Effect of thermophoresis and Brownian motion on the melting heat transfer of a Jeffrey fluid near a stagnation point towards a stretching surface: Buongiorno's model

This analysis intends to address the coupled effect of phase change heat transfer, thermal radiation, and viscous heating on the MHD flow of an incompressible chemically reactive nanofluid in the vicinity of the stagnation point toward the stretching surface, taking a Jeffrey fluid as the base fluid. Convergent analytical solutions for the nonlinear boundary layer equations are obtained by the successive application of scaling variables and the highly efficacious homotopy analysis method. Error analysis is implemented to endorse the convergence of the solutions. Through parametric examination, influence of various physical parameters occurring in analysis of the profiles of velocity, temperature, and nanoparticle concentration, coefficient of surface drag, rates of mass and heat transfer is explored pictorially. The Deborah number and the melting parameter are found to enhance velocity, and the associated momentum boundary layers are thicker, whereas the magnetic field depreciates the flow rate. Temperature is observed to enhance with the thermophoresis parameter, Prandtl number and Eckert number, whereas a reduction is seen with the thermal radiation parameter and Brownian motion parameter. Nanoparticle concentration is depleted by the chemical reaction parameter, the thermophoresis parameter, and the Lewis number.     

Using porous inserts to enhance heat transfer in laminar fully-developed flows

The objective of this work is to investigate if it is possible to use porous inserts to enhance heat transfer in rectangular channels. A mathematical model that includes inertia and viscous effects is used to determined the velocity profile in the porous region. For the fluid region, momentum transfer is modeled using the Navier-Stokes equation. These equations and the energy equations are solved numerically via a finite-difference method. Heat transfer between the channel walls and the fluid is determined as a function of Darcy number, inertia parameter, ratio of the fluid and porous medium thermal conductivities, and the porous insert thickness. It is shown that heat transfer could be enhanced by placing a porous insert in the channel. Moreover, for some conditions heat transfer is maximized by using a porous insert thinner than the channel height while a porous insert that completely fills the channel is needed for other conditions.     

Entropy analysis in MHD Couette flow of chemically reacting viscoelastic fluid past a deformable porous channel

Here, an investigation of MHD Couette flow of a chemically reacting viscoelastic fluid past a deformable porous layer with entropy generation using Walters liquid model has been considered. A binary, homogeneous, and isotropic mixture of fluid and solid phases in the porous medium is considered. The impact of heat source parameter and Soret effect are taken into account. The governing equations are solved analytically to obtain the expressions for solid displacement, fluid velocity, temperature, and concentration. The impact of relevant parameters on the flow system, temperature, concentration, mass transfer flux, entropy generation number, and Bejan number are discussed graphically. It is observed that solid displacement enhances due to the growth of drag and viscoelastic parameter, while it reduces due to rising volume fraction parameter. Fluid velocity rises when the volume fraction parameter increases. Rising Brinkmann number enhances the temperature, while Brinkmann number and Soret number reduces the species concentration. The irreversibility of heat transfer dominates the flow near the channel plates, while the effect of fluid friction irreversibility can be observed within the channel centerline region.     

A note on heat transfer to MHD oscillatory flow in an asymmetric wavy channel

This note deals with the MHD oscillatory flow of an optically thin fluid in an asymmetric wavy channel filled with porous medium. Based on some simplifying assumptions, the governing momentum and energy equations are solved and analytical solutions for fluid velocity, temperature distribution, Nusselt number and skin friction are constructed. The effects of radiation parameter, Peclet number, Hartmann number, porous medium shape factor and geometric parameters on flow and heat transfer characteristics have been examined in detail.     

