Entropy generation minimization and nonlinear heat transport in MHD flow of a couple stress nanofluid through an inclined permeable channel with a porous medium,thermal radiation and slip

Irreversible losses and heat transport in a magnetohydrodynamic flow of a viscous, steady, incompressible, and fully developed couple stress Al₂O₃–water nanofluid through a sloping permeable wall channel with porous medium and under the effect of radiation heat flux and slip were analyzed. The fundamental equations were solved numerically by using Runge-Kutta together with the shooting technique and the results were in qualitative agreement with an exact solution obtained for a limit case. The impacts of couple stress, Darcy number, solid nanoparticle concentrations, conduction-radiation parameter, Hartmann number and hydrodynamic slip on flow, temperature, heat transport, and entropy production were examined. It was possible to achieve values of minimum entropy production not yet reported in previous studies. In this way, optimal values of couple stress and slip were obtained. The heat transport was also explored and optimal values of slip flow and conduction-radiation parameter with maximum heat transfer were found. Finally, in addition to the alumina, the distributions of velocity, temperature, and entropy generation in TiO₂–water and Cu–water were presented for different solid nanoparticle concentrations. It was obtained that the local entropy of TiO₂–water was lower than Cu–water and Al₂O₃–water in the channel bottom region while it was greater in the upper region.     

Magnetohydrodynamics slip flow of a nanofluid through an oscillatory disk under porous medium supremacy

Unsteady, three‐dimensional, hydromagnetic, nanofluid flow via a circular disk in porous medium is considered. The fluid motion is subject to disk rotation and time‐based sinusoidal oscillations. The flow problem is normalized via similarity variables. Partial slip boundary conditions on velocity, concentration, and temperature are considered. A well‐established numerical technique (successive over relaxation method) is used for the time‐based flow problem. Results are discussed for both the time‐based and linearly rotating disk case. Graphical representations for one, two, and three dimensions are sketched. The results are also discussed through tabular forms.     

Numerical solution for natural convection flow near a vertical porous plate having convective boundary condition with nonlinear thermal radiation

This article presents the theoretical study of the effects of suction/injection and nonlinear thermal radiation on boundary layer flow near a vertical porous plate. The importance of the convective boundary condition as regards the heat transfer rate is taken into account. The coupled nonlinear boundary layer equations are translated into a set of ordinary differential equations via a similarity transformation. The consequences of the active parameters like the suction parameter, injection parameter, convective heat transfer parameter, nonlinear thermal radiation parameters, and Grashof number dictating the flow transport are examined. The numerical result obtained shows that with suction/injection, the heat transfer rate could be increased with nonlinear thermal radiation parameter augment whereas decays with the convective heat transfer parameter and Grashof number. In the presence of suction/injection, the wall shear stress generally increases with nonlinear thermal radiation parameter, convective heat transfer parameter, and Grashof number. The suction has an increasing effect on Nusselt number and shear stress whereas a decreasing effect on Nusselt number and skin friction is seen with injection augment. The nonlinear thermal radiation is an increasing function of the temperature gradient far away from the plate whereas a decreasing function near the porous plate.     

Influence of slip condition on transient laminar flow over an infinite vertical plate with ramped temperature in the presence of chemical reaction and thermal radiation

An analysis was made using the numerical approach of a transient laminar slip flow over an infinite vertical plate with ramped and constant temperatures in which chemical reaction is involved and thermal radiation had to be considered. Slip conditions have caused much concern because of their broad applicability in industry and chemical engineering. By following the finite element technique, the equation of momentum together with the equations of energy and species was numerically solved. The expressions for skin friction, Nusselt number, and Sherwood number are also derived. The variations in fluid velocity, fluid temperature, and species concentration are displayed graphically whereas numerical values of skin friction, Nusselt number, and Sherwood number are presented in tabular form for various values of the pertinent flow parameters. The findings indicate that the radiation has a noticeable impact to a minor intensity of R and is more apparent in the constant condition than in the ramped condition. Radiation and buoyancy effects produce a strong flow near the plate, which is accelerated by slip. Finally, it is shown logically and mathematically that when two buoyancies are opposite and equal in magnitude with equal solutal and thermal diffusions, the flow should be taken as stationary flow in the absence of radiation and the presence/absence of slip.     

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.     

