Heat transfer enhancement in oscillatory two-phase flow of Casson and ferrofluid comprising differently shaped nanoparticles in a horizontal composite channel

The most commonly discussed topic at the present time is the fluid flow in a channel having a porous area, as it is of practical importance for petroleum extraction, frequently isolated irrigation, coolant circulation, biofluid transportation in living organisms, and industrial cleaning systems. An investigation of heat transfer characteristics of unsteady magnetohydrodynamics oscillatory two-immiscible fluid flow of Casson fluid (CF) and ferrofluid (FF) in a long-infinite horizontal composite channel is performed analytically. The channel is divided into two regions. Region I is occupied by a porous region with CF, while Region II is a clear region filled with FF. The mathematical system of coupled partial differential equations is solved analytically considering the two-term periodic and nonperiodic functions. The influences of physical parameters such as CF parameter, porosity parameter, nanoparticles volume fraction, Hartmann number, periodic frequency parameter, oscillations amplitude, and pressure on momentum as well as heat transfer are presented through graphical illustrations (two-dimensional along with three-dimensional) and in tabular form using the MATHEMATICA program. Four different shaped nano-size ferroparticles are used in this study. The investigation of four different nanosized ferroparticles exhibits that the momentum transfer is higher when brick-shaped nanosized ferroparticles are added to the base fluid, water. It is also observed that thermal performance enhances in the case of brick-shaped nanosized ferroparticles compared to the blade, cylinder, and platelet-shaped nanosized ferroparticles. It is observed that the dispersion of brick-shaped nanosized ferroparticles is recommended in base fluid water for greater thermal performance through a horizontal channel.     

Influences of Soret and Dufour numbers on mixed convective and chemically reactive Casson fluids flow towards an inclined flat plate

The purpose of this study is to examine the magnetohydrodynamic mixed convection Casson fluid flow over an inclined flat plate along with the heat source/sink. The present flow problem is considered under the assumption of the chemical reaction and thermal radiation impacts along with heat and mass transport. The leading nonlinear partial differential equations of the flow problem were renovated into the nonlinear ordinary differential equations (ODEs) with the assistance of appropriate similarity transformations and then we solved these ODEs with the employment of the bvp4c technique using the computational software MATLAB. The consequences of numerous leading parameters such as thermophoretic parameter, local temperature Grashof number, solutal Grashof number, suction parameter, magnetic field parameter, Prandtl number, chemical reaction parameter, Dufour number, Soret number, angle of inclination, radiation parameter, heat source/sink, and Casson parameter on the fluid velocity, temperature, and concentration profiles are discoursed upon  and presented through different graphs. Some important key findings of the present investigation are that the temperature of the Casson fluid becomes lower for local temperature Grashof number and solutal Grashof number. It is initiated that the Casson fluid parameter increases the velocity of the fluid whereas the opposite effect is noticed in the temperature profile. Higher estimation of Prandtl number and magnetic parameter elevated the Casson fluid concentration. Finally, the skin friction coefficient, Nusselt number, and Sherwood number are calculated and tabulated. It is also examined that the Nusselt number is weakened for both the Dufour number and Soret number but the skin fraction coefficient is greater for both the Dufour number and Soret number.     

Peristaltic motion with heat and mass transfer of nano-Williamson fluids in two layers

In this paper, we have investigated the peristaltic motion with heat and mass transfer through a vertical channel divided into two equal regions, the right region filled with a clear non-Newtonian fluid obeying the Williamson model and the left region with a nano-Williamson fluid. The system is stressed by a gravity force with a uniform external magnetic field. The problem is modulated mathematically with a system of coupled nonlinear partial differential equations that describe the velocities, temperatures, and concentration of the fluids. The system of nondimensional, nonlinear, and partial differential equations is solved analytically with the homotopy perturbation method after using the approximations of low Reynolds number and long wavelength. The obtained solutions are functions of the physical parameters of the problem. Then, the effects of these parameters on velocities, temperatures, and concentration are discussed numerically and illustrated graphically through a set of figures. It is found that the parameters play an important role in controlling the solutions. It is shown that the stream function decreases on the left side and increases on the right side with an increase in the Wissenberger parameter and thermal conductivity ratio. Also, the temperature in the two regions increases with an increase in the thermophoretic parameter, whereas it decreases with an increase in the Brownian motion parameter. Furthermore, the concentration increases with an increase in the Brownian motion parameter and decreases with an increase in the thermophoretic parameter.     

