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.     

Analysis of a boundary layer flow over moving an exponentially stretching surface with variable viscosity and Prandtl number

Boundary layer flow phenomenons on a stretching sheet find numerous applications in industrial processes such as manufacture and extraction of rubber and polymer sheets. The current study focuses on two‐dimensional water boundary layer flow on exponential stretching surface with a vertical plate for variable physical properties of fluid such as viscosity and Prandtl number. The Quasilinearization technique has been used on governing equations to transform nonlinear to linear equations and these equations are discretized by finite difference techniques to get numerical solutions. The effect of buoyancy parameters (λ), velocity ratio parameter () and streamwise coordinator (ξ) on velocity profiles (F), temperature profiles (θ), local skin‐friction coefficient (C_fx(Re_Lξexp(ξ)^)1/2) and the local Nusselt number (Nu_x(Re_Lξexp(ξ)^)?1/2) has been analyzed graphically based on numerical outcome. The magnitude of velocity profiles increases and temperature profile decreases approximately by 4% and 16% with increases the buoyancy parameter from λ = 1 to λ = 3 at = 0.5 and ξ = 1.0. The skinfriction and heat transfer coefficient increases approximately by 22% and 27% with an increase in ξ from 0.5 to 1.0 at fixed = 0.5 and λ = 1.0. The variations of velocity profiles and temperature profiles have more impact with as compared to ξ and λ. The benchmark studies were carried out to validate the current results with previously published work and found to be in excellent agreement.     

Heat and mass transfer of water-based copper and alumina hybrid nanofluid over a stretching sheet

Hybrid nanofluids (HNFs) are vital in engineering and industrial applications due to significant effective thermal conductivity as compared with regular fluid and nanofluid (NF). The HNF is a process of the conglomeration of two or more nanoparticles of different thermophysical properties to affect the thermal transport characteristics of base fluid, particularly in gearing up heat switch charge. Further, the impact of HNF combined with stretching and squeezing of bounding surface has direct application in thinning/thickening of polymeric sheets in the chemical industry. The current study analyzes the flow of HNF over a stretching sheet under the influence of chemical reaction as well as suction/injection. We have considered water $\left({\mathrm{H}}_2\mathrm{O}\right)$ as the base fluid and copper $\left(\mathrm{Cu}\right)$, and aluminum oxide $\left({\mathrm{Al}}_2{\mathrm{O}}_3\right)$ as nanoparticles. The consequences of the magnetic field, viscous dissipation, and Joule heating are also to be investigated. The resulting partial differential equations are transformed into nonlinear ordinary differential equations using suitable similarity transformations. The numerical solutions to governing equations are obtained with the help of MATLAB software using the bvp4c solver. The important finding is: the rate of heat transfer of HNF is higher than that of NF as well as base fluid. Moreover, contributions of higher Eckert number and radiation parameter are to increase the temperature in the flow domain, whereas the Prandtl number reduces it. It is further noticed that heavier species as well as viscous dissipation decline the level of concentration across the flow field.     

MHD heat transfer flow over a moving wedge with convective boundary conditions with the influence of viscous dissipation and internal heat generation/absorption

In this investigation, the problem of the study is the effect of the magnetic field and viscous dissipation on heat transfer flow through a moving wedge in the existence of the internal heat generation/absorption and also suction/injection. The governing equations are changed to some coupled nonlinear differential equations with aid of similarity variables. The numerical calculations of the equations are solved by the MATLAB package solver bvp5c. The changes of the pertinent constraints on the momentum and temperature have been discussed through graphs and numerical values of skin friction and heat transfer factor are listed in the tabular pattern. Although maintaining a constant value for the convection parameter, the Nusselt number is increased for $Q>0$ and decreased for $Q<0$. The temperature rises in conjunction with an increase in $\mathit{Ec}$ and $\mathit{Nc}$ variables.     