Numerical simulation of nanoparticle shape and thermal ray on a CuO/C2H6O2–H2O hybrid base nanofluid inside a porous enclosure using Darcy's law

In this study, the physical aspects of magnetohydrodynamic flow and heat transfer of a hybrid base nanofluid in a porous medium under the effect of the shape, thermal radiation, and Lorentz force have been examined using the finite element method. Copper oxide (CuO) of various shapes was dispersed into ethylene glycol 50%‐water 50% (likewise for Fe₃O₄). The Darcy model is chosen because of the porous medium. The effect of changeable, diverse parameters, for example, Hartmann number (Ha), volume fraction (), radiation parameter (), and buoyancy force (Ra), on the streamlines, temperature gradient, and Nusselt number are shown through contours. Outputs show that the Fe₃O₄ nanoparticles have a smaller temperature gradient than that of CuO nanoparticles. The Nusselt number decreases for a larger (Ha) number, but increases for a larger Ra, Rd. The blade shaped nanoparticle has a larger impact on increasing compared with that of other shapes.     

Joule heating impacts on MHD pulsating flow of Au/CuO-blood Oldroyd-B nanofluid in a porous channel

This article deals, the pulsating flow of blood carrying Au/CuO Oldroyd-B nanofluid through a porous channel with the effects of viscous dissipation, thermal radiation, and Joule (Ohmic) heating, and applied magnetic field. The perturbation technique is employed to get analytic solutions for flow variables. A comparison between analytical and numerical results shows a good agreement. The effect of various parameters is addressed extensively aided by pictorial results. The obtained results present that the velocity is reduced with the higher values of Hartmann number and volume fraction of nanoparticles. The temperature of nanofluid is enhanced with an enhancement of Eckert number and radiation parameter while it reduces with a rise in Hartmann number. Furthermore, the rise of the volume fraction of nanoparticles boosts up the rate of heat transfer.     

Effects of slip conditions on stretching flow with ohmic dissipation and thermal radiation

The present work addresses the magnetohydrodynamic (MHD) flow and heat transfer over a permeable stretching sheet. Analysis has been carried out in the presence of thermal radiation and ohmic dissipation. The velocity and thermal slip effects are given main attention. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The non‐linear partial differential equations are reduced to a set of non‐linear ordinary differential equations which are solved analytically by the homotopy analysis method (HAM). The effects of emerging physical parameters on the velocity and temperature profiles are interpreted. Numerical data for skin friction coefficient and Nusselt number have been tabulated for various values of the parameters. The results have been compared with the known exact solution from the literature in a limiting sense. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20367     

The effects of thermal radiation on unsteady MHD free convective flow through the porous medium between two vertical plates with Hall effects

The effects of thermal radiation and Hall current on magnetohydrodynamic free convection three-dimensional flow in a vertical channel filled with a porous medium have been studied. We consider an incompressible viscous and electrically conducting incompressible viscous fluid in a parallel plate channel bounded by a loosely packed porous medium. The fluid is driven by a uniform pressure gradient parallel to the channel plates, and the entire flow field is subjected to a uniform inclined magnetic field of strength inclined at an angle of inclination $\alpha$ with the normal to the boundaries in the transverse xy-plane. The temperature of one of the plates varies periodically, and the temperature difference between the plates is high enough to induce radiative heat transfer. The effects of various parameters on the velocity profiles, the skin friction, the temperature field, and the rate of heat transfer in terms of their amplitude and phase angles are shown graphically.     

A study on entropy generation and heat transfer in a magnetohydrodynamic flow of a couple-stress fluid through a thermal nonequilibrium vertical porous channel

The effect of local thermal nonequilibrium (LTNE) on the entropy generation and heat transfer characteristics in the magnetohydrodynamic flow of a couple-stress fluid through a high-porosity vertical channel is studied numerically using the higher-order Galerkin technique. The Boussinesq approximation is assumed to be valid and the porous medium is considered to be isotropic and homogeneous. Two energy equations are considered one each for solid and fluid phases. The term involving the heat transfer coefficient in both equations renders them mutually coupled. Thermal radiation and an internal heat source are considered only in the fluid phase. The influence of inverse Darcy number, Hartmann number, couple-stress fluid parameter, Grashof number, thermal radiation parameter, and interphase heat transfer coefficient on velocity and temperature profiles is depicted graphically and discussed. The entropy generation, friction factor, and Nusselt number are determined, and outcomes are presented via plots. The effect of LTNE on the temperature profile is found to cease when the value of the interphase heat transfer coefficient is high, and in this case, we get the temperature profiles of fluid and solid phases are uniform. The physical significance of LTNE is discussed in detail for different parameters' values. It is found that heat transport and friction drag are maximum in the case of LTNE and minimum in the case of local thermal equilibrium. We observe that LTNE opposes the irreversibility of the system. The corresponding results of a fluid-saturated densely packed porous medium can be obtained as a limiting case of the current study.     