Couple stress effects on the MHD oscillatory flow in a fluid-saturated porous layer

In this paper, the oscillatory flow of hydromagnetic couple stress fluid-saturated porous layer with inhomogeneous wall temperatures is studied. The flow is modeled using the modified Darcy equation. The fluid is subjected to a transverse magnetic field and the velocity slip at the lower plate is taken into deliberation. The governing coupled partial differential equations of the flow are transformed to coupled ordinary differential equations and are solved analytically. The impact of the physical parameters such as the Grashof number, Prandtl number, Darcy number, Hartmann number, and couple stress parameters on velocity profiles, temperature, rate of heat transfer, and skin friction are emphasized. The velocity field increased as either the Grashof number, the Darcy number, the suction/injection parameter, and Prandtl number increased nevertheless reverse growth can be seen by increasing the Hartmann number and the couple stress parameter. The temperature field in the channel increases with increasing the suction/injection parameter and Prandtl number but a conflicting development can be seen with increasing the oscillation amplitude. It is interesting to note that skin friction increases on both channel plates as injection increases on the heated plate.     

Heat and mass transfer of two immiscible flows of Jeffrey fluid in a vertical channel

In this article, we examined the effect of heat and mass transfer flow of two immiscible Jeffrey fluids in a vertical channel. The highly nonlinear coupled ordinary differential equations are evaluated using regular perturbation parameters, for small values of perturbation parameter. The effect of Jeffrey's parameter on the flow and the effects of various physical parameters entering into the problem on dimensionless velocity, temperature, and concentration distribution is illustrated graphically. We observe that the Jeffrey parameter, thermal, and mass Grashof number enhance the fluid flow, while the chemical reaction parameter suppresses the fluid flow, also it is established that the Nusselt number is boosted by enhancing the thermal and mass Grashof number. We observed that the results are in very good agreement with the results obtained for a viscous fluid.     

Pulsating hydromagnetic flow of Casson fluid in a vertical channel filled with non-Darcian porous medium

This paper analyzes the Joule heating, Dufour number, and Soret number effects on hydromagnetic pulsatile flow of a Casson fluid in a vertical channel filled with a non-Darcian porous medium. The governing partial differential equations (PDEs) of the Casson fluid flow are transformed to ordinary differential equations (ODEs) using perturbation technique and solved by employing shooting method with Runge–Kutta (R–K) fourth-order technique using MATHEMATICA function NDSolve. The influence of Forchheimer number, Casson fluid parameter, Dufour number, radiation parameter, and Soret number on flow variables has been studied and the numerical results obtained are presented. The results reveal that the velocity rises with the rise of Darcy number, whereas it decreases for a given rise in the Forchheimer number. Furthermore, the temperature distribution enhances by increasing the Dufour number.     

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

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

Effects of chemical reaction,Soret and Lorentz force on Casson fluid flow past an exponentially accelerated vertical plate: A comprehensive analysis

The aim of the current study is to explore the effects of heat and mass transfer on unsteady chemically reacted Casson liquid flow over an exponentially accelerated vertical plate in a porous medium. It is assumed that the bounding plate has varying temperatures as well as concentrations in a porous medium under a uniform magnetic field. This phenomenon is modeled in the form of a system of partial differential equations (PDEs) with boundary conditions. The governing dimensionless PDEs are solved using Laplace transform method for velocity, temperature, and concentration. The impact of nondimensional parameters, which are controlling the flow like Casson parameter, Soret number, magnetic parameter, heat generation parameter, Prandtl number, radiation parameter, and Schmidt number is analyzed through graphs. The incremental values of the Casson fluid parameter lead to a reduction in velocity and discovered that for large values of the Casson parameter, the fluid is near to the Newtonian fluid. Also, the Sherwood number increases with enhancing dissimilar estimators of the Schmidt and Soret numbers. A comparison has been made with the published work (Kataria et al.) for a particular case, which was in good agreement.     