Heat and mass transfer in MHD stagnation-point flow toward an inclined stretching sheet embedded in a porous medium

The present study elucidates the magnetohydrodynamics boundary layer free convective stagnation-point flow toward an inclined nonlinearly stretching sheet embedded in a porous medium. The recent search explores the consequence of permeability of the medium, thermal as well as mass buoyancy, most importantly obliqueness, and thermal slip at the bounding surface. The solutions of the essential equations are achieved with MATLAB'S inbuilt solver bvp4c. The novelty of the present study is to account for the effect of dissipative heat, nonuniform space-dependent volumetric heat power, and a linear first-order chemical reaction of diffusive species and convective flow phenomena on an inclined plate subjected to thermal slip and space-dependent transverse magnetic field acting at a distance. The important findings are laid down as follows: The oblique-surface reduces the effect of body forces, low permeability of the medium causes instability in the flow due to sudden fall in velocity, Biot number contributes to the Newtonian cooling of the surface, these may be of use in a design requirement of the heat exchanger.     

Viscous dissipation effect on mixed convective heat transfer of MHD flow of Williamson nanofluid over a stretching cylinder in the presence of variable thermal conductivity and chemical reaction

The effect of viscous dissipation and thermal radiation on mixed convective heat transfer of an MHD Williamson nanofluid past a stretching cylinder in the existence of chemical reaction is analyzed in this study. When energy equation is formulated, the variable thermal conductivity is deliberated. By proposing applicable similarity transformations, nonlinear ordinary differential equations (ODEs) are attained from partial differential equations. These nondimensional ODEs are computed through Runge-Kutta method integrated with shooting method using MATLAB software. The results found numerically are in agreement with that of the published works of similar nature in a limiting case. The results of the local Nusselt number, skin friction coefficient, and Sherwood numbers are organized in tables. The influence of protuberant parameters on temperature, velocity, and concentration is presented by graphs. From the results, it is seen that for higher values of variable thermal conductivity parameter, the local Sherwood number and skin friction coefficient upsurge, whereas the local Nusselt number diminishes.     

Numerical study of Williamson fluid flow and heat transfer over a permeable stretching cylinder with the effects of Joule heating and heat generation/absorption

The present study aims to discuss the Williamson fluid flow and heat transfer across a permeable stretching cylinder with heat generation/absorption effects. The effects of viscous dissipation, Joule heating, and magnetic field are also taken into account. The BVP-4C numerical solver in MATLAB is adopted for all the numerical simulations in the present study. For this, the modeled partial differential equations are translated into dimensionless ordinary differential equations using some well-developed similarity transformations. A good agreement between the numerical results of the present study and existing literature is exhibited. The dimensionless physical parameters being investigated are Reynolds number, magnetic field parameter, suction parameter, heat source/sink parameter, Williamson fluid parameter, and mixed convection parameter. The numerical calculations are also performed for the skin friction coefficient and local Nusselt number to get an understanding of the shear stress rate and heat transfer rate, respectively. Furthermore, the impact of all these physical parameters on the velocity and temperature profiles is investigated and represented throughout the literature.     

On the effectiveness of viscous dissipation and Joule heating on steady MHD flow and heat transfer of a Bingham fluid over a porous rotating disk in the presence of Hall and ion-slip currents

The combined effects of viscous dissipation and Joule heating on steady magnetohydrodynamics (MHD) flow of an electrically conducting viscous incompressible non-Newtonian Bingham fluid over a porous rotating disk in the presence of Hall and ion-slip currents is studied. An external uniform magnetic field is applied in the z-direction and the fluid is subjected to uniform suction. Numerical solutions are obtained for the governing momentum and energy equations. Results for the details of the velocity as well as temperature are shown graphically and the numerical values of the skin friction and the rate of heat transfer are entered in tables.     

