Effect of melting heat transfer and thermal radiation on Casson fluid flow in porous medium over moving surface with magnetohydrodynamics

In this study, the effects of variable fluid properties on heat transfer in MHD Casson fluid melts over a moving surface in a porous medium in the presence of the radiation are examined. The relevant similarity transformations are used to reduce the governing equations into a system of highly nonlinear ordinary differential equations and those are then solved numerically using the Runge–Kutta–Fehlbergmethod. The effects of different controlling parameters, namely, the Casson parameter,melting and radiation parameters, Prandtl number,magnetic field, porosity, viscosity and the thermal conductivity parameters on flow and heat transfer are investigated. The numerical results for the dimensionless velocity and temperature as well as friction factor and reducedNusselt number are presented graphically and discussed. It is found that the rate of heat transfer increases as the Casson parameter increases.     

Effects of variable properties on MHD heat and mass transfer flow near a stagnation point towards a stretching sheet in a porous medium with thermal radiation

The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic(MHD) heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching sheet embedded in a porous medium are presented,taking into account thermal radiation and internal heat genberation/absorbtion.The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point.The Rosseland approximation is used to describe the radiative heat flux in the energy equation.The governing fundamental equations are first transformed into a system of ordinary differential equations using a scaling group of transformations and are solved numerically by using the fourth-order Rung-Kutta method with the shooting technique.A comparison with previously published work has been carried out and the results are found to be in good agreement.The results are analyzed for the effect of different physical parameters,such as the variable viscosity and thermal conductivity,the ratio of free stream velocity to stretching velocity,the magnetic field,the porosity,the radiation and suction/injection on the flow,and the heat and mass transfer characteristics.The results indicate that the inclusion of variable viscosity and thermal conductivity into the fluids of light and medium molecular weight is able to change the boundary-layer behavior for all values of the velocity ratio parameter λ except for λ = 1.In addition,the imposition of fluid suction increases both the rate of heat and mass transfer,whereas fluid injection shows the opposite effect.     

Slip flow of MHD Casson fluid in an inclined channel with variable transport properties

Due to the instructive role of the peristaltic phenomenon in the human body, interests have been developed in recent years towards peristaltic transport with various thermo-physical features. The current investigation reveals the effects of the magnetic field and variable transport properties on the peristaltic transport of a Casson fluid slip flow through an inclined channel. Nonlinear coupled partial differential equations regulate the fluid flow. Through the perturbation method, the momentum and energy equations are solved for small values of variable viscosity and thermal conductivity, and the closed-form solution is obtained for mass transfer. The impact on physiological quantities of related parameters of interest is evaluated and discussed via graphs. The results obtained for the current flow represent some interesting behaviors which have applications in the biomedical field.     

Variable Fluid Property Effect on Heat Transfer and Frictional Flow Characteristics of Water Flowing through Microchannel

The effects of temperature-dependent viscosity and thermal conductivity on heat transfer and frictional flow characteristics of water flowing through a microchannel are numerically investigated in this work. The hydrodynamically and thermally developing flow with no-slip, notemperature jump, and constant wall heat flux boundary condition is numerically studied using 2D continuum-based conservation equations. A significant deviation in Nusselt number from conventional theory is observed due to flattening of axial velocity profile due to temperaturedependent viscosity variation. The Nusselt number shows a significant deviation from conventional theory due to flattening of the radial temperature profile due to temperature-dependent thermal conductivity variation. It is noted that the deviation in Nusselt number from conventional theory is maximum for combined temperature-dependent viscosity and thermal conductivity variations. The effects of temperature-dependent viscosity and thermal conductivity on the Fanning friction factor are also investigated. Additionally, the effects of variable fluid properties on Poiseuille number, Prandtl number, and Peclet number are also investigated.     

Peristaltic Flow of Shear Thinning Fluid via Temperature-Dependent Viscosity and Thermal Conductivity

In this paper Williamson fluid is taken into account to study its peristaltic flow with heat effects. The study is carried out in a wave frame of reference for symmetric channel. Analysis of heat transfer is accomplished by accounting the effects of non-constant thermal conductivity and viscosity and viscous dissipation. Modeling of fundamental equations is followed by the construction of closed form solutions for pressure gradient, stream function and temperature while assuming Reynold's number to be very low and wavelength to be very long. Double perturbation technique is employed, considering Weissenberg number and variable fluid property parameter to be very small. The effects of emerging parameters on pumping, trapping, axial pressure gradient, heat transfer coefficient, pressure rise, velocity profile and temperature are analyzed through the graphical representation. A direct relation is observed between temperature and thermal conductivity whereas the indirect proportionality with viscosity. The heat transfer coefficient is lower for a fluid with variable thermal conductivity and variable viscosity as compared to the fluid with constant thermal conductivity and constant viscosity.     