A numerical study on heat transfer and MHD flow of a Newtonian through a porous channel—Local thermal nonequilibrium model

 Vast numbers of studies concentrate on the thermal equilibrium state whereas in many real-world applications the model exists in the nonequilibrium state. Also, local thermal non-equilibrium precisely represents the thermohydroflow characteristics. Therefore, the current study examines the heat transfer and fluid flow characteristics of the magnetohydrodynamic flow of a Newtonian fluid through a local thermal non-equilibrium (LTNE) porous channel in the presence of the induced magnetic field. The mathematical model of the prescribed flow encloses the coupled nonlinear equations which are difficult to approach analytically. Hence, they are solved numerically using the shooting method with the Newton–Raphson method. The implications of various physical parameters of the problem on fluid flow, induced magnetic field, current density, temperature profiles, and heat transfer are elucidated with the aid of plots and tables. From the examination, it is clear that the porous medium significantly influences the characteristics of the fluid flow. That is, the least value of the Darcy number is related to a higher momentum field. Another interesting phenomenon is that the induced magnetic field remarkably enhances when the Darcy number is high, whereas the process is contrary to the current density. The effect of LTNE on the flow characteristics and heat transfer ceases for higher values of inter-phase heat transfer coefficient and the ratio of thermal conductivities, which gives rise to the local thermal equilibrium (LTE) situation. Furthermore, the amount of heat transport is maximum in the LTE case compared to that of the LTNE case.     

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.     

Oscillatory slip flow of Fe3O4 and Al2O3 nanoparticles in a vertical porous channel using Darcy's law with thermal radiation

The heat transfer phenomena and oscillatory flow of an electrically conducting viscous nanofluid (NF) in a channel with porous walls and saturated porous media exposed to the thermal radiation are studied. The nanoparticles (NPs) Fe₃O₄ and Al₂O₃ are taken with water as base fluid along with nonuniform temperature and velocity slip at the wall of channel (y′ = 0). The basic laws of momentum and energy conservation are converted into the dimensionless system of the partial differential equations (PDEs) using similarity variables. Closed‐form solutions of these coupled PDEs are constructed for all values of time by taking the oscillatory pressure gradient. The physical insight of involved parameters on the fluid velocity, temperature profile, heat transfer rate, and surface friction is studied and analyzed graphically. It is noted from this study that the fluid velocity shows a decreasing behavior with the volume fraction of NPs. Furthermore, the amplitude of the oscillatory motion in case of skin friction decreases for a large magnetic field.     

Hall effects on magnetohydrodynamic rotating flow through porous medium in a parallel plate channel with various oscillations of pressure gradient

We explored the unsteady flow of an incompressible electrically conducting viscous fluid in a gyratory porous medium with a changeable pressure gradient by taking Hall currents into account. The governing equations are then solved analytically with the help of the Laplace transforms methodology. It is regarded as three dissimilar cases, namely, an impulsive change, cosine as well as sine oscillations of the pressure gradient. The physical significances of different dimensionless parameters on velocity distributions are explored analytically and computationally. It is observed that a thin boundary layer is formed near the plate of the channel and the thicknesses of the layer increase with the increase in either the Hall parameter or Reynolds number while it decreases with an increase in Hartmann number. It is interesting to note that the rotation and Lorentz forces are having noteworthy effects on velocity profiles with pressure gradient and Hall currents.     

Heat transfer analysis for particle–fluid suspension thermomagnetohydrodynamic peristaltic flow with Darcy–Forchheimer medium

This theoretical analysis explores the effect of heat and mass transfer on particle–fluid suspension for the Rabinowitsch fluid model with the stiffness and dynamic damping effects through Darcy–Brinkman–Forchheimer porous medium. In this study, we also incorporate slip and transverse magnetic field effects. Using low Reynolds number, to neglect inertial forces and to keep the pressure constant during the flow, channel height is used largely as compared with the ratio of length of the wave. A numerical technique is used to solve flow governing system of differential equations. Particular attention is paid to viscous damping force parameter, stiffness parameter, and rigidity parameter; also, the numerical data for thermal profile, momentum, and concentration distribution are presented graphically. Outcomes are deliberated in detail for different fluid models (thinning, thickening, and viscous models). It is found that velocity profile increases for greater values of viscous damping effect and stiffness and rigidity parameter for shear thinning, but conflicting comportment is showed for thickening nature model. Viscous dissipation effects increases the thermal profile for all cases of fluid models. The scope of the present article is valuable in explaining the blood transport dynamics in small vessels while considering the important wall features with chemical reaction characteristics. The current analysis has extensive applications in biomedical engineering field, that is, peristaltic pumps.     