Effect of Prandtl number on the average exit temperature of coolant in a heat‐generating vertical parallel plate channel: A conjugate analysis

A coupled conduction–convection heat transfer analysis is carried out for a two‐dimensional rectangular, vertical parallel plate channel producing volumetric energy (uniform and nonuniform), subjected to laminar forced‐convection incompressible fluid flow under steady‐state conditions. The equations governing the thermal and flow field are solved by using finite difference method, and the resulting algebraic equations are solved by using the tridiagonal matrix algorithm method. Four coolants with their Prandtl numbers (Pr), namely, liquid sodium (Pr = 0.005), sodium‐potassium (Pr = 0.00753), lead (Pr = 0.02252), and helium (Pr = 0.666) are used for the present conjugate analysis. Effects of different thermal and fluid flow parameters such as Reynolds number (Re_H) ranging from 500 to 1500, conduction–convection parameter (N_cc), and total heat generation (Q_t) on average exit temperature (θ_ae) of coolants are studied. From the obtained results, it is found that the θ_ae of coolant strongly depends on Pr, Re_H, N_cc, and Q_t when the aspect ratio (A_r) is kept constant. It is also found that with a nonuniform rate of heat generation, the coolant θ_ae is high compared to uniform heat generation rate, whereas with increasing N_cc, the θ_ae decreases, and with increasing Q_t, the θ_ae increases irrespective of coolants.     

Mixed convective peristaltic flow of Eyring‐Prandtl fluid with chemical reaction and variable electrical conductivity in a tapered asymmetric channel

The influence of inconstant electrical conductivity and chemical reaction on the peristaltic motion of non‐Newtonian Eyring‐Prandtl fluid inside a tapered asymmetric channel is investigated. The system is concerned by a uniform external magnetic field. The heat and mass transfer are considered. The problem is controlled mathematically by a system of nonlinear partial differential equations which describe the velocity, temperature, and nanoparticle concentration of the fluid. By means of long wavelength and low Reynolds numbers, our system is simplified. It is explained by using the multi‐step differential transform method as a semi‐analytical technique. The distributions of velocity, temperature, nanoparticle concentration, as well as pressure gradient and pressure rise are obtained as a function of the physical parameters of the problem. The effects of these parameters on these distributions are deliberated numerically and illustrated graphically through a set of figures. The results indicate that the parameters play a significant role in controlling the velocity, temperature, nanoparticle concentration, pressure gradient, and pressure rise.     

Effects of Prandtl number on three‐dimensional mixed convection in a horizontal square duct with heated and cooled side walls

We examined the effects of Prandtl number on three‐dimensional mixed convection in a horizontal square duct with heated and cooled side walls numerically. Non‐dimensional governing equations were solved for Re = 100, Pr = 0.1–10, and Ri = 36.44 by the SIMPLE method. The numerical results show that the swirl flow was generated along the flow direction, and its pitch lengthened with the increase of Pr. We also examined the strength of swirl flow using the swirl number, S, and we discuss heat transfer behavior as it corresponded to the flow. Heat transfer was promoted by the swirl flow with all Pr, and the optimum value existed within these Pr. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20319     

Heat and mass transfer in three‐dimensional flow through a porous medium with periodic permeability

In this paper, a theoretical study of a three‐dimensional mixed convective mass transfer flow past a semi‐infinite vertical plate embedded in a porous medium has been presented. The novelty of the present work is to analyze the influence of periodic permeability on the flow and transport characteristics in the presence of viscous dissipation and chemical reaction. The equations governing the flow, heat, and mass transfer are solved analytically by using asymptotic series expansion method. The variations in fluid velocity, temperature, and concentration fields due to change of various physical parameters are demonstrated graphically, whereas the numerical values of skin friction and the rate of mass transfer at the plate are compiled in tabular form. It is found that fluid velocity is increased for increasing permeability. Further, it is seen that concentration level of the fluid drops due to chemical reaction.     