Entropy generation in a micropolar fluid past an inclined channel with velocity slip and heat flux conditions: Variation parameter method

An investigation is carried out on the analysis of entropy on the flow of non-Newtonian fluid, in particular, micropolar fluid past an inclined channel. To enhance the fluid properties, velocity and thermal slip conditions are taken into consideration. At the outset, the novelty of the present investigation lies on the analysis of entropy generation that occurs due to the temperature differences between the media. The governing nonlinear equations are transformed to nonlinear ODE by the use of suitable transformed nondimensional variables. Furthermore, the motivation for the study is the solution of these governing equations using the semi-analytical technique, namely, the variation parameter method. The behavior of the flow phenomena is characterized by the contributing parameters, in particular, the Bejan number, on the entropy are displayed via graphs and tables and elaborated in Section 5. The results reveal that the microrotation profile exhibited its dual character with an augmentation of the inclined angle, and both the coupling parameter and the Reynolds number are favorable in resisting entropy.     

Irreversibility analysis of micropolar nanofluid flow in a vertical channel with the impact of inclined magnetic field and heat source or sink

This article examines the inclined magnetic field effect on the flow of micropolar nanofluids in a vertical channel with convective boundary conditions and heat source or sink. Thermodynamics second law is employed to analyze the aspects of entropy generation. The governing differential equations are modified into dimensionless form by using suitable nondimensional variables. These transformed equations are solved by implementing the differential transform technique. The results are analyzed graphically. Skin friction and Nusselt number values are evaluated at the boundary walls of the channel. The major findings of the study are material parameter enhances the microrotation but suppresses both velocity and temperature. Magnetic parameter and angle of the implication of magnetic field decrease the velocity and microrotation. Material parameter and angle of imposed magnetic field minimize the entropy generation.     

Thermal analysis of buoyancy-motivated Casson fluid flow with time-independent chemical reaction under Lorentz forces

The present research study examines the magneto-hydrodynamic natural convection visco-elastic boundary layer of Casson fluid past a nonlinear stretching sheet with Joule and viscous dissipation effects under the influence of chemical reaction. To differentiate the visco-elastic nature of Casson fluid with Newtonian fluids, an established Casson model is considered. The present physical problem is modeled by utilizing the considered geometry. The resulting system of coupled nonlinear partial differential equations is reduced to a system of nonlinear ordinary differential equations by applying suitable similarity transformations. Numerical solutions of these reduced nondimensional governing flow field equations are obtained by applying the Runge-Kutta integration scheme with the shooting method (RK-4). The physical behavior of different control parameters is described through graphs and tables. The present study describes that the velocity and temperature profiles decreased for increasing values of Casson fluid parameter. Velocity field diminished for the increasing nonlinear parameter whereas velocity profile magnified for increasing free convection parameter. Thermal field enhanced with increasing magnetic parameter in the flow regime. The concentration profile decreased for the rising values of the chemical reaction parameter. The magnitude of the skin-friction coefficient enhanced with increasing magnetic parameter. Increasing Eckert number increases the heat transfer rate and increasing chemical reaction parameter magnifies the mass transfer rate. Finally, the similarity results presented in this article are excellently matched with previously available solutions in the literature.     

Thermal radiation and magnetic field effects on squeezing motion analysis for Cu–kerosene and Cu–water nanofluids

This article examines the squeezing motion of Cu–kerosene and Cu–water nanofluids with thermal radiation and magnetic field between two parallel sheets. By appropriate transformation, the governing nonlinear partial differential equations are converted into ordinary differential equations and then solved numerically by the Runge–Kutta technique. The motion characteristics have been examined with graphs by relevant parameters. It is observed that fluid temperature reduces if squeezing parameter, thermal radiation, and Hartmann number increases, but fluid temperature improves if nanoparticle volume fraction, Eckert number, and Prandtl number increases and it is observed that liquid momentum improves if the squeezing parameter increases, but fluid velocity reduces if nanoparticle volume fraction and Hartmann number increases.     

