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Marangoni convection flow of Carreau liquid by an inclined porous surface is addressed. Magnetic field is taken inclined. Non-linear thermal radiation effects are incorporated considering the Rosseland?s approximation. Runge-Kutta-Fehl?berg fourth fifth order scheme is utilized to solve the non-linear equations subject to non-linear convective boundary conditions. Non-linear expression of Nusselt number is derived. Concrete graphical description is present out for flow velocity, temperature and Nusselt number. Numerical treatment of non-linear Nusselt number is performed and analyzed.

Purpose The purpose of this study is to examine the simultaneous effects of Hafnium particles and partially submerged metallic particles for the flow of bi-phase coupled stress fluid over an inclined flat plane. Design/methodology/approach An unflinching free stream flow that stretches far from the surface of the plane with the possibility of containing some partially submerged metallic particles is considered. Innovative model has been proposed and designed using Runge–Kutta–Fehlberg method. Findings The findings show that the drag force resists the couple stress fluid, whereas the Newtonian flow is supported by increasing the velocity. For both types of flows, movement of the particle is retarded gradually against the drag force coefficient. Originality/value To the best of the authors’ knowledge, this model is reported for the first time.

Numerical analysis is performed for magnetohydrodynamics (MHD) couple stress nanofluid flow over a stretching sheet with melting and nonlinear radiation. The second law of thermodynamics is also incorporated with first-order slip. Nanofluid characteristics for thermophoresis and Brownian moments are encountered. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved numerically through the Runge–Kutta–Fehlberg fourth-fifth (RKF-45) order technique. The physical parameters, which emerges from the derived system are discussed in graphical format. The significant outcomes of the current investigation are that the velocity field decays for a higher magnetic parameter. Another, important outcome of the study is both temperature and concentration are increasing functions of the first-order slip. Nusselt and Sherwood numbers are decreasing with an increase in magnetic strength. Further, Bejan number augment due to enhancement in the first-order slip and couple stress fluid parameters whereas a differing tendency is shown for magnetic and radiation parameters.

The inherent irreversibility in boundary-layer flow of a radiating water/functionalized carbon nanotubes nanofluid over a convectively heated moving wedge and a horizontal/vertical plates is examined. The water-based nanofluid contains two types of carbon nanotubes, namely SWCNTs and MWCNTs. Using a suitable similarity transformation, the model partial differential equations are reduced to ordinary differential equations along with the corresponding boundary conditions. Solutions are obtained for the nanofluid velocity and temperature profiles analytically via optimal homotopy asymptotic method and numerically via shooting method with Runge–Kutta–Fehlberg integration scheme. Entropy generation analysis is conducted based on second law of thermodynamic, and the Bejan number is determined. Results are presented in graphical and tabular forms in order to scrutinize the effects of various geometrical, dynamical and thermophysical parameters on velocity, temperature, skin friction, Nusselt number, entropy generation rate and Bejan number. Generally, it is found that the entropy production can be minimized by reducing the convection through boundaries, moving the obstacle at the same velocity and direction as the flow (λoptimal = 1) and controlling the penetration of viscous dissipation, while increasing nanoparticles rate and thermal radiation has influence to increase the entropy generation. In addition, horizontal plate corresponding to the wedge angle value m = 0 is the optimum geometry to reduce entropy production.

The present work concentrates on the two-dimensional steady incompressible flow of an Oldroyd-8 constant fluid between vertical plates influenced by a magnetic field. The cross diffusive and second-order chemical reactions are incorporated into the study. The homotopy analysis method (HAM) is used to obtain the series solutions of the transformed system of nonlinear equations. The effects of these parameters on the dimensionless velocity, temperature, concentration, skin friction, and Nusselt and Sherwood numbers are also investigated for various values of relevant parameters affecting the flow and heat transfer phenomena. The most relevant outcomes of the present study are that enhancement in magnetic field strength undermines the flow velocity, temperature, and concentration establishing thinner related boundary layer. Another important outcome is that an increase in the Dufour parameter upsurges the rate of heat transfer at the wall y = 0 while peters out at y = 1. Finally, the second-order chemical reaction parameter reduces the concentration distribution. The novel outcomes of this investigation will be helpful in the field of the aerosol technology.