Numerical exploration of thermal radiation and Biot number effects on the flow of a non‐Newtonian MHD Williamson fluid over a vertical convective surface

A theoretical and computational study of the magnetohydrodynamic flow and free convection heat transfer in an electroconductive polymer on the external surface of a vertical plate under radial magnetic field is presented. The Biot number effects are considered at the vertical plate surface via modified boundary conditions. The Williamson viscoelastic model is employed which is representative of certain industrial polymers. The nondimensional, transformed boundary layer equations for momentum and energy are solved with the second‐order accurate implicit Keller box finite difference method under appropriate boundary conditions. Validation of the numerical solutions is achieved via benchmarking with earlier published results. The influence of Weissenberg number (ratio of the relaxation time of the fluid and time scale of the flow), magnetic body force parameter, stream‐wise variable, and Prandtl number on thermo fluid characteristics are studied graphically and via tables. A weak elevation in temperature accompanies increasing Weissenberg number, whereas a significant acceleration in the flow is computed near the vertical plate surface with increasing Weissenberg number. Nusselt number is reduced with increasing Weissenberg number. Skin friction and Nusselt number are both reduced with increasing magnetic field effect. The model is relevant to the simulation of magnetic polymer materials processing.     

Three‐dimensional visualization of an electrically conducting and viscous dissipative fluid flow over a moving permeable vertical cylinder

This study numerically scrutinizes the boundary layer flow of an electrically conducting and viscous dissipative fluid past an impulsively started permeable vertical cylinder together with thermal radiation. The solutions of the governing problem are accomplished using the Crank‐Nicholson scheme. The impressions of pertinent parameters on the flow patterns of the fluid particles as well as on the velocity, temperature, and distributed regions are captured and visualized three‐dimensionally.     

Electroosmotic flow of a fractional second-grade fluid with interfacial slip and heat transfer in the microchannel when exposed to a magnetic field

We investigated the time-dependent viscoelastic fluid flow through a parallel-plate microchannel under the influence of a transversely applied magnetic field and an axially imposed electric field. We performed the analysis by employing the Poisson-Boltzmann equation under the Debye-Huckel approximation. The generalized second-grade fluid model with a fractional-order time derivative is used to observe the non-Newtonian and fractional behavior rates of deformation employing the Riemann-Liouville fractional operator. We considered the asymmetric zeta potentials and different slip effects at the walls to study the flow behavior near the vicinity of the channel. We obtained an analytical solution in terms of Mittag-Leffler function, applying Fourier and Laplace transformations. We imposed the heat transfer phenomena with the dissipation of energy and Joule heating effects on the model. The governing equations were also solved numerically by employing an implicit finite difference scheme. The numerical solution was compared with the analytical results, considering the influence of the pertinent parameters involved in the problem. The study delineates that the flow rate decreases with a rise in the fractional-order parameter, while the opposite trend is observed with the electroosmotic parameter. Due to the application of sufficient strength of the magnetic field and the Joule heating effects, the temperature increases within the channel.     

Role of mixed nanofluids on fluid flow and intensify energy transfer in a boundary layer region driven by a free convective force

This research study explores boundary layer flow and intensification of heat transfer through a porous medium accompanied by buoyant forces with the support of appended mixed nanofluids. The generated partial differentiation model is altered to a couple of the highly complicated nonlinear differentiation model by support of the similarity conversion. The resultant model is then resolved by the shooting method for finding the initial approximation and thereafter the Runge‐Kutta‐Fehlberg 45th‐order method is used to get the desired result. The energy transfer and the flow of mixed nanofluids are analyzed by considering vital factors, like convection, porous and volume fraction. The acquired results fairly agree with erstwhile published articles. The major finding is that for greater values of the volume fraction, both fluid flow and energy transfer of a mixed nanofluid will be greater when compared with a regular nanofluid.     

Heat transfer enhancement in hydromagnetic dissipative flow past a moving wedge suspended by H2O-aluminum alloy nanoparticles in the presence of thermal radiation

This letter investigates the two dimensional magnetohydrodynamic Falkner Skan flow of water saturated with AA7072–H₂O and AA7075–H₂O nanoparticles over a moving wedge. Influence of viscous dissipation and thermal radiation is also under consideration. The model is reduced into nondimensional form by using defined self-similar transformations. Then, numerical study (Runge-Kutta numerical scheme) is carried out for solution purpose. The effects of pertinent flow parameters are discussed in the flow regimes by means of graphical aid. Graphical results for special cases (static wedge and when the movement of flow and wedge is in opposite direction) of the model are also elucidated graphically. It is noted that fluid velocity decreases for volumetric fraction and magnetic force favor the velocity. Significant effects of thermal radiation and nanoparticles volume fraction pointed for thermal filed and the influence of Eckert number is almost inconsequential. For more radiative fluid heat transfer coefficient decreases and nanoparticles volumetric fraction favor the local rate of heat transfer. In the presence of AA7075 nanoparticles, rate of heat transfer is quite rapid as compared to that of AA7072 nanoparticles. To validate the present computations, some present results are compared with already existing results in the literature and found better agreement between them. Finally, major points of the study ingrained in the last section of the letter.     

Numerical Study of Heat and Mass Transfer MHD Viscous Flow Over a Moving Wedge in the Presence of Viscous Dissipation and Heat Source/Sink with Convective Boundary Condition

In this article, the effects of viscous dissipation and internal heat generation/absorption on combined heat and mass transfer MHD viscous fluid flow over a moving wedge in the presence of mass suction/injection with the convective boundary condition are carried out numerically for the various values of dimensionless parameters. With the help of similarity transformation, the momentum, energy, and concentration equations are reduced to a set of dimensionless non‐linear ordinary differential equations. The significance of the dimensionless velocity, temperature, mass profiles, and their gradients are presented in graphical form. Three types of flows—particularly the flat plate, vertical wedge, and stagnation point flows—in favorable and unfavorable regimes are analyzed. The obtained results confirm that the flow field is substantially influenced by the magnetic, stretching/shrinking, pressure, Prandtl number, heat generation/dissipation, and mass suction/injection parameters. Current results indicate that stretching a wall boundary causes an increase in velocity, temperature, shear stress, temperature, and mass gradients while shrinking causes a decreasing trend with these profiles. The special modified form of the current problem is found to be in good agreement with the other published data. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(1): 17–38, 2014; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21063     

Heat transfer in the flow of blood‐gold Carreau nanofluid induced by partial slip and buoyancy

Dynamics of blood containing gold nanoparticles on a syringe and other objects with a nonuniform thickness is of importance to experts in the industry. This study presents the significance of partial slip (i.e. combination of linear stretching and velocity gradient) and buoyancy on the boundary layer flow of blood‐gold Carreau nanofluid over an upper horizontal surface of a paraboloid of revolution (uhspr). In this report, the viscosity of the Carreau fluid corresponding to an infinite shear‐rate is assumed as zero, meanwhile, the viscosity corresponding to zero shear‐rate, density, thermal conductivity, and heat capacity were assumed to vary with the volume fraction of nanoparticles. The governing equation that models the transport phenomenon were non‐dimensionalized and parameterized using suitable similarity variables and solved numerically using classical Runge–Kutta method with shooting techniques and MATLAB bvp4c package for validation. The results show that temperature distribution across the flow decreases more significantly with buoyancy‐related parameter when the influence of partial slip was maximized. Maximum velocity of the flow is ascertained at larger values of partial slip and buoyancy parameters. At smaller values of Deborah number and large values of volume fraction, maximum local skin friction coefficient, and local heat transfer rate are ascertained.     

Heat and mass transfer effects on MHD flow of a couple‐stress fluid in a horizontal wavy channel with viscous dissipation and porous medium

This paper looks at heat and mass transfer effects on an unsteady MHD flow of a couple‐stress fluid in a horizontal wavy porous space with travelling thermal waves in the presence of a heat source and viscous dissipation. Initially the temperatures of the walls are maintained at different constant temperatures. The analytical expressions for velocity, temperature, and concentration field are obtained by the regular perturbation technique. The results are presented graphically for various values of emerging dimensionless parameters of the problem and are discussed to show interesting aspects of the solution. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21040 PACS: 44.15.+a, 44.30.+f, 44.27.nd, 47.50.Cd