govern the flow field, are solved by using a regular perturbation method. The behavior of the velocity, micro rotation, temperature, concentration, skin-friction, Nusselt number, and Sherwood number has been discussed for variations in the physical parameters with the help of the graphs.

An analytical solution of MHD free convective, dissipative boundary layer flow past a vertical porous surface in the presence of thermal radiation, chemical reaction and constant suction, under the influence of uniform magnetic field which is applied normal to the surface is studied. The governing equations are solved analytically using a regular perturbation technique. The expressions for velocity, temperature and concentration fields are obtained. With the aid of these, the expressions for the coefficient of skin friction, the rate of heat transfer in the form of Nusselt number and the rate of mass transfer in the form of Sherwood number are derived. Finally the effects of various physical parameters of the flow quantities are studied with the help of graphs and tables. It is observed that the velocity and concentration increase during a generative reaction and decrease in a destructive reaction. The same observed to be true for the behavior of the fluid temperature. The presence of magnetic field and radiation diminishes the velocity and also the temperature.

An analytical study is carried out for an unsteady MHD two dimensional free convection flow of a viscous, incompressible, radiating, chemically reacting and radiation absorbing Kuvshinski fluid through a porous medium past a semi-infinite vertical plate. The dimensionless equations governing the flow are solved by simple perturbation technique. The expressions for velocity, temperature and concentration are derived. The influence of various material parameters on flow quantities are studied and discussed with the help of graphs. The expressions for Skin friction, Nusselt number and Sherwood number are also derived and discussed numerically. Temperature increases with an increase in radiation parameter and radiation absorption parameter where as it decreases with an increase in Prandtl number. Concentration is observed to be decreased when chemical reaction parameter and Schmidt number increase.

The present study deals with an unsteady magneto hydrodynamic free convective, Viscoelastic, dissipative fluid flow embedded in porous medium bounded by an infinite inclined porous plate in the presence of heat source, and Ohmic heating under the influence of transversely applied magnetic field of uniform strength. The equations governing the fluid flow are solved using a multiple parameter perturbation technique, subject to the relevant boundary conditions. Expressions for velocity and temperature distributions are obtained. Non dimensional skin friction coefficient and the rate of heat transfer in the form of Nusselt number are also derived and illustrated using graphs and tables. The effects of various physical parameters on the above flow quantities are discussed.