Thermophoresis and Brownian motion effects on Williamson nanofluid flow past a stretching surface with thermal radiation and chemical reaction

The heat transfer mechanism of nanofluids has numerous industrial applications owing to the non-Newtonian behavior and has been exercised as a thermophysical phenomena in presence of thermal radiation. The present paper deals with the thermal transfer characteristics of time-independent magnetohydrodynamics Williamson fluid past a stretching surface in presence of the reaction of chemical equilibrium is dealt. The flow constitutive nonlinear partial differential coupled equations are transmitted into ordinary differential equalities by employing relevant similarity transmutations. These deduced equations are determined by using the Runge–Kutta numerical technique with a shooting approach with the aid of MATLAB software. Influences of distinct pertinent flow parameters like an inclined uniform magnetic field, Soret number, heat generation/absorption, and Schmidt number constrained to convective boundary condition is displayed through graphs with relevant physical interpretations. Computed numerical values for the friction factor coefficient, local Nusselt parameter, and Sherwood number are tabulated.      

Flow and heat transfer analysis of MHD third-grade fluid flow through a vertical microchannel subjected to entropy generation

This paper analyses the generation of entropy in an electrically conducting third-grade fluid through a vertical channel considering the variable thermal conductivity. Aspects of radiation, viscous dissipation, porous medium, Joule heating, convective boundary condition, and heat generation are studied. Nonlinear systems of ordinary differential equations are obtained via applying suitable dimensionless variables. After that, the system is solved with the aid of using the Runge–Kutta–Fehlberg method. The numerical solutions are used to characterize the irreversibility and irreversibility ratio. It is established that the entropy is enhanced with accelerating estimations of the third-grade material parameter, Brinkman number, magnetism, Biot number, porous parameter, and the impact is decelerated with elevating values of the radiation. The rate of heat transfer is higher for the Brinkman number, and a similar impact on drag force is noticed for magnetic and Grashof numbers. All the parameters on flow, temperature, fluid irreversibility and irreversibility ratio are discussed through graphical illustration.     

Entropy optimized MHD fluid flow over a vertical stretching sheet in presence of radiation

The present article describes the influence of radiation on two-dimensional laminar magnetohydrodynamic fluid flow passing over a convective surface. The behavior of the thermal equation is explored through Joule heating, heat generation/absorption, and viscous dissipation. The aim of this study is to examine the physical behavior of the entropy optimization rate. The Cartesian coordinates system is used to model the flow equations. Using similarity variables, a system of partial differential equations is converted into a system of ordinary differential equations. The problem is solved using HAM. The influence of various pertinent parameters on fluid characteristics is graphically explored. Velocity decreases for an increased amount of magnetic parameter, suction parameter, and velocity slip parameter, while behaves the opposite for Grashof number. Temperature increases for a large amount for Brinkman number, magnetic parameter, and radiation parameter, while decreases for Prandtl number. Entropy generation rate increases for Brinkman number, magnetic parameter, and temperature difference parameter. Bejan number decreases for Brinkman number while behaves the opposite for magnetic parameter and temperature difference parameter. Skin friction decreases for large values of magnetic parameters while behaving the opposite for a large amount of velocity slip parameter. Nusselt number decreases for a large amount of Brinkman number. For a better understanding of the study, comparison between numerical outcomes of entropy generation rate and Bejan number for different values of Prandtl number has been done through tables. Also, numerical outcomes of skin friction and Nusselt number are discussed using pertinent parameters through tables.     