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.     

A Numerical Investigation of Nanocomposite of Copper and Titanium Dioxide in Water Based Fluid Influenced by Instigated Magnetic Region

Presence of external electrical field plays a vital role in heat transfer and fluid flow phenomena. Keeping this in view present article is a numerical investigation of stagnation point flow of water based nanoparticles suspended fluid under the influence of induced magnetic field. A detailed comparative analysis has been performed by considering Copper and Titanium dioxide nanoparticles. Utilization of similarity analysis leads to a simplified system of coupled nonlinear differential equations, which has been tackled numerically by means of shooting technique followed by Runge-Kutta of order 5. The solutions are computed correct up to 6 decimal places. Influence of pertinent parameters is examined for fluid flow, induced magnetic field, and temperature profile. One of the key findings includes that magnetic parameter plays a vital role in directing fluid flow and lowering temperature profile. Moreover, it is concluded that Cu-water based nanofluid high thermal conductivity contributes in enhancing heat transfer efficiently.     

A Numerical Investigation of Nanocomposite of Copper and Titanium Dioxide in Water Based Fluid Influenced by Instigated Magnetic Region

Presence of external electrical field plays a vital role in heat transfer and fluid flow phenomena. Keeping this in view present article is a numerical investigation of stagnation point flow of water based nanoparticles suspended fluid under the influence of induced magnetic field. A detailed comparative analysis has been performed by considering Copper and Titanium dioxide nanoparticles. Utilization of similarity analysis leads to a simplified system of coupled nonlinear differential equations, which has been tackled numerically by means of shooting technique followed by Runge-Kutta of order 5. The solutions are computed correct up to 6 decimal places. Influence of pertinent parameters is examined for fluid flow, induced magnetic field, and temperature profile. One of the key findings includes that magnetic parameter plays a vital role in directing fluid flow and lowering temperature profile. Moreover, it is concluded that Cu-water based nanofluid high thermal conductivity contributes in enhancing heat transfer efficiently.     

Variable viscosity and thermal conductivity effects on MHD flow and heat transfer in viscoelastic fluid over a stretching sheet

The problem of flow and heat transfer of an electrically conducting viscoelastic fluid over a continuously stretching sheet in the presence of a uniform magnetic field is analyzed for the case of power-law variation in the sheet temperature. The fluid viscosity and thermal conductivity are assumed to vary as a function of temperature. The basic equations comprising the balance laws of mass, linear momentum, and energy modified to include the electromagnetic force effect, the viscous dissipation, internal heat generation or absorption and work due to deformation are solved numerically.     

Physics and mechanics of heat exchange processes in nanofluid flows

Nanofluids present a new type of dispersed fluids consisting of a carrier fluid and solid nanoparticles. Unusual properties of nanofluids, particularly high thermal conductivity, make them eminently suitable for many thermophysical applications, e.g., for cooling of equipment, designing of new heat energy transportation and production systems and so on. This requires a systematic study of heat exchange properties of nanofluids. The present paper contains the measurement results for the heat transfer coefficient of the laminar and turbulent flow of nanofluids on the basis of distilled water with silica, alumina and copper oxide particles in a minichannel with circular cross section. The maximum volume concentration of particles did not exceed 2%. The dependence of the heat transfer coefficient on the concentration and size of nanoparticles was studied. It is shown that the use of nanofluids allows a significant increase in the heat transfer coefficient as compared to that for water. However, the obtained result strongly depends on the regime of flow. The excess of the heat transfer coefficient in the laminar flow is only due to an increase in the thermal conductivity coefficient of nanofluid, while in the turbulent flow the obtained effect is due to the ratio between the viscosity and thermal conductivity of nanofluid. The viscosity and thermal conductivity of nanofluids depend on the volume concentration of nanoparticles as well as on their size and material and are not described by classical theories. That is why the literature data are diverse and contradictory; they do not actually take into account the influence of the mentioned factors (size and material of nanoparticles). It has been shown experimentally and by a molecular dynamics method that the nanofluid viscosity increases while the thermal conductivity decreases with the decreasing dispersed particle size. It is found experimentally for the first time that the nanofluid viscosity coefficient depends on the particle material. The higher is the density of particles, the higher is the thermal conductivity coefficient of nanofluid.     