Influence of Hall and Joule heating on a magnetic nanofluid (Fe3O4) flow on a rotating disk with generalized slip condition

This study analyzes Hall current and Joule heating effects on the ferro-nanofluid flow by the rotation of the disk incorporated with generalized slip condition. By using the well-known Von Karman transformation, formulated flow equations are modeled into ordinary differential equations. Numerical solutions of the governing flow equations are attained by utilizing the shooting method consolidated with the fourth-order Runge–Kutta scheme. The impacts of different parameters on skin friction coefficient, velocity, temperature, and Nusselt number are given in graphs and tables and investigated in detail. Furthermore, an association with formerly published articles is given and met in remarkable correspondence.     

Unsteady thermally radiative and chemically reactive viscoelastic fluid flow past a vertical porous plate with a heat source

An analytical study is performed to investigate the thermal radiation effect on the unsteady two-dimensional magnetohydrodynamic flow of a viscoelastic incompressible fluid (Walters $B\prime$ fluid model) along an infinite hot vertical sheet embedded in a porous medium. Further, the addition of a heat source in the energy equation as well as a chemical reaction in the concentration equation renders the present analysis realistic in the field of engineering and technology. The governing equations of mass, momentum, energy, and concentration are solved with successive perturbation techniques. The effects of pertinent parameters on fluid velocity, temperature, concentration, and bounding surface coefficients are shown graphically and in tabular form. The salient feature of the present study is to impose control on magnetic field strength vis-à-vis electromagnetic force by regulating voltage in the electric circuit. The important findings are: the elasticity property of the fluid is more sensitive to heated bounding surface consequently free convection current in enhancing the velocity near the plate than the inherent property viscosity. This outcome contributes to the design requirement to control the flow near the heated surface, higher values of frequency parameters contribute to the attainment of a free stream state in temperature distribution. Besides the aforesaid outcome, the present model is conducive to thinning of boundary layer as the elasticity, magnetic as well as free convection parameters enhance the force coefficients at the bounding surface.     

Free convection flow with thermal radiation and mass transfer past a moving vertical porous plate

The combined free convection boundary layer flow with thermal radiation and mass transfer past a permeable vertical plate is studied when the plate moves in its own plane. The plate is maintained at a uniform temperature with uniform species concentration and the fluid is considered to be gray, absorbing–emitting. The coupled unsteady non-linear momentum, energy and concentration equations governing the problem is obtained and made similar by introducing a time-dependent length scale. The similarity equations are solved numerically using superposition method. The resulting velocity, temperature and concentration distributions are shown graphically for different values of parameters entering into the problem. The numerical values of the local wall shear stress, local surface heat and mass flux are shown in tabular form.     

Unsteady bioconvection Darcy-Forchheimer nanofluid flow through a horizontal channel with impact of magnetic field and thermal radiation

Unsteady bioconvection Darcy-Forchhiemer nanofluid flow is considered in the current investigation in the presence of micro-organisms. The flow is exposed to thermal radiation and a uniform magnetic field in a horizontal channel. The impacts of Brownian motion and thermophoresis are also considered for the flow problem. The unsteady governing equations are modeled and transformed into a nondimensional form by employing a suitable group of similar variables. The solution of the modeled equations is determined by the semianalytical method homotopy analysis method. The features of flow characteristics such as temperature, concentration, velocity, and the motile micro-organism distributions in response to the variations of the emerging parameters are simulated and examined in detail. Among the many results of the study, it is found that velocity upsurges with rising values of the unsteadiness parameter while declining with growth in the magnetic, inertial, and porosity parameters. Temperature augments with growing estimations of Brownian, unsteadiness, and radiation parameters and declines with enhancing values of Prandtl number. Amassed estimations of the Brownian factor reduce the concentration of nanoparticles while growing values of thermophoresis, unsteadiness parameters, and Schmidt number increase it. Moreover, the motile micro-organism profile is a reducing function of the bioconvection Lewis numbers, Peclet, and bioconvection concentration difference parameter.