Multiple characteristics of three-dimensional radiative Cross fluid with velocity slip and inclined magnetic field over a stretching sheet

This article focuses on the three-dimensional Cross fluid flow of a radiative nanofluid over an expanding sheet with aligned magnetic field, chemical reaction, and heat generation phenomenon. The stretching sheet has convective heat and slip boundary conditions. The similarity variables are properly used for the conversion of a dimensional mathematical model into a nondimensional one. The transformed ordinary differential equations are handled for the numerical outcomes of the suggested fluidic model by incorporating the shooting scheme. Furthermore, the numeric investigations are also compared by bvp4c MATLAB built-in package. In a limited case, both the techniques are checked with already published articles, thereby revealing good agreement. Furthermore, the effects of few parameters like Prandtl number, Weissenberg number, heat generation, stretching rate parameter, magnetic parameter, thermal radiation, Brownian and thermophoresis parameters, and Lewis number on concentration, temperature, and velocity profiles have been presented using figures and numerical tables. The strong intensity of the magnetic field across the fluid and increment in the inclination angle (ϑ) result in a lower velocity profile. Temperature is more prominent for the higher slip mechanism. Furthermore, there in an increase in thermophoretic force, which pushes the nanoparticles, and this mixing of nanoparticles helps to increase the concentration profile. A higher Cross fluid index responds to a larger velocity.     

Flow and heat transfer of couple‐stress permeable fluid sandwiched between viscous fluid layers

The fully developed flow and heat transfer in a horizontal channel consisting of couple‐stress permeable fluid sandwiched between viscous fluid layers is investigated analytically. The channel walls are maintained at two different constant temperatures. The transport properties of the fluids in all regions are assumed to be constant. The governing equations are linear ordinary differential equations and hence closed form solutions are obtained. Effects of physical parameters such as viscosity ratio, thermal conductivity ratio, Eckert number, and Prandtl number on the flow are reported. An interesting and new approach is incorporated to analyze the flow for strong, weak, and comparable porosity with couple‐stress parameter. The variation of rate of heat transfer for different values of couple stress parameter and porosity is also discussed. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21007     

The effects of variable fluid properties on the hydro-magnetic flow and heat transfer over a non-linearly stretching sheet

The influence of temperature-dependent fluid properties on the hydro-magnetic flow and heat transfer over a stretching surface is studied. The stretching velocity and the transverse magnetic field are assumed to vary as a power of the distance from the origin. It is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature, respectively. Using the similarity transformation, the governing coupled non-linear partial differential equations are transformed into coupled non-linear ordinary differential equations and are solved numerically by the Keller–Box method. The governing equations of the problem show that the flow and heat transfer characteristics depend on five parameters, namely the stretching parameter, viscosity parameter, magnetic parameter, variable thermal conductivity parameter, and the Prandtl number. The numerical values obtained for the velocity, temperature, skin friction, and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of the parameters on the flow and heat transfer characteristics are discussed.     

Squeezed MHD tangent hyperbolic fluid flow across a sensor surface

In the present numerical study, the combined effect of temperature-dependent thermal conductivity, linear thermal radiation, and magnetic effect on shear-thinning tangent hyperbolic fluid past a sensor surface has been studied. After converting the modelled partial differential equations into ordinary differential equations by using similarity transformation, the system of equations is tackled with the aid of the shooting method. The influence of important parameters on the fluid motion and energy distribution is displayed graphically and analyzed in detail. The presented simulations depict that a significant rise in fluid velocity is noticed for an enhancement in the magnetic parameter while an opposite trend is observed for the temperature distribution. Moreover, the skin friction coefficient decreases as the squeezed flow index is increased.     

Heat and mass transfer flow over a stretching surface with Ohmic heating and chemical reaction

The present study analyzes the effect of chemical reaction on an unsteady magnetohydrodynamic boundary layer viscous fluid over a stretching surface embedded in a porous medium with a uniform transverse magnetic field. A Darcy‐Forchheimer drag force model is employed to simulate the effect of second‐order porous resistance. Dissipative heat energy based on both viscous and Joule dissipation along with a heat source/sink is considered to enhance the energy equation. Similarity analysis is imposed to transform the governing differential equations into a set of nonlinear coupled ordinary differential equations. These sets of equations are solved numerically using the Runge‐Kutta fourth‐order scheme followed by the shooting algorithm. The effects of physical parameters such as magnetic field, Prandtl number, Eckert number, Schmidt number, unsteadiness parameter, and chemical reaction parameters have been discussed on velocity, temperature, and concentration fields. Computation for the coefficient of skin friction, rate of heat and mass transfer is done and presented in a table for validation of the present outcomes.