Thermal radiation effects on Williamson fluid flow due to an expanding/contracting cylinder with nanomaterials: Dual solutions

The phenomena of heat and mass transfer during the flow of non-Newtonian transfer are amongst the core subjects in mechanical sciences. Recently, the nanomaterials are among the eminent tools for improving the low thermal conductivity of working fluids. Therefore, in view of the existing contributions, this article presents a two-dimensional numerical simulation for the transient flow of a non-Newtonian nanofluid generated by an expanding/contracting circular cylinder. This critical review further explores the impacts of variable magnetic field, thermal radiation, velocity slip and convective boundary conditions. The basic governing equations for Williamson fluid flow are formulated with the assistance of boundary layer approximations. The non-dimensional form of partially coupled ordinary differential equations has been tackled numerically by utilizing versatile Runge–Kutta integration scheme. The momentum, thermal and concentration characteristics are investigated with respect to several critical parameters, like, Weissenberg number, unsteadiness parameter, viscosity ratio parameter, slip parameter, suction parameter, magnetic parameter, thermophoresis parameter, Brownian motion parameter, Prandtl number, Lewis number and Biot number. The outcomes of the systematic reviews of these parameters and forest plots are illustrated. The study reveals that multiple solutions for the considered problem occurs for diverse values of involved physical parameters. The computed results indicate that the friction and heat transfer coefficients are significantly raised by the magnetic parameter for upper branch solutions.     

Effect of Hall current on the velocity and temperature distributions of Couette flow with variable properties

The unsteady hydromagnetic Couette flow and heat transfer between two parallel porous plates is studied with the Hall effect and temperature dependent properties. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field as well as uniform suction and injection applied perpendicular to the parallel plates. A numerical solution for the governing non-linear equations of motion and the energy equation are obtained. The effect of the Hall term and the temperature-dependent viscosity and thermal conductivity on both velocity and temperature distributions is examined.     

MHD free convection flow over an isothermal vertical cone with temperature dependent viscosity

Free convection flow over an isothermal vertical cone immersed in a fluid with variable viscosity and MHD is studied in this paper. Using appropriate variables, the basic equations are transformed into the non-dimensional boundary-layer equations. These equations are then solved numerically using a very efficient implicit finite-difference method known as Crankl-Nicolson scheme. Detailed results for the velocity, temperature, skin friction, and heat transfer rates for a selection of parameter sets consisting of the viscosity parameter, magnetic field parameter, and Prandtl number are discussed. In order to validate our numerical results, the present results are compared with the available work in the literature and are found to be in an excellent agreement.     

Convective and peristaltic viscous fluid flow with variable viscosity

In the present investigation we have analyzed the peristaltic flow when the viscous fluid with variable viscosity is bounded with convective walls. The combined effects of thermaldiffusion (Soret effects) and diffusion-thermo (Dufour effect) are considered. Convective form of the heat and mass transport phenomenon has been given special attention in addition to the effects of magnetic field. Mathematical formulation for the physical systemis derived and simplified using long wavelength and low Reynolds number approximation. Series solutions for the velocity, temperature andmass concentration fields are computed and elaborated for different physical quantities including magnetic parameter, Soret and Dufour effects, Biot numbers, etc. Streamlines analysis is presented showing the effects of bolus movement.     