This article deals with the analytical study of MHD flow and heat transfer over a permeable stretching sheet via homotopy analysis method (HAM). The effect of thermal radiation is included in the energy equation, while velocity and thermal slips are included in the boundary conditions. The governing boundary layer equations are transformed into a set of ordinary differential equations by means of similarity transformations. The effects of different parameters on the flow field and heat transfer characteristics are examined. The results obtained were shown to compare well with the numerical results and for some special cases with the published data available in the literature, which are in favorable agreement. Keywords: MHD; Slip flow; Stretching sheet; Thermal radiation; Homotopy analysis method

The current study is modelled to evaluate numerous flow applications in applied sciences espeically in nuclear reacting cooling, geothermal reservoirs, chemical engineering and thermal oil recovery. The present research investigates the magnetohydrodynamic transport of non-Newtonian Casson Nano fluid past due to stretching permeable cylinder by employing Buongiorno's mathematical model. Unlike the frequently used constant temperature and concentration boundary conditions, the present study employed convective boundary conditions. The influences of important sundary parameters like an inclination of magnetic field, joule heating, viscous dissipation, thermophoresis, Brownian motion, Arrhenius activation energy, and chemical reaction are taken into account. The physical flow phenomenon is modelled and after that transformed into a non-dimensional form by incorporating suitable similarity transforms. For solution purpose, Runge-Kutta-Fehlberg fourth-fifth order (RKF45) numerical integrating procedure along with shooting algorithm is adopted. Impacts of several emerging parameters on the velocity distribution, temperature distribution, and concentration distribution, coefficient of skin friction, Sherwood number, and Nusselt number are clarified via graphical and tabular results. It seems to establish that with the rise of chemical reaction parameter chemical reaction parameter the nanoparticles concentration distributions decline while the contrasting trend is perceived for activation energy parameter.

In this paper, steady 2-D MHD free convective boundary-layer flows of an electrically conducting nanofluid over a non-linear stretching sheet taking into account the chemical reaction and heat source/sink are investigated. The governing equations are transformed into a system of non-linear ODE using suitable similarity transformations. Analytical solution for the dimensionless velocity, temperature, concentration, skin friction coefficient, heat and mass transfer rates are obtained by using homotopy analysis method. The obtained results show that the flow field is substantially influenced by the presence of chemical reaction, radiation, and magnetic field.

Steady flow of non-Newtonian nanofluid impinging on a vertical lubricated surface is numerically investigated. The rheological behaviour of the base fluid is characterized by the constitutive equation of third-grade fluid and the power-law fluid model is used for lubricant. Higher-order chemical reaction and nonlinear radiative heat flux are also taken into account. The governing nonlinear partial differential equations are simplified using the Prandtl boundary layer theory and similarity transformations. An efficient and accurate implicit finite difference method is applied to approximate the resulting nonlinear coupled differential equations with complicated boundary conditions for several values of parameters of interest. The velocity, temperature, nanoparticles concentration profiles Nusselt number, and streamlines are illustrated through graphs for full slip and no–slip case as well as assisting and opposing flow cases. The temperature and concentration profiles are also described for linear and non-linear thermal radiation and for different order chemical reactions. The numerical results are compared with the existing literature and found good agreement. It is found that heat and mass transfer rates reduces over the lubricated surface compared with the rough surface.

