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This paper investigates the Magnetohydrodynamics (MHD) convective flow over a cone with the influence of viscous dissipation, variable viscosity, chemical reaction and variable thermal conductivity effects. Related equations are tackled by the Homotopy analysis method (HAM). The impacts of physical variables on concentration, velocity and temperature are presented through numerical tables and graphs. It is noticed that the heat transfer rate (Nusselt number) increases against Prandtl number. Similarly, the mass transfer rate (Sherwood number) increases against Schmidt number. Also, it is seen that skin friction in tangential and azimuthal direction increases against the buoyancy forces ratio parameter. Current results are validated with previous literature work. [ABSTRACT FROM AUTHOR]

AbstractThis paper analyzes the flow of the Reiner-Rivlin hybrid nanofluid, considering the magnetic field and varying thermal conductivity between two spinning disks. Appropriate similarity variables are used to transform all dimensional equations into dimensionless form. A semi-analytical homotopy analysis approach applied to solve dimensionless equations and velocity profiles, temperature distribution, Nusselt number, skin friction, entropy generation, and Bejan number are presented graphically. Some key outcomes include that axial and tangential velocities decreases when porosity parameters increase. Additionally, higher Eckert number when varying from 1 to 1.3, increases the temperature near the center of the two disks from 1.02 to 1.18. The heat transfer rate goes up from 10.2767 to 10.3043 when thermal conductivity rises from 0.1 to 0.7. The entropy generation grows in proportion to the Brinkman number, Reynolds number, and the porosity parameter values. This research might enhance cooling, lubrication, and thermal management in automotive, aerospace, and biomedical industries. [ABSTRACT FROM AUTHOR]

This study examines different fluid flow through an elaborated plate. In the modeling of the physical phenomena under investigation, the impacts of viscous dissipation, activation energy and chemical reaction are considered. Also, the heat transport phenomena are explained by the variable thermal conductivity theory. By using the right transformations, the flow-generating PDEs are converted into nonlinear ordinary differential equations. The parameters' impacts on the velocity, temperature and mass fields are analyzed in detail. The modeled problem is graphically handled in MATLAB using the numerical technique (BVP4c). Graphical representations of the important factors affecting temperature and velocity fields are illustrated through graphs. The findings disclose that the effectiveness of the velocity field is determined by the changing values of the magnetic parameter. The Prandtl values are decreased, the temperature profile becomes more pronounced. [ABSTRACT FROM AUTHOR]

This work objective focuses on studying the combined influences of variable thermal conductivity, chemical reaction, and magnetohydrodynamics (MHD) on the flow of a tangent hyperbolic nanofluid flow over an exponentially stretching surface, considering a first-order velocity slip condition. Additionally, thermophoresis and Brownian motion impacts are taken into account. The phenomena of heat transfer are analyzed considering several factors such as thermal radiation, Joule heating and nonlinear heat source. On the other hand, mass transfer is explored under the effect of chemical reaction. Tangent hyperbolic fluid is an important branch of non-Newtonian fluids known for its ability to describe shear thinning effects. Understanding fluid flow on exponentially stretched surfaces is of great significance due to its applications in various industrial processes. These applications include fluid film condensing methods, plastic production for making plastic covers, fiber manufacturing (where it is used to spin fibers), glass blowing, metallurgical procedures, and the paper industry. The concept of magnetohydrodynamics (MHD) is significant due to its various engineering applications, such as MHD generators, flow meters, heat reservoirs, small components in different devices, and cooling systems for nuclear reactors. To analyze the system, using similarity transformations, the governing equations of continuity, velocity, and concentration are transformed into non-dimensional differential equations. The numerical solution is obtained using the shooting technique. The study presents the physical significance of all the fluid parameters involved, focusing on the velocity, temperature, and concentration profiles. These profiles are presented graphically and discussed in detail. The results show that the fluid velocity profile increases with enhancing values of the We and the magnetic number M. The thermal profile increases with higher Nt and Rd The concentration profile decreases with higher values of Q t and Nb. [ABSTRACT FROM AUTHOR]

In the current research, a thorough examination unfolds concerning the attributes of magnetohydrodynamic (MHD) boundary layer flow and heat transfer inherent to nanoliquids derived from Sisko Al2O3-Eg and TiO2- Eg compositions. Such nanoliquids are subjected to an extending surface. Consideration is duly given to slip boundary conditions, as well as the effects stemming from variable viscosity and variable thermal conductivity. The analytical approach applied involves the application of suitable similarity transformations. These conversions serve to transform the initial set of complex nonlinear partial differential equations into a more manageable assembly of ordinary differential equations. Through the utilization of the FEM, these reformulated equations are solved, considering the specified boundary conditions. The outcomes attained are graphically depicted by means of plots and tables. These visual aids facilitate a comprehensive exploration of how diverse parameters exert influence over the distributions of velocity, temperature, and concentration. Furthermore, detailed scrutiny is directed towards the fluctuations characterizing pivotal parameters, viz., Nusselt number, skin-friction coefficient, and Sherwood number. It is identified that the Nusselt number showcases a diminishing trend coinciding with increasing values of the volume fraction parameter (φ). This trend remains consistent regardless of whether the nanoliquid under consideration is Al2O3-Eg or TiO2-Eg based. In contrast, both the skin-friction coefficient and Sherwood number assume lower values as the volume fraction parameter (φ) escalates. This pattern remains congruent across both classifications of nanoliquids. The findings of the study impart valuable insights into the complex interplay governing the characteristics of HMT pertaining to Sisko Al2O3-Eg and TiO2-Eg nanoliquids along an extending surface. [ABSTRACT FROM AUTHOR]

In this study, we numerically explore the impact of varying viscosity and thermal conductivity on a magnetohydrodynamic flow problem over a moving nonisothermal vertical plate with thermophoretic effect and viscous dissipation. The boundary conditions and flow‐regulating equations are converted into ordinary differential equations with the aid of similarity substitution. The MATLAB bvp4c solver is used to evaluate the numerical solution of the problem and it is validated by executing the numerical solution with previously published studies. The impacts of several factors, including the magnetic parameter, Eckert number, heat source parameter, thermal conductivity parameter, stratification parameter, Soret, Dufour, Prandtl number, and Schmidt number are calculated and shown graphically. Also, the skin friction coefficient, Nusselt number, and Sherwood number are calculated. Fluid velocity, temperature, and concentration significantly drop as the thermophoretic parameter and thermal stratification parameter increases. As thermal conductivity rises, it is seen that the velocity of the fluid and temperature inside the boundary layer rise as well. Also, the Soret effect drops temperature and concentration profile. The applications of this type of problem are found in the processes of nuclear reactors, corrosion of heat exchangers, lubrication theory, and so forth. [ABSTRACT FROM AUTHOR]

The mixed convection MHD boundary layer flow, heat and mass transfer of a Newtonian fluid mixture across an exponentially stretched permeable sheet in porous medium with Soret and Dufour effects subject to temperature-dependent fluid properties have been investigated numerically. The distribution of temperature and concentration at the surface is supposed to grow exponentially. Temperature is considered to affect fluid viscosity and thermal conductivity. The guiding partial differential equations with appropriate boundary conditions are converted into coupled, nonlinear ordinary differential equations with variable coefficients via a similarity transformation. Matlab's built in solver bvp4c is used to find numerical solutions. Using a graphical approach, the effects of several emerging physical parameters on velocity, temperature and concentration distributions on a flow field of a chemically nonreacting fluid mixture are examined and discussed. Results are compared to earlier literature available and found to be in good agreement. Furthermore, this research demonstrates that flow, heat and mass transmission are greatly influenced by mixed convection parameters, magnetic field, Prandtl number, viscosity, conductivity, permeability, and Schmidt number. Skin friction grows for mixed convection parameter, magnetic, viscosity. Highest growths of wall temperature and wall concentration gradients are observed for Prandtl number and Schmidt number, respectively. Heat and mass transfer rates increase with higher values of mixed convection parameters and Darcy parameter. To reduce heat transfer rate magnetic field may be used. Fluid with lower thermal conductivity and with higher Prandtl number may be employed to boost the cooling rate in conducting flows. Higher Schmidt enhances mass transfer rates. Suction stabilizes boundary layer growth. Soret effect can be used to separate light and medium molecular weight components from a fluid mixture and hence can be used for control of air pollution. [ABSTRACT FROM AUTHOR]

The primary interest of this study is to investigate the results of magnetohydrodynamics Casson and Carreau fluid heat via a porous medium at the aspect of a stretching sheet. Variable thermal physical phenomena and suction/injection parameter results are also taken into account. Similarity transformations are applied to convert the governing equations of the magnetohydrodynamics Casson and Carreau fluid glide model into dimensionless non-linear normal differential equations. The results on velocity, concentration, temperature profiles, surface drag, Nusselt number, and Sherwood number are discussed for various flow parameters and presented the results through plots and tables. The fluid flow is analyzed for every suction and injection case. From the analysis it is noted that the velocity profile reduces by increasing the magnetic parameter and the reverse trend is observed for increasing values of Weissenberg number in the case of suction and injection. The temperature space and heat transfer rate enhances by increasing the variable thermal conductivity and more in the case of suction. [ABSTRACT FROM AUTHOR]

Research into the effects of different parameters on flow phenomena is necessary due to the wide range of potential applications of non-Newtonian boundary layer nanofluid flow, including but not limited to production industries, polymer processing, compression, power generation, lubrication systems, food manufacturing, and air conditioning. Because of this impetus, we investigated non-Newtonian fluid flow regimes from the perspectives of both heat and mass transfer aspects. In this study, heat transfer of electrical MHD non-Newtonian flow of Casson nanofluid over the flat plate is investigated under the effects of variable thermal conductivity and mass diffusivity. Emerging problems occur as nonlinear partial differential equations (NPDEs) in opposition to the conservation laws of mass, momentum, heat, and species transportation. The shown problem can be recast as a set of ordinary differential equations by making the necessary changes. A modified finite element method is adopted to solve the obtained set of ODEs. The numerical method is based on Galerkin weighted residual approach, and Gauss–Legendre numerical integration is adopted in the modified finite element method application procedure. To clarify the obtained results, another numerical technique is employed to solve the reduced ODEs. With the help of error tables and the flowing behavior of complicated physical parameters on estimated solutions, this study graphically and tabulatively explains the convergence of analytic solutions. Comparing some of the obtained results with those given in past research is also done. From the obtained results, it is observed that the velocity profile escalates by improving the electric parameter. Our intention is for this paper to serve as a guide for academics in the future who will be tasked with addressing pressing issues in the field of industrial and engineering enclosures. [ABSTRACT FROM AUTHOR]

The study of electro-osmosis, peristalsis and heat transfer with numerous slips, such as velocity slip, thermal slip and concentration slip, may be used to construct biomimetic thermal pumping systems at the microscale of interest in physiological transport phenomena. A mathematical model has been developed to investigate magnetohydro-dynamics non-Newtonian (Carreau fluid) flow induced by the forces to produce a pressure gradient. The walls of the microchannels erode as they expand. The Poisson and Nernst–Planck equations are used to model electro-osmotic processes. This procedure results in Boltzmann circulation of the electric potential across the electric double layer. The governing equations are simplified by approximations such as a low Reynolds number and a long wavelength. The ND Solver in Mathematica simulates and compares simplified coupled nonlinear governing equations. We investigate novel physical parameters affecting flow, heat transfer and pumping. Additionally, a fundamental peristaltic pumping phenomenon known as trapping is graphically provided and briefly discussed. The model's findings show that the velocity increases as the electric field intensifies, implying that electro-osmosis may improve peristaltic flow. [ABSTRACT FROM AUTHOR]

In the present work, the mathematical model for the solar thermal collectors is considered in the form of a nonlinearly stretching sheet. The radiative heat transfer due to solar radiation in magnetohydrodynamic Sisko nanofluid flow over a stretching sheet in the presence of variable thermal conductivity and a heat source is analyzed effectively. The Sisko fluid has been used as a working fluid in the solar collector. The governing boundary value problem is transformed into a system of nonlinear ordinary differential equations using the similarity transformation technique, which is then solved numerically using the finite difference method combined with the quasilinearization technique. The results shown graphically are discussed for the effects of the thermal conductivity parameter, radiation parameter, and heat source parameter on the flow regime. It is observed that increasing values of radiation parameters imply greater thermal conduction and less thermal radiation, as a result of which the nanofluid temperature in the fluid regime will decrease. [ABSTRACT FROM AUTHOR]

In this article, we consider the effects of double diffusion on magnetohydrodynamics (MHD) Carreau fluid flow through a porous medium along a stretching sheet. Variable thermal conductivity and suction/injection parameter effects are also taken into the consideration. Similarity transformations are utilized to transform the equations governing the Carreau fluid flow model to dimensionless non-linear ordinary differential equations. Maple software is utilized for the numerical solution. These solutions are then presented through graphs. The velocity, concentration, temperature profile, skin friction coefficient, and the Nusselt and Sherwood numbers under the impact of different parameters are studied. The fluid flow is analyzed for both suction and injection cases. From the analysis carried out, it is observed that the velocity profile reduces by increasing the porosity parameter while it enhances both the temperature and concentration profile. The temperature field enhances with increasing the variable thermal conductivity and the Nusselt number exhibits opposite behavior. [ABSTRACT FROM AUTHOR]

The variable nature of the thermal conductivity of nanofluid with respect to temperature plays an important role in many engineering and industrial applications including solar collectors and thermoelectricity. Thus, the foremost motivation of this article is to investigate the effects of thermal conductivity and electric conductivity due to variable temperature on the flow of Williamson nanofluid. The flow is considered between two stretchable rotating disks. The mathematical modeling and analysis have been made in the presence of magnetohydrodynamic and thermal radiation. The governing differential equations of the problem are transformed into non-dimensional differential equations by using similarity transformations. The transformed differential equations are thus solved by a finite difference method. The behaviors of velocity, temperature and concentration profiles due to various parameters are discussed. For magnetic parameter, the radial and tangential velocities have showed decreasing behavior, while converse behavior is observed for axial velocity. The temperature profile shows increasing behavior due to an increase in the Weissenberg number, heat generation parameter and Eckert number, while it declines by increasing electric conductivity parameter. The nanoparticle concentration profile declines due to an increase in the Lewis number and Reynolds number. [ABSTRACT FROM AUTHOR]

In this paper an examination is completed to explore the influence of variable thickness and variable thermal conductivity on MHD stream. We have considered the governing stream and heat transfer conditions as partial differential equations. These non-linear partial differential equations are changed to non-linear ordinary differential equations at that point explained numerically utilizing fourth order RK strategy with shooting procedure. The influence of governing factors on velocity and temperature is concentrated through diagrams and numerical estimations of skin frictions and wall temperature inclination are determined, classified and examined. [ABSTRACT FROM AUTHOR]

In this paper, the influence of the transverse magnetic field is unraveled on the development of steady flow regime for an incompressible fluid in the boundary layer limit of a semi-infinite vertical plate. The sensitivity of real fluids to changes in temperature suggests a variable thermal conductivity modeling approach. Using appropriate similarity variables, solutions to the governing nonlinear partial differential equations are obtained by numerical integration. The approach used here is based on using the shooting method together with the Runge-Kutta-Fehlberg integration scheme. Representative velocity and temperature profiles are presented at various values of the governing parameters. The skin-friction coefficient and the rate of heat transfer are also calculated for different parameter values. Pertinent results are displayed graphically and discussed. It is found that the heat transfer rate improves with an upsurge in a magnetic field but lessens with an elevation in the fluid thermal conductivity. [ABSTRACT FROM AUTHOR]

This article studies the boundary layer flow analysis and heat and mass transfer of magnetohydrodynamic (MHD) Carreau fluid around a stretchable circular cylinder, comprehensively studying the suspended dust particles' impact. Here, the viscous fluid is theorized to be incompressible and loaded with spherical dust particles of the same size. Additionally, heat and sink sources are examined in the thermal boundary layer in the existence of both chemical reaction and activation energy influences. A compatible similarity set of transformations are utilized to mutate the system of partial differential equation formed in momentum and temperature equations of the fluid and dust phases as well the concentration equation into a set of ordinary differential equations. Therefore, the mathematical analysis of the problem facilitates and the numerical estimates of the problem are obtained using MATLAB bvp4c function. Computations are iterated for various values of emerging physical parameters from dimensionless boundary layer conservation equations in terms of temperature and non‐Newtonian Carreau velocity of fluid and dust phases and concentration distribution. Moreover, the terminology of skin friction and Nusselt and Sherwood numbers have been obtained and studied numerically. Some interesting findings in this study are the heat transfer rate dwindles due to the increase of mass concentration of the dust particle. Also, there is a strengthening of the flow with variance in values of the curvature parameter while a weakening has been observed in the thickness of the thermal boundary layer and this hence improves the heat transfer rate. Therefore, the fluid flow around a stretched cylinder would be better, due to its multiple applications in various progressing industrial technologies such as the cement processing industry, plastic foam processing, watering system channels, and so forth. Also, activation energy plays a significant role in various areas such as the oil storage industry, geothermal, and hydrodynamics. The dusty fluid flow is very important in the field of fluid dynamics and can be found in many natural phenomena such as blood flow, the flow of mud in rivers, and atmospheric flow during mist. Moreover, MHD applications are numerous including power generation, plasma, and liquid metals, and so forth. A perfect agreement between our results and other studies available in the literature is obtained through carrying out a comparison with treating the problem in special circumstances. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A numerical investigation has been made to study the effects of variable viscosity and thermal conductivity over a vertical hot stretching sheet by using Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) fractional derivatives. As the viscosity and thermal conductivity of a fluid are dependent on temperature, these properties are considered as a variable. We have also considered radiation and chemical reaction. The governing partial differential equations along with the boundary conditions are made dimensionless using suitable similarity transformations so that physical parameters appear in the equations and interpretations on these parameters can be done suitably. The equations so obtained are discritized using ordinary finite difference scheme and we solved the discritized equations numerically adopting a method based on the Gauss-Seidel iteration scheme. Numerical techniques are used to find the values from AB and CF formulae for fractional derivatives on time. The effects of various parameters involved in the problem viz., viscosity parameter, thermal conductivity parameter, magnetic field parameter, radiation parameter, Schmidt number, prandlt number, chemical reaction parameter etc. on velocity, temperature, and concentration distribution at the plate have been shown graphically. The coefficient of skin-friction, heat transfer rate, and Sherwood number are also obtained and presented in tabular form. The effects of each parameter are prominent. A comparison has been given on AB and CF methods in tabular form. It is observed that both the methods agreed well. [ABSTRACT FROM AUTHOR]

The present work focused here is a mixed convective MHD flow of cross fluid in the presence of heat generation/absorption and variable thermal conductivity over a bidirectional stretchable sheet. To elaborate the mechanism of heat transfer is analyzed in view of non-Fourier heat flux based upon Cattaneo–Christov theory. The influence of a simple isothermal model of homogeneous–heterogeneous reactions is further used for solute concentration. As a result, the relevant Buongiorno fluid model is utilized in mathematical modeling and then it is simplified through lubrication technique. By using appropriate transformations, the raised PDEs initially converted to ODEs. Convergent solutions of ODEs are obtained by the implementation of the numerical procedure bvp4c technique. However, the velocity, temperature and concentration profiles have been sketched by distinct physical flow parameter. Drag coefficients and heat transport are also computed numerically. Our results reveal that temperature profile has an inverse relation between the relaxation parameter and variable thermal conductivity. [ABSTRACT FROM AUTHOR]

The current work intends to look into the effects of variable liquid properties on the magnetohydrodynamics of peristaltic flow exhibited by Jeffrey fluid through a compliant-walled channel. In order to make realistic approximations for the flow characteristics of blood, the channel is considered to be inclined and porous. Furthermore, convective boundary conditions and concentration slip have been employed in the analysis. The mathematical formulation is established on the grounds of low Reynolds number and long wavelength approximations. Perturbation solution is obtained for the resulting non-linear differential equations of momentum and energy for small values of variable viscosity and variable thermal conductivity, whereas exact solution is found for the concentration field. The impact of various parameters included in the study is displayed graphically. A rise in the parameter for variable viscosity is found to accelerate the fluid flow, hence resulting in an increased bolus size. For variable thermal conductivity, a similar influence on the heat transfer was observed. The behaviour of the skin-friction coefficient, Nusselt and Sherwood numbers have also been plotted for the pertinent parameters. [ABSTRACT FROM AUTHOR]

The current endeavor is communicated to perceive the characteristics of tangent hyperbolic fluid confined by a deformable sheet in the existence of both variable thermal conductivity and magneto hydrodynamics. An exertion is reported to calculate the numerical solutions of tangent hyperbolic fluid. Mathematical model is contrived in the embodiment of PDEs and after that renovated into ODEs by implementing self-felicitous transformations. Furthermore the obtained ODEs are simplified by utilizing Bvp4c (MATLAB package). Numerical computations of Nusselt number, skin friction, temperature and velocity profiles for miscellaneous values of involved parameters are manifested via graphs and tables. A comparison of contemporary outcomes with existing published work has been taken into account which shows excellent agreement of results. [ABSTRACT FROM AUTHOR]

Abstract The effect of nanofluid and thermal radiation on MHD Williamson fluid over a stretching cylinder in the presence of convective boundary conditions is analyzed. The variable thermal conductivity is considered during the formulation of energy equation. Nonlinear ordinary differential equations are attained by proposing relevant similarity transformations on partial differential equations. These non-dimensional ordinary differential equations are then converted to the system of first order ODEs and solved numerically by shooting method. Results are further compared by using bvp 4 c , a MATLAB built-in function. The results obtained from MATLAB codes are compared with previously published results of the same nature in limiting case. Numerical results of skin-friction coefficient, local Nusselt and Sherwood numbers are systematized in the form of tables. The effect of prominent parameters on velocity, temperature and concentration is displayed by using graphs. It is observed that velocity profile diminishes for the higher values of Weissenberg number but a reverse relation is noticed for the temperature profile. [ABSTRACT FROM AUTHOR]

In countless applications, there is a thoughtful necessity for augmenting the poor thermal conductivity of conventional liquids to improve effectual heat transfer liquids. Nanofluids are fluids interruptions of nanoparticles and broad scrutiny have been presented on nanoliquid solicitations in heat transfer progressions. The intention of this exertion is to scrutinize the dual nature solutions of unsteady magnetite Carreau nanofluid influenced by porous stretching/shrinking surface. The phenomena of heat and mass transfer have been established in the manifestation of combined convective conditions with heat sink/source and variable thermal conductivity. By utilizing compatible conversions to rehabilitate the structure of nonlinear partial differential equations (PDEs) into nonlinear ordinary differential equations (ODEs) which were then elucidated numerically via bvp4c. Under the impact of diverse somatic parameters the graphical depiction of all the probable dual solutions of velocity, temperature, concentration, skin-friction coefficient, local Nusselt and Sherwood numbers are scrutinized. These outcomes specify that the liquid velocity display similar tendency for both upper and lower solutions and decline for unsteadiness parameter, while it enhance for Weissenberg number. [ABSTRACT FROM AUTHOR]

In this paper, unsteady magnetohydrodynamic (MHD) boundary layer slip flow and heat transfer of power-law nanofluid over a nonlinear porous stretching sheet is investigated numerically. The thermal conductivity of the nanofluid is assumed as a function of temperature and the partial slip conditions are employed at the boundary. The nonlinear coupled system of partial differential equations governing the flow and heat transfer of a powerlaw nanofluid is first transformed into a system of nonlinear coupled ordinary differential equations by applying a suitable similarity transformation. The resulting system is then solved numerically using shooting technique. Numerical results are presented in the form of graphs and tables and the effect of the power-law index, velocity and thermal slip parameters, nanofluid volume concentration parameter, applied magnetic field parameter, suction/injection parameter on the velocity and temperature profiles are examined from physical point of view. The boundary layer thickness decreases with increase in strength of applied magnetic field, nanoparticle volume concentration, velocity slip and the unsteadiness of the stretching surface. Whereas thermal boundary layer thickness increase with increasing values of magnetic parameter, nanoparticle volume concentration and velocity slip at the boundary. [ABSTRACT FROM AUTHOR]

The aim of this article is to investigate MHD Carreau fluid slip flow with viscous dissipation and heat transfer by taking the effect of thermal radiation over a stretching sheet embedded in a porous medium with variable thickness and variable thermal conductivity. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The constitutive equations of Carreau fluid are modeled in the form of partial differential equations (PDEs). Concerning boundary conditions available, the PDEs are converted to ordinary differential equations (ODEs) by means of similarity transformation. The homotopy analysis method (HAM) is used for solution of the system of nonlinear problems. The effects of various parameters such as Weissenberg number $\mathit{We}^{2}$ , magnetic parameter $M^{2}$ , power law index n, porosity parameter D, wall thickness parameter α, power index parameter m, slip parameter λ, thermal conductivity parameter ε, radiation parameter R and Prandtl number on velocity and temperature profiles are analyzed and studied graphically. [ABSTRACT FROM AUTHOR]

The present work studies the MHD two-dimensional flow of Eyring-Powell fluid with thermophoresis and Brownian motion. Flow caused is due to convection type stretching cylinder. Thermal radiation and heat source/sink phenomenon characterizes the heat transfer process. Computations for strong nonlinear systems are presented after non-dimensionalization. Thermal and nanoparticles concentration fields for nonlinear boundary value problems are calculated and discussed. The velocity, temperature and concentration gradients are also evaluated. The major outcome of the present study is that Brownian motion and thermophoretic phenomenon boosts temperature however nanoparticles concentration distribution has opposite behavior for these phenomena. Moreover thermal and concentration Biot numbers have similar impacts on temperature and concentration. [ABSTRACT FROM AUTHOR]

The motion of nanofluid (water and 36 nm alumina nanoparticles) along upper horizontal surface of a paraboloid of revolution in the presence of nonlinear thermal radiation, Lorentz force and space dependent internal heat source within thin boundary layer is investigated theoretically. It is assumed that buoyancy induces the flow over this kind of surface which is neither a horizontal/vertical nor cone/wedge, hence suitable buoyancy model for this case of fluid flow is presented. The viscosity and thermal conductivity are assumed to vary with volume fraction and suitable models for the case 0 % ≤ ϕ ≤ 0.8% are adopted. The transformed governing equations are solved numerically using Runge-Kutta fourth order along with shooting technique (RK4SM). Good agreement is obtained between the solutions of RK4SM and MATLAB bvp5c for limiting case. The influence of pertinent parameters are illustrated graphically and discussed. It is found that temperature and velocity functions are maximum at higher values of internal space dependent heat source. Local heat transfer rate is maximum at smaller values of internal space dependent heat source. [ABSTRACT FROM AUTHOR]

The problem of carbon nanotubes suspended magnetohydrodynamic (MHD) stagnation point flow over a stretching sheet for variable thermal conductivity with thermal radiation is studied in this paper. The boundary of the sheet are convective. The physical problem is modeled using a system of nonlinear partial differential equations and are then transformed into ordinary (similarity) differential equations using a proper transformation. These equations along with the corresponding boundary conditions are solved numerically using shooting technique. The solution is found to be dependent on the governing parameters. The results illustrated include the velocity and temperature profiles, as well as local skin-friction coefficient, the local Nusselt number and streamlines. Velocity profile and boundary layer thickness increases with the increase in nanoparticle volume fraction φ for SWCNT with Grashof number λ and Nanoparticle volume fraction φ for MWCNT with Grashof number λ. [ABSTRACT FROM AUTHOR]

This study models the magnetohydrodynamic (MHD) three-dimensional boundary layer flow of viscoelastic fluid. The flow is due to the exponentially stretching surface. The heat transfer analysis is performed through prescribed surface temperature (PST) and prescribed surface heat flux (PHF). The thermal conductivity is taken temperature dependent. Series solutions of velocities and temperatures are constructed. Graphical results for PST and PHF cases are plotted and analyzed. Numerical values of skin-friction coefficients and Nusselt numbers are presented and discussed. [ABSTRACT FROM AUTHOR]

This article is concerned with the two-dimensional flow of Powell–Eyring fluid with variable thermal conductivity. The flow is caused due to a stretching cylinder. Temperature dependent thermal conductivity is considered. Both numerical and analytic solutions are obtained and compared. Analytic solution is found by homotopy analysis method. Numerical solution by shooting technique is presented. Discussion to different physical parameters for the velocity and temperature is assigned. It is observed that the velocity profile enhances for larger magnetic parameter. It is also further noted that for increasing the value of Prandtl number temperature profile decreases. [ABSTRACT FROM AUTHOR]

The problem of unsteady as well as steady hydromagnetic natural convection and mass transfer flow of viscous reactive, incompressible and electrically conducting fluid between two vertical walls in the presence of uniform magnetic field applied normal to the flow region is studied. Thermal diffusion, temperature dependent variable viscosity and thermal conductivity are assumed to exist within the channel. The governing partial differential equations are solved numerically using implicit finite difference scheme. Results of the computations for velocity, temperature, concentration, skin friction, rate of heat and mass transfer are presented graphically to study the hydrodynamic behavior of fluid in the channel. [ABSTRACT FROM AUTHOR]

This work considers the two-dimensional steady MHD boundary layer flow of heat and mass transfer over a flat plate with partial slip at the surface subjected to the convective heat flux. The particular attraction lies in searching the effects of variable viscosity and variable thermal diffusivity on the behavior of the flow. In addition, non-linear thermal radiation effects and thermophoresis are taken into account. The governing nonlinear partial differential equations for the flow, heat and mass transfer are transformed into a set of coupled nonlinear ordinary differential equations by using similarity variable, which are solved numerically by applying Runge–Kutta fourth–fifth order integration scheme in association with quasilinear shooting technique. The novel results for the dimensionless velocity, temperature, concentration and ambient Prandtl number within the boundary layer are displayed graphically for various parameters that characterize the flow. The local skin friction, Nusselt number and Sherwood number are shown graphically. The numerical results obtained for the particular case are fairly in good agreement with the result of Rahman [6]. [ABSTRACT FROM AUTHOR]

Entropy generation rate which is a tool to measure exergy destruction has attracted considerable attention these years. This work is about temperature and entropy generation rate modeling within cylindrical systems using magnetohydrodynamic (MHD) flow. Two solid co-rotating cylindrical geometries with temperature-dependent thermal conductivities and constant, but different, internal heat generations are considered. The inner one is solid and the outer one is hollow. The MHD flow is within the empty space between these cylindrical geometries. Since the middle geometry is considered as fluid flow, the temperature field is coupled with the velocity field. By obtaining the velocity formula as Bessel functions and approximating it with a series form, and employing a combined analytical–numerical solution technique, the temperature formula within all three components of the system can be formulated. Incorporating the obtained temperature field into the provided fundamental entropy generation rates formulas, the local and volumetric averaged entropy generation rates are calculated. Assuming constant thermal conductivity for all materials, completely analytical solution can be achieved for the considered problem. The accuracy and correctness of the combined analytical–numerical solution technique are checked against available analytical solution. After verification, effects of thermophysical parameters such as magnetic field, Brinkman number, different radii, etc. on the velocity field, temperature distribution and entropy generation rates are examined. [ABSTRACT FROM AUTHOR]

The effect of an inclined magnetic field in the peristaltic flow of a Jeffrey fluid with variable thermal conductivity is discussed. The temperature dependent thermal conductivity of fluid in an asymmetric channel is taken into account. A dimensionless nonlinear system subject to a long wavelength and a low Reynolds number is solved. The explicit expressions of the stream function, the axial velocity, the pressure gradient, and the temperature are obtained. The effects of all physical parameters on peristaltic transport and heat transfer characteristics are observed from graphical illustrations. The behaviors of θ ∈ [0, π/2] and θ ∈ [ π/2, π] on fluid flow and heat transfer are found to be opposite. Further, the size of trapped bolus is greater for the case of the inclined magnetic field ( θ ≠ π/2) than that for the case of the transverse magnetic field ( θ = π/2). The heat transfer coefficient decreases when the constant thermal conductivity (Newtonian) fluid is changed to the variable thermal conductivity (Jeffrey) fluid. [ABSTRACT FROM AUTHOR]

The behaviour of unsteady non-Darcian magnetohydrodynamic fluid flow past an impulsively started vertical porous surface is investigated. The effect of thermophoresis due to migration of colloidal particles in response to a macroscopic temperature gradient is taken into account. It is assumed that both dynamic viscosity and thermal conductivity are linear functions of temperature. The governing equations are non-dimensionalized by using suitable similarity transformation which can unravel the behaviour of the flow at short time and long time periods. A novel iteration scheme, called bivariate spectral local linearization method is developed for solving the corresponding systems of highly non-linear partial differential equations. The results of the numerical solutions obtained are presented graphically and analyzed for the effects of the various important parameters entering into the problem on velocity, temperature, and concentration field within the boundary layer. [ABSTRACT FROM AUTHOR]

The present paper focuses on the analysis of thermophoretic hydromagnetic slip flow over a permeable flat plate with convective surface heat flux at the boundary and temperature dependent fluid properties in the presence of non-uniform heat source/sink. The transverse magnetic field is assumed to be a function of the distance from the origin. Also it is assumed that the liquid viscosity and the thermal conductivity vary as an inverse function and a linear function of temperature, respectively. The shooting method is employed to yield the numerical solutions for the model. Results show that the thermal boundary layer thickness reduces with increase of surface convection parameter whereas reverse effect occurs for viscosity parameter. It is also observed that the thermophoretic parameter decreases the concentration distribution across the boundary layer. [ABSTRACT FROM AUTHOR]

An analysis is made to study magnetohydrodynamic flow and heat transfer for Maxwell fluid over an exponentially stretching sheet through a porous medium in the presence of non-uniform heat source/sink with variable thermal conductivity. The thermal conductivity is assumed to vary as a linear function of temperature. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using implicit finite difference scheme known as Keller-box method. The effect of the governing parameters on the flow field, skin friction coefficient, wall temperature gradient (in prescribed surface temperature case), wall temperature (in prescribed heat flux case) and Nusselt number are computed, analyzed and discussed through graphs and tables. The present results are found to be in excellent agreement with previously published work of El Aziz and Magyari and Keller on various special cases of the problem. [ABSTRACT FROM AUTHOR]

This article addresses the three-dimensional stretched flow of the Jeffrey fluid with thermal radiation. The thermal conductivity of the fluid varies linearly with respect to temperature. Computations are performed for the velocity and temperature fields. Graphs for the velocity and temperature are plotted to examine the behaviors with different parameters. Numerical values of the local Nusselt number are presented and discussed. The present results are compared with the existing limiting solutions, showing good agreement with each other. [ABSTRACT FROM AUTHOR]

In this paper, the effects of variable thermal conductivity and thermal radiation on the MHD flow and heat transfer of a non-Newtonian power-law liquid film at a horizontal porous sheet in the presence of viscous dissipation is studied. The governing time dependent boundary layer equations are transformed to coupled, non-linear ordinary differential equations with power-law index, unsteady parameter, film thickness, magnetic parameter, injection parameter, variable thermal conductivity parameter, thermal radiation parameter, the Prandtl number and the Eckert number. These coupled non-linear equations are solved numerically by an implicit, finite difference scheme known as the Keller box method. The obtained numerical results for velocity and temperature profiles are presented graphically. Also, the obtained results of our study for some special cases are compared with the previously published results, and the results are found to be in very good agreement. The effects of unsteady parameter on the skin friction, wall-temperature gradient and the film thickness are explored for different values of the power-law index and the magnetic parameter. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. [ABSTRACT FROM AUTHOR]

An analysis has been carried out to examine the two-dimensional and magnetohydrodynamic (MHD) flow of thixotropic fluid over a stretched surface. The thermal radiation effect in the heat transfer is considered when the thermal conductivity is not constant. Conservation of mass, momentum and energy leads to the governing partial differential equations of the present study. The resulting equations are solved for convergent series solutions. Numerical values of the skin-friction coefficient are presented and analyzed. [ABSTRACT FROM AUTHOR]

Abstract: The present paper is concerned with the study of flow, heat and mass transfer characteristics in the unsteady free convective flow of an incompressible viscoelastic fluid over a moving vertical cone and a flat plate in the presence of magnetic field and higher order chemical reaction. The fluid viscosity and thermal conductivity are assumed to vary as a linear function of temperature. The governing partial differential equations are solved numerically using the implicit finite difference method of Crank–Nicolson type. The features of the fluid flow, heat and mass transfer characteristics are analyzed by plotting graphs and the physical aspects are discussed in detail. The results obtained show that the impact of magnetic field, buoyancy ratio parameter, viscosity variation parameter, Ecart number and chemical reaction parameter plays an important role in the viscoelastic fluid flow through porous medium. The mass transfer of the reactive species strongly depends on the chemical reaction parameter as well as the order of chemical reaction. [Copyright &y& Elsevier]

Abstract: An investigation is made to study the effects of transverse curvature and the temperature dependent thermal conductivity on the magneto-hydrodynamic (MHD) axisymmetric flow and heat transfer characteristics of a viscous incompressible fluid induced by a non-isothermal stretching cylinder in the presence of internal heat generation/absorption. It is assumed that the cylinder is stretched in the axial direction with a linear velocity and the surface temperature of the cylinder is subjected to vary non-isothermally. Here the thermal conductivity is assumed to vary linearly with temperature. Using a similarity transformation, the governing system of partial differential equations is first transformed into coupled non-linear ordinary differential equations with variable coefficients. The resulting intricate non-linear boundary value problem is solved numerically by a second order finite difference scheme for different values of the pertinent parameters for two cases: (i) the prescribed surface temperature (PST case) and (ii) the prescribed heat flux (PHF case). Numerical results are obtained for two different cases namely, zero and non-zero values of the curvature parameter to get the effects on the velocity and temperature fields. The combined effects of the curvature parameter and the thermal conductivity parameter are examined. The physical significances of the numerical results are presented for several limiting cases. [Copyright &y& Elsevier]

Abstract: This work investigates the effect of thermophoresis and chemical reaction on heat and mass transfer in hydromagnetic micropolar fluid flow over an inclined permeable plate with constant heat flux and non-uniform heat source/sink in the presence of thermal radiation. It is assumed that the transverse magnetic field is a function of the distance from the origin. The analysis accounts for both temperature dependent fluid viscosity and thermal conductivity. Using the similarity transformation, the governing system of equations are transformed into non-linear ordinary differential equations and are solved numerically using symbolic software MATHEMATICA. Numerical results for the velocity, microrotation, temperature and species concentration as well as for the skin friction, heat and mass transfer are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution. [Copyright &y& Elsevier]

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