Numerical Simulation of MHD Peristaltic Flow with Variable Electrical Conductivity and Joule Dissipation Using Generalized Differential Quadrature Method

In this paper, the MHD peristaltic flow inside wavy walls of an asymmetric channel is investigated, where the walls of the channel are moving with peristaltic wave velocity along the channel length. During this investigation,the electrical conductivity both in Lorentz force and Joule heating is taken to be temperature dependent. Also, the long wavelength and low Reynolds number assumptions are utilized to reduce the governing partial differential equations into a set of coupled nonlinear ordinary differential equations. The new set of obtained equations is then numerically solved using the generalized differential quadrature method(GDQM). This is the first attempt to solve the nonlinear equations arising in the peristaltic flows using this method in combination with the Newton-Raphson technique. Moreover, in order to check the accuracy of the proposed numerical method, our results are compared with the results of built-in Mathematica command NDSolve. Taking Joule heating and viscous dissipation into account, the effects of various parameters appearing in the problem are used to discuss the fluid flow characteristics and heat transfer in the electrically conducting fluids graphically. In presence of variable electrical conductivity, velocity and temperature profiles are highly decreasing in nature when the intensity of the electrical conductivity parameter is strengthened.     

Heat transfer in MHD flow of dusty viscoelastic (Walters’ liquid model-B) stratified fluid in porous medium under variable viscosity

The paper investigates the effects of heat transfer in MHD flow of viscoelastic stratified fluid in porous medium on a parallel plate channel inclined at an angle θ. A laminar convection flow for incompressible conducting fluid is considered. It is assumed that the plates are kept at different temperatures which decay with time. The partial differential equations governing the flow are solved by perturbation technique. Expressions for the velocity of fluid and particle phases, temperature field, Nusselt number, skin friction and flow flux are obtained within the channel. The effects of various parameters like stratification factor, magnetic field parameter, Prandtl number on temperature field, heat transfer, skin friction, flow flux, velocity for both the fluid and particle phases are displayed through graphs and discussed numerically.     

Electroosmosis-Optimized Thermal Model for Peristaltic Transportation of Thermally Radiative Magnetized Liquid with Nonlinear Convection

The present study addresses the heat transfer efficiency and entropy production of electrically conducting kerosene-based liquid led by the combined impact of electroosmosis and peristalsis mechanisms. Effects of nonlinear mixed convection heat transfer, temperature-dependent viscosity, radiative heat flux, electric and magnetic fields, porous medium, heat sink/source, viscous dissipation, and Joule heating are presented. The Debye–Huckel linearization approximation is employed in the electrohydrodynamic problem. Mathematical modeling is conducted within the limitations of δ << 1 and Re → 0. Coupled differential equations after implementing a lubrication approach are numerically solved. The essential characteristics of the production of entropy, the factors influencing it, and the characteristics of heat and fluid in relation to various physical parameters are graphically evaluated by assigning them a growing list of numeric values. This analysis reveals that heat transfer enhances by enhancing nonlinear convection and Joule heating parameters. The irreversibility analysis ensures that the minimization of entropy generation is observed when the parameters of viscosity and radiation are held under control. Fluid velocity can be regulated by adjusting the Helmholtz–Smoluchowski velocity and magnetic field strength.     

Chemical reaction effects on MHD rotating fluid over a vertical plate embedded in porous medium with heat source

Several boundary layer flowswith heat and mass transfer problems do arise from a pebble bed nuclear reactor system. In this study, we examine the combined effects of variable thermal conductivity, thermal diffusion, diffusion thermo, heat source, chemical reaction and fluid rotation on hydromagnetic mixed convective flow with heat and mass transfer over a vertical plate embedded in porous medium. The governing partial differential equations have been transformed into a system of ordinary differential equations by employing the similarity transformation and solved numerically using the Runge–Kutta–Fehlberg method with a shooting technique. Pertinent results obtained are presented graphically and in tabular form with respect to variation in various thermophysical parameters. A comparison of the special case of this study with the previously published work shows excellent agreement.     

Thermal radiation effects on MHD flow of a micropolar fluid over a stretching surface with variable thermal conductivity

In this paper, the effects of variable thermal conductivity and radiation on the flow and heat transfer of an electrically conducting micropolar fluid over a continuously stretching surface with varying temperature in the presence of a magnetic field are considered. The surface temperature is assumed to vary as a power-law temperature. The governing conservation equations of mass, momentum, angular momentum and energy are converted into a system of non-linear ordinary differential equations by means of similarity transformation. The resulting system of coupled non-linear ordinary differential equations is solved numerically. The numerical results show that the thermal boundary thickness increases as the thermal conductivity parameter S$S$ increases, while it decreases as the radiation parameter F$F$ increases. Also, it was found that the Nusselt number increases as F$F$ increases and decreases as S$S$ increases.