An efficient analytical decomposition and numerical procedure for boundary layer flow on a continuous stretching surface

An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.

Unsteady heat and mass transfer in MHD flow over an oscillatory stretching surface with Soret and Dufour efects

In this paper, we study the unsteady coupled heat and mass transfer of two-dimensional MHD fluid over a moving oscillatory stretching surface with Soret and Dufour effects. Viscous dissipation effects are adopted in the energy equation. A uniform magnetic field is applied vertically to the flow direction. The governing equations are reduced to non-linear coupled partial differential equations and solved by means of homotopy analysis method （HAM）. The effects of some physical parameters such as magnetic parameter, Dufour number, Soret number, the Prandtl num- ber and the ratio of the oscillation frequency of the sheet to its stretching rate on the flow and heat transfer characteristics are illustrated and analyzed.

Influences of Marangoni convection and variable magnetic field on hybrid nanofluid thin-film flow past a stretching surface

Investigations on thin-film flow play a vital role in the field of optoelectronics and magnetic devices.Thin films are reasonably hard and thermally stable but quite fragile.The thermal stability of a thin film can be further improved by incorporating the effects of nanoparticles.In the current work,a stretchable surface is considered upon which hybrid nanofluid thin-film flow is taken into account.The idea of augmenting heat transmission by making use of a hybrid nanofluid is a focus of the current work.The flow is affected by variations in the viscous forces,along with viscous dissipation effects and Marangoni convection.A time-constrained magnetic field is applied in the normal direction to the flow system.The equations governing the flow system are shifted to a non-dimensional form by applying similarity variables.The homotopy analysis method is employed to find the solution to the resultant equations.It is noticed in this study that the flow characteristics decline with augmentation of magnetic,viscosity and unsteadiness parameters while they increase with enhanced values of thin-film parameters.Thermal characteristics are supported by increasing values of the Eckert number and the unsteadiness parameter and opposed by the viscosity parameter and Prandtl number.The numerical impact of different emerging parameters upon skin friction and the Nusselt number is calculated in tabular form.A comparison of current work with established results is carried out,with good agreement.

Exact solutions for the flow of Casson fluid over a stretching surface with transpiration and heat transfer effects

The effects of transpiration on forced convection boundary layer non-Newtonian fluid flow and heat transfer toward a linearly stretching surface are reported. The flow is caused solely by the stretching of the sheet in its own plane with a velocity varying linearly with the distance from a fixed point. The constitutive relationship for the Casson fluid is used. The governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations by using similarity transformations. Exact solutions of the resulting ordinary differential equations are obtained. The effect of increasing Casson parameter, i.e., with decreasing yield stress （the fluid behaves as a Newtonian fluid as the Casson parameter becomes large）, is to suppress the velocity field. However, the temperature is enhanced as the Casson parameter increases. It is observed that the effect of transpiration is to decrease the fluid velocity as well as the temperature. The skin-friction coefficient is found to increase as the transpiration parameter increases.

Effects of thermal radiation on Casson fluid flow and heat transfer over an unsteady stretching surface subjected to suction/blowing

The unsteady flow of a Casson fluid and heat transfer over a stretching surface in presence of suction/blowing are investigated. The transformed equations are solved numerically by using the shooting method. The exact solution corre- sponding to the momentum equation for the steady case is obtained. Fluid velocity initially decreases with the increase of unsteadiness parameter. Due to an increasing Casson parameter the velocity field is suppressed. Thermal radiation enhances the effective thermal diffusivity and the temperature rises.

Stretching surface in rotating viscoelastic fluid

The boundary layer flow over