Mixed convection–radiation interaction in a vertical porous channel: Entropy generation

The present work examines analytically the effects of radiation heat transfer on magnetohydrodynamic mixed convection through a vertical channel packed with fluid saturated porous substances. First and Second Laws of thermodynamics are applied to analyze the problem. Special attention is given to entropy generation characteristics and their dependency on the various dimensionless parameters, i.e., Hartmann number (Ha), Plank number (Pl), Richardson number (Ri), group parameter (Br/II), etc. A steady-laminar flow of an incompressible-viscous fluid is assumed flowing through the channel with negligible inertia effect. The fluid is further considered as an optically thin gas and electrically conducting. Governing equations in Cartesian coordinates are solved analytically after reasonable simplifications. Expressions for velocity, temperature, local, and average entropy generation rates are analytically derived and presented graphically.     

Influence of conjugate heat transfer on the minimization of entropy generation for forced convective flow through parallel plate channel filled with porous material

A fluid–solid conjugate heat transfer model is developed to analyze the characteristics of entropy generation for forced convective steady hydrodynamically fully developed laminar flow of a Newtonian fluid through a parallel plate channel filled with porous material by modulating the following parameters: substrate thickness, the ratio of thermal conductivity of wall to fluid, Biot number, the axial temperature gradient in the fluid, and Peclet number. The exteriors of both the walls are subjected to the thermal boundary conditions of the third kind. The mass and Brinkman momentum conservation equations in the fluidic domain and the coupled energy conservation in both the solid and fluidic domain are solved analytically using the local thermodynamic equilibrium model, so as to derive closed-form expressions for the velocity in the fluid and the temperature both in the fluid and solid walls in terms of relevant parameters. Suitable combinations of influencing factors, namely the geometric parameters of the system, fluid, flow, and substrate properties are identified for which global entropy generation rate is minimized. The findings may be helpful in the design of thermal systems frequently used in diverse engineering applications having heat transfer in the solid wall being a crucial 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.     

The Couette flow of a conducting Jeffrey fluid when the walls are lined with deformable porous material

The paper deals with the flow, past a deformable porous channel bounded by finite deformable porous layer with moving rigid parallel plates. Transverse magnetic field is also applied and incorporated in the momentum equation. The coupled nonlinear equations are transformed to ordinary differential equations (ODEs) with suitable choice of similarity transformation. Further, these sets of nonlinear ODEs are solved analytically and are used to get results for the flow phenomena. The effects of the porous layer thickness and the drag on the flow phenomena are discussed graphically. It is observed that rigid velocity decreases with increasing in the drag, whereas the decrease in the deformable is noted. It is clear to see that the retards in solid displacement are shown with enhancing viscosity parameter η.     

Run-up flow of MHD fluid between parallel porous plates in the presence of transverse magnetic field

This paper investigated the run-up flow of magnetohydrodynamics (MHD) incompressible, viscous, Newtonian fluid bounded by two parallel horizontal porous plates in the presence of transverse magnetic field. The fluid flow is initially due to constant pressure gradient, placed parallel to the plates. On attaining steady state, the pressure gradient is suddenly withdrawn and the lower porous plate is set into motion in its own plane, this phenomenon is termed as run-up flow. The transfer of momentum is as a result of the disturbances emanating from the boundary into the fluid. The initial value problem is solved using Laplace transform technique to obtain the closed-form solution for the velocity in the Laplace domain. Semi-analytical result is obtained by an inversion technique based on Riemann-sum approximation to invert the solution for velocity into its corresponding time domain. The mathematical simulation conducted shows that increasing the Hartmann number is observed to decrease the fluid velocity while increasing the pressure gradient is found to enhance the fluid velocity. Furthermore, the opposing effects of suction/injection parameter on the fluid velocity have been established in the research.     

MHD Flow of a Couple‐Stress Fluid and a Viscous Fluid in a Vertical Wavy Porous Space with Traveling Thermal Waves and Temperature‐Dependent Heat Source

In this article, the heat transfer analysis is investigated for magnetohydrodynamic (MHD) flow in a vertical wavy porous space with one region filled with couple‐stress fluid and the other region with a viscous fluid in the presence of a temperature‐dependent heat source. The flow is generated by the periodic thermal waves prescribed at the wavy walls of the channel and the transport properties of both fluids are assumed constant. The resulting dimensionless coupled nonlinear equations are assumed into a mean (zeroth‐order) part and a perturbed part, using amplitude as a small parameter. The perturbed quantities are obtained by using the regular perturbation method. The results are graphically presented and the role of pertinent parameters on the heat transfer characteristics of the fluid flow is discussed. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 134‐147, 2014; Published online 3 September 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21068     

Impacts of the periodic wall conditions on the hydromagnetic convective flow of viscoelastic fluid through a vertical channel with Hall current and induced magnetic field

In this study, a mathematical analysis is presented for the hydromagnetic convective flow of an incompressible, chemically reacting, and electrically and thermally conducting viscoelastic fluid through a vertical channel bounded by the porous regime under the action of an applied magnetic field with Hall current and induced magnetic field effects. The left wall of the channel is considered to be nonmagnetic, whereas the right wall of the channel is periodically magnetized. The flow within the channel is induced due to the nonuniform wall temperature and concentration, periodic pressure gradient, and periodic movement of the right wall. The method of separation of variable is used to convert the flow governing coupled partial differential equations into the ordinary differential equations that are solved analytically, and the solution for fluid velocity, induced magnetic field, temperature, and concentration is presented in a closed form. Numerical computation has been performed to demonstrate the impact of various system parameters on the fluid flow behavior. It is observed that oscillations increase the primary flow and primary induced magnetic field. Buoyancy forces have a tendency to lessen the secondary induced magnetic field. Furthermore, it is examined that magnetic diffusivity increases the primary flow, whereas it decreases the secondary flow and primary induced magnetic field.     

Steady revolving flow and heat transfer of a non-Newtonian Reiner–Rivlin fluid

The steady revolving flow and heat transfer of a non-Newtonian Reiner–Rivlin fluid is studied. The momentum equation gives rise to a highly nonlinear boundary value problem. Attempt has been made to study the properties of the solution of the momentum equation analytically before proceeding for numerical solution. The effects of non-Newtonian fluid characteristic on the velocity and temperature fields have been discussed in detail and shown graphically.     

Developing fluid flow and heat transfer in a channel partially filled with porous medium

A three-dimensional computational model is developed to analyze fluid flow in a channel partially filled with porous medium. In order to understand the developing fluid flow and heat transfer mechanisms inside the channel partially filled with porous medium, the conventional Navier–Stokes equations for gas channel, and volume-averaged Navier–Stokes equations for porous medium layer are adopted individually in this study. Conservation of mass, momentum and energy equations are solved numerically in a coupled gas and porous media domain along a channel using the vorticity–velocity method with power law scheme. Detailed development of axial velocity, secondary flow and temperature field at various axial positions in the entrance region are presented. The friction factor and Nusselt number are presented as a function of axial position, and the effects of the size of porous media inside the channel partially filled with porous medium are also analyzed in the present study.     

Unsteady boundary layer flow and heat transfer past a porous stretching sheet in presence of variable viscosity and thermal diffusivity

The aim of this paper is to present the unsteady boundary layer flow and heat transfer of a fluid towards a porous stretching sheet. Fluid viscosity and thermal diffusivity are assumed to vary as linear functions of temperature. Using similarity solutions partial differential equations corresponding to the momentum and energy equations are converted into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the help of shooting method. It is noted that due to increase in unsteadiness parameter, fluid velocity decreases up to the crossing over point and after this point opposite behaviour is noted. The temperature decreases significantly in this case. Fluid velocity decreases with increasing temperature-dependent fluid viscosity parameter (i.e. with decreasing viscosity) up to the crossing over point but increases after that point and the temperature decreases in this case. Due to increase in thermal diffusivity parameter, temperature is found to increase.     

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.