Bioconvection with gyrotactic microorganisms has a significant role in biotechnology and biosensors. This paper communicates a theoretical numerical investigation regarding the transient bioconvection flow of chemically reactive cross nanofluid over a permeable cylinder under the impact of nonlinear radiation and binary chemical reactions. Additionally, Arrhenius activation energy influences are taken into account. Further, revise model of nanoparticles is considered in present investigation. Boundary layer theory is invoked to develop the basic PDEs of microorganisms field, nanoparticles concentration, energy, momentum and mass for bioconvection flow of cross nanofluid in cylindrical coordinate system and then altered into nonlinear ODEs by utilizing the transforming variables. Numerical solutions of obtained highly nonlinear ODEs system are achieved through shooting Fehlberg approach for both the cases of stretching cylinder aw well as shrinking cylinder. Numerical computations for surface drag force, mass transfer rate, density number of microorganisms and heat transfer rate are executed. It is interesting to found that the density number of microorganisms is depreciated for higher estimation of Peclet number, microorganisms difference parameter and bioconvection Rayleigh number in both cases of stretching cylinder as well as shrinking cylinder. Furthermore, nanoparticles concentration is accelerated for the augmented values of activation energy parameter in shrinking as well as stretching cylinder. For the authenticity of considered study, we have also made a comparative analysis with existing study and noticed to be in excellent agreement.

In this paper, the non-Newtonian Casson flow of nanofluid past a thin needle is considered. The effect of combined nonlinear thermal radiation and internally generated heat on porous embedded fluid flow, heat transfer and volume concentration are studied. This study investigates the transport phenomena for flow over fixed needle and moving needle through stationary fluid. As the mechanics describing fluid dynamics are highly successive and nonlinear. The Runge-Kutta-Fehlberg forth-fifth (RKF-45) numerical method with shooting scheme is applied to obtain the approximate solution. Analysis obtained from approximate solution were utilized to investigate the parametric effect on fluid transport and heat transfer. Results obtained reveals enhanced fluid heat generation during transport improves fluid temperature at a high rate within 0 ≤ η ≤ 10 for moving fluid phenomena, while for moving needle fluid temperature slightly increases within0 ≤ η ≤ 4. Similarly, radiation effect on moving fluid shows high rate of heat transfer while for moving needle flow, rate of heat transfer improves slightly has radiation parameter is varied between 0.2 ≤ R ≤ 0.4. Obtained results compared with literatures shows good agreement. This study provides useful insight to practical applications including aircraft technology, manufacturing, medicine and solar nanofluids systems amongst others.

This research study explores the effects of entropy generations on the pulsatile blood flow through a w-shape curved stenosed channel. The mathematical formulations of this physical problem are derived from the couple equations of momentum and energy. These equations are first normalized, and then solved numerically using the explicit finite difference technique. Subsequently, the solutions of these equations are utilized in the calculation of the Bejan number (Be) and entropy generations (NG). To simplify this problem, a few assumptions are taken into consideration; for instance, a mild stenotic condition is assumed in order to reduce the order of differential equations. The results are based on various velocity graphs sketched under the influence of the curvature (Rc) and magnetic (M) parameters. The magnitude of velocity as well as streamline profiles are highly affected due to the curvature effects of channel wall. The results demonstrate that the value of Bejan (Be) number is highly influenced by increasing the value of curvature parameter (Rc) as depicted in the graphs. Similarly, the shape of velocity profile reduces to symmetric in the unbent vessel. Moreover, it is also observed that the magnitude of velocity has decelerated in the presence of magnetic field.

The flow, heat and mass transfer of water-based nanofluid are examined between two horizontal parallel plates in a rotating system. The effects of Brownian motion, thermophoresis, viscosity and Hall current parameters are considered. The governing partial differential equations are reduced to ordinary differential equations that are then solved numerically using the Runge–Kutta–Fehlberg method. Validation of numerical solution is achieved with an exact solution of primary velocity and found to be in good agreement. Results show that both surfaces experience opposite behavior regarding skin friction, Nusselt and Sherwood numbers in both primary and secondary flows. These physical quantities depend upon dimensionless parameters and numbers.

Several boundary layer flowswith heat and mass transfer problems do arise from a pebble bed nuclear reactor system. In this study, we examine the combined effects of variable thermal conductivity, thermal diffusion, diffusion thermo, heat source, chemical reaction and fluid rotation on hydromagnetic mixed convective flow with heat and mass transfer over a vertical plate embedded in porous medium. The governing partial differential equations have been transformed into a system of ordinary differential equations by employing the similarity transformation and solved numerically using the Runge–Kutta–Fehlberg method with a shooting technique. Pertinent results obtained are presented graphically and in tabular form with respect to variation in various thermophysical parameters. A comparison of the special case of this study with the previously published work shows excellent agreement.

The magnetohydrodynamic (MHD) stagnation point flow of Casson nanofluid over a nonlinear stretching sheet in the presence of velocity slip and convective boundary condition is examined. In this analysis, various effects such as velocity ratio, viscous dissipation, heat generation/absorption and chemical reaction are accentuated. Possessions of Brownian motion and thermophoresis are also depicted in this study. A uniform magnetic field as well as suction is taken into account. Suitable similarity transformations are availed to convert the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations and then series solutions are secured using a homotopy analysis method (HAM). Notable accuracy of the present results has been obtained with the earlier results. Impact of distinct parameters on velocity, temperature, concentration, skin friction coefficient,Nusselt number and Sherwood number is canvassed through graphs and tabular forms.

The elevated temperature electromagnetic materials production system in chemical engineering requires increasingly more refined theoretical and computational models for describing multiple, simultaneous thermophysical effects. Motivated by this application, the present paper addresses heat and mass transfer in a chemically reacting laminar mixed convection flow from a vertical sheet with inducedmagnetic field. The governing equations of the flow are solved analytically using a perturbation technique. The influences of various established parameters on the flow, induced magnetic field, and heat and mass transfer are studied graphically in the present analysis. Finally, we also obtained expressions for shear stress, current density and Nusselt number, and discussed the results through tables.

Emerging engineering and industrial needs made the prime concern of this article to investigate the thermal management on the cross flow of micropolar fluids over a thin needle moving in a parallel stream. The flow is subject to binary chemical reaction and Arrhenius activation energy. The mathematical model of the considered physical problem consists of coupled nonlinear partial differential equations: conservation of mass, momentum, energy, and concentration equation. The dimensionless transformed governing equations subject to the given boundary conditions have been solved directly by the Runge-Kutta Fehlberg fourth- fifth-order method followed by the shooting technique. Graphical results relative to the interaction effects of dynamic thermo-physical dimensionless parameters such as Richardson parameter, Dufour number, Soret number, Prandtl number, temperature ratio parameter, nondimensional activation energy, chemical reaction parameter and velocity ratio parameter controlling the flow, heat and mass transfer features are presented and analyzed. It can be seen, from the study, that the skin friction due to angular velocity reduces with increase in size of the needle and it upsurges due to the increase in material parameter. The obtained numerical results revealed that the augmented Richardson parameter is in favor of a greater heat transfer enhancement. The obtained results show a better agreement of this model with the previously published results.

The present study particularizes the effects of nonlinear thermal radiation and the novel accepts of activation energy in the axisymmetric rotational stagnation point flow of hybrid fluid. Thermophysical properties of water and CWCNT/MWCNT are used for base fluid and nanoparticles respectively. The modeled partial differential equations are reduces to system of ordinary differential equations. The resulting equations are integrated numerically and the impact of involved parameters on velocity, temperature and nanoparticle concentration presented graphically. The tabular values for local Nusselt numbers in case of linear and nonlinear thermal radiation and the Sherwood number with and without activation energy are documented. It is observed that concentration of nanoparticles reduces with activation energy and increasing the solid volume fraction of SWCNT as well as MWCNT nanoparticles. Moreover the axial velocity increases while secondary velocity decreases by increasing the rotation parameter.

The current study presents a bioconvective model to investigate the dynamics of water conveying single-wall carbon nanotubes (SWCNTs) and magnetite nanoparticles on the stagnation point flow along a stretching sheet subject to chemical reaction, viscous dissipation, induced magnetic field, and stratification effects. With applications ranging from biomedical imaging, hyperthermia, targeted drug delivery, and cancer therapy, the present study provides a theoretical perspective that is beneficial in biomedical engineering. Relevant similarity formulas are effectuated in converting the governing equations into a system of ODEs and are further treated numerically using the Runge-Kutta-Fehlberg method with the shooting technique. Illustrations on the effect of temperature, microorganisms, concentration, and velocity profiles due to the varying parameter values are achieved with the aid of graphs. It is observed that augmenting volume fraction of single-wall carbon nanotube and magnetite nanoparticles exhibit a constructive effect on temperature profile, which helps in killing cancerous cells. Further, the simultaneous impact of effectual parameters on surface drag, heat transfer rate, mass transfer rate, and microorganism density number is studied using graphs. It is seen that augmenting chemical reaction parameter tends to elevate the mass transfer rate and the microorganism density number.

The Coriolis effect with forced convective heat transfer on steady ferrohydrodynamic flow past a rotating porous disk in the presence of viscous dissipation has been investigated. The basic idea of the Neuringer-Rosensweig model has been used for the equation of motion of the nanofluid flow. With help of suitable transformations, the governing non-linear system of coupled partial differential equations is simplified into the dimensionless system of ordinary differential equations. Further, the dimensionless system of equations is solved numerically by the MATLAB routine bvp4c solver package. The findings for the motivating parameters of physical interest are expressed by the table and discussed with graphs. The outcomes show that heat transfer rate and thermal boundary layer thickness increase due to the higher value of the dissipation parameter.

The study of incompressible steady Williamson fluid flow is conducted in a curvilinear coordinate system. The flow is bounded below through curves stretchable sheet. Linear thermal radiation effects are considered to observe the heat flow in the system. The model was designed as an application to solar energy in thermal engineering processes. Employing suitable similarity transformations, a set of partial differential equations obtained from the flow situations are converted into a system of non-linear coupled ordinary differential equations. The subsequent equations are elucidated numerically via Runge-Kutta-4 along with the shooting algorithm. The outcomes for different flow properties are displayed and discussed both graphically and numerically. The observations shows that the curvature parameter reduces both velocity and temperature. Radiation parameter boosts the temperature of the fluid but reduces the local Nusselt number. Williamson fluid parameter has a reverse impact on velocity field but it works as a provoking agent for the case of thermal profile. The visual effects in the form of streamlines and isotherms are also presented for different Reynolds number.

In this paper, a generalized Newtonian nanofluid in a bio-microfluidics channel due to combined effects of peristalsis and external applied electric field in the presence of thermal radiation and Joule heating is considered. The Poisson and Nernst-Planck equations are taken into account. The obtained non-linear coupled ordinary differential equations are simulated numerically. The impacts of several parameters under the applied electric field on velocity, temperature, concentration, trapping isothermal lines, Nusselt, and Sherwood numbers are presented graphically. It is observed that the number of isothermal lines increases with the electro-osmotic parameter thermophoresis parameter and Brownian motion parameter while perter out with thermal radiation. The results are helpful to design the micro pumps/chips used in medical engineering and improved the thermal efficiency and the durability of microchip cooling devices.

In this study, the stability of flowing viscous hybrid nanofluid over a stretching surface under uniform magnetic effect and radiation are investigated. The mechanics governing the system of coupled momentum and energy equations are formulated using the Navier Stokes model, which is transformed from the partial form of differential equations into an ordinary form of differentials adopting suitable transforms. As this model is highly non-linear, the Runge-Kutta Fehlberg numerical method is utilized as a suitable method of analysis. Significant parameters such as radiation, magnetic, and volume concentration effects are studied amongst other pertinent parameters. The result presented graphically reveals a numeric increase of radiation parameter enhances thermal distribution, this connotes an improved heat transfer rate. While the volume concentration-effect reveals velocity decrease with an enhanced nanoparticle concentration. Moreover, it is seen that the velocity decreases with the magnetic parameter but increases with the suction/injection parameter. The fluid temperature enhances with the radiation and Eckert number. The result compared with suitable literature shows good agreement with the present study. Applications of the study include heat exchanger, lubrication, microelectronics, air conditioning, and refrigeration amongst others.

In this article, the semi-analytical/numerical technique known as the homotopy analysis method (HAM) is employed to derive solutions for partial slip effects on the heat transfer of nanofluids over a stretching sheet. An accurate analytical solution is presented which depends on the Prandtl number, slip factor, Lewis number, Brownian motion number, and thermophoresis number. The variation of the reduced Nusselt and reduced Sherwood numbers with Brownian motion number, and thermophoresis number for various values Prandtl number, slip factor, Lewis number is presented in tabular and graphical forms. The results of the present article show the flow velocity and the surface shear stress on the stretching sheet and also reduced Nusselt number and reduced Sherwood number are strongly influenced by the slip parameter. It is found that hydrodynamic boundary layer decreases and thermal boundary layer increases with slip parameter. Comparison of the present analysis is made with the previously existing literature and an appreciable agreement in the values is observed for the limiting case.

In this study, MHD mixed convection stagnation point flow toward a nonlinearly stretching vertical sheet in the presence of thermal radiation and viscous dissipation is numerically analyzed. The partial momentum and heat transfer equation are transformed into a set of ordinary differential equations by employing suitable similarity transformations. Using the Runge-Kutta Fehlberg fourth-fifth order method, numerical calculations to the desired level of accuracy are obtained for different values of dimensionless parameters. The results are presented graphically and in tabular form. The results for special cases are also compared to those obtained by other investigators and excellent agreements were observed. The effect of injection on the MHD mixed slip flow near a stagnation point on a nonlinearly vertical stretching sheet is to enhance the velocity field which results from the suppression of the skin friction on the wall surface. The heat transfer rate at the surface increases with increasing values of the nonlinearity parameter. The velocity and thermal boundary layer thicknesses are found to be decreasing with increasing values of the nonlinearity parameter.

This article examines the effects of melting heat transfer and thermal radiation in stagnation point flow towards a stretching/shrinking surface. Mathematical formulation is made in the presence of mass transfer and second order slip condition. Numerical solutions to the resulting nonlinear problems are obtained by Runge-Kutta fourth fifth order method. Physical quantities like velocity, temperature, concentration, skin friction, Nusselt and Sherwood number are analyzed via sundry parameters for stretching/shrinking, first order slip, second order slip, radiation, melting, Prandtl and Schmidt. A comparative study with the previously published results in limiting sense is made. Keywords: Melting heat transfer, Second order slip, Stagnation-point flow, Numerical solution

A mathematical model has been developed using Tiwari-Das model to study the MHD stagnation-point flow and heat transfer characteristics of an electrically conducting nanofluid over a vertical permeable shrinking/stretching sheet in the presence of viscous dissipation. Formulated partial differential equations are converted into a set of ordinary differential equations using suitable similarity transformation. Runge-Kutta-Fehlberg method with shooting technique is applied to solve the resulting coupled ordinary differential equations. The profiles for velocity, temperature, skin friction coefficient and local Nusselt number for various parameters are displayed through graphs and tabular forms. In this problem, we considered two types of nanoparticles, namely, copper (Cu) and Alumina (Al2O3) with water as base fluid. Keywords: Nanofluid, Stagnation-point flow, Shrinking/stretching sheet, Viscous dissipation

The present study investigates a Casson fluid flow in the presence of free convection of combined heat and mass transfer toward an unsteady permeable stretching sheet with thermal radiation, viscous dissipation and chemical reaction. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations and then solved by an efficient Runge–Kutta–Fehlberg method. The dimensionless velocity is decreased by increasing values of the chemical reaction and magnetic parameter while fluid temperature is significantly reduced by increasing values of the Prandtl number. The heat transfer rate is reduced with increasing values of thermal radiation and magnetic parameters.

A numerical investigation has been conducted to investigate the steady forced convection boundary layer nanofluid flow past a horizontal circular cylinder placed in water-based copper (Cu) and alumina (Al 2 O 3 ) nanofluids. Using appropriate transformations, the system of partial differential equations is converted into an ordinary differential system of three equations, which is solved numerically using Keller box and Newton-Raphson methods. The effects of thermal and solutal convective boundary conditions are taken into account which makes the present analysis practically applicable. Numerical results are obtained for the dimensionless velocity, temperature and concentration as well as the skin-friction, Nusselt and Sherwood numbers for specific values of the governing parameters with fixed Prandtl number ( Pr = 6.2) and Schmidt number ( Sc = 0.68) for water. It is shown that, for a regular fluid ( ϕ = 0), a very good agreement exists between the present numerical results and those reported in open literature.

In this study, the effects of variable fluid properties on heat transfer in MHD Casson fluid melts over a moving surface in a porous medium in the presence of the radiation are examined. The relevant similarity transformations are used to reduce the governing equations into a system of highly nonlinear ordinary differential equations and those are then solved numerically using the Runge–Kutta–Fehlbergmethod. The effects of different controlling parameters, namely, the Casson parameter,melting and radiation parameters, Prandtl number,magnetic field, porosity, viscosity and the thermal conductivity parameters on flow and heat transfer are investigated. The numerical results for the dimensionless velocity and temperature as well as friction factor and reducedNusselt number are presented graphically and discussed. It is found that the rate of heat transfer increases as the Casson parameter increases.

Hydromagnetic Couette-Poiseuille flow of variable viscosity nanofluids with heat and mass transfer between two parallel plates in a rotating permeable channel is investigated numerically. The model nonlinear problem which incorporates thermophoresis, Brownian motion, viscous dissipation, Joule heating and Hall effects are obtained and tackled numerically using a fourth order Runge–Kutta–Fehlberg integration scheme with shooting technique. The effects of various thermophysical parameters on nanofluid velocity, temperature, concentration, skin friction coefficient, and Nusselt and Sherwood numbers are discussed thoroughly and analyzed through graphs. The results show that Hall current significantly affects the flow system. Results for some special cases of the present analysis are in good agreement with the existing literature.

A numerical treatment for axisymmetric flow and heat transfer due to a stretching cylinder under the influence of a uniform magnetic field and prescribed surface heat flux is presented. Numerical results are obtained for dimensionless velocity, temperature, skin friction coefficient and Nusselt number for several values of the suction/injection, magnetic and curvature parameters as well as the Prandtl number. The present study reveals that the controlling parameters have strong effects on the physical quantities of interest. It is seen that the magnetic field enhances the dimensionless temperature inside the thermal boundary layer, whereas it reduces the dimensionless velocity inside the hydrodynamic boundary layer. Heat transfer rate reduces, while the skin friction coefficient increases with magnetic field.

An analysis is carried out to obtain analytical solution of an unsteady two-dimensional MHD nanofluid flow with heat and mass transfer over a heated surface. The governing partial differential equations are reduced to system of nonlinear ordinary differential equations using suitable transformations. The resulting nonlinear coupled system subject to the boundary conditions is solved using homotopy analysis method (HAM). Graphical and numerical demonstrations of the convergence of the HAM solutions are provided. A detailed study illustrating the influences of the magnetic, unsteady, suction/injection and nanofluid parameters, on the dimensionless velocity, temperature, concentration as well as on the skin friction coefficient, the reduced Nusselt and Sherwood numbers is conducted. It is found out that the flow field is substantially influenced due to unsteadiness, transpiration and magnetic field.

This study investigates the combined effects of thermal radiation, thermophoresis, Brownian motion, magnetic field and variable viscosity on boundary layer flow, heat and mass transfer of an electrically conducting nanofluid over a radially stretching convectively heated surface. The stretching velocity is assumed to vary linearly with the radial distance. Using similarity transformation, the governing nonlinear partial differential equations are reduced to a set of nonlinear ordinary differential equations which are solved numerically by employing shooting method coupled with Runge-Kutta Fehlberg integration technique. Graphical results showing the effects of various pertinent parameters on the dimensionless velocity, temperature, nanoparticle concentration, local skin friction, local Nusselt and local Sherwood numbers are presented and discussed quantitatively. Comparisons with the earlier results have been made and good agreements are found. The present results reveal that the heat transfer rate is reduced with viscosity and nanofluid parameters whereas the mass transfer rates is enhanced with Brownian motion parameter and Lewis number.

The boundary-layer flow and heat transfer characteristics of an incompressible thermally radiating second-grade fluid on a linearly stretching permeable vertical slender hollow cylinder subject to viscous dissipation and convection heat exchange at the wall with the surroundings in conjunction with augmented far-field condition is studied. The free-stream or ambient velocity is considered to be linearly stretching while the prescribed surface temperature of the cylinde varies nonlinearly as the axial distance in the presence of elastic deformation and volumetric heat generation. The model incorporates the temperature dependent fluid properties as per dynamic viscosity and thermal conductivity while the viscoelastic or second-grade parameters are temperature-free. In virtue of appropriate transformation, the energy and momentum equations are reduced to nonlinear ordinary differential equations, and then solved numerically using forty-fifth order Runge-Kutta-Fehlberg (RKF45) integration scheme in tandem with shooting method. Analysis is carried out through simulated tables and codes generated graphs. This study reveals that the wall shear stress factor increases with the velocity ratio, mixed convection, curvature and suction parameters but reduces with the stretching parameter. Also the local heat transfer rate enhances with the Prandtl number, suction, curvature, velocity ratio and stretching parameters in contrast to that due to viscoelastic parameter.

An incompressible flow of Casson-Maxwell fluids over stretchable disk rotating with constant angular speed is demonstrated in this research. Buongiorno theory of nanomaterials is utilized in the flow model to reveals the impacts of Brownian movement and thermophoresis. Cattaneo-Christov heat diffusion theory along with variable thermal conductivity is elaborated in the energy equation. The convective boundary condition for thermal analysis is imposed at the disk surface. The governing equations are normalized by means of similarity functions. Numerical approach is adopted to solve the complex non-linear system by Runge–Kutta-Fehlberg (RKF) procedure. The influence of dimensionless variables on velocity, thermal and concentration fields is illustrated through graphs, while the numerical values of thermal and concentration rates are explained in tabular way.

A boundary layer analysis of three dimensional electromagnetic flows of single and multi walls carbon nanotubes over the surface of a thin needle is addressed. Both single wall (SWCNTs) and multi wall (MWCNTs) are considered as nanoparticles whereas water is considered as base liquid. The energy equation is modeled by using non-linear thermal radiation because it has a major impact on the solar energy absorption capacity of nanofluid. Because of such solar energy utilization at greater scale, global warming/pollution levels can be controlled. Homogeneous-heterogeneous reactions are taken into consideration as they find their applications in catalysis, biochemical systems, combustion, batteries, corrosion phenomenon and electrolytic cells. Xue model describing the augmentation of thermal conductivity of carbon nanotubes is invoked. Entropy generation model is adopted because its minimization prevents the loss of available energy which in turn boosts the efficiency of thermal systems. Nonlinear differential equations representing flow expressions are numerically solved by shooting technique. The outcome of the present study is that velocity field lines are grown due to strengthening of electric field parameter in the flow of SWCNT-water and MWCNT-water nanofluids. Brinkman number uplifts the entropy generation.

Oblique stagnation point flow of incompressible Maxwell nanofluid past a stretching cylinder with active and passive controlled nanoparticles concentration condition is discussed numerically. The suitable coordinate decomposition reduce the governing boundary layer equations into the system of nonlinear ordinary differential equations which are approximated by Keller box procedure for several values of pertinent parameters. The Numerical results are compared and validated with existing ones as particular cases and found to be an excellent agreement. Velocity profile and lines of flow are sketched to discuss the Obliqueness of the flow. The temperature and concentration profiles drawn to illustrate the influence of involved parameters also variations in local Nusselt and Sherwood numbers are presented through tabular data. It is observed that the behavior of tangential velocity for the viscoelastic fluid and concentration of nanoparticles against thermophoresis diffusion over the cylinder are quite opposite when compared with the results over flat sheet. The temperature distribution and concentration of nanoparticles decreases with elasticity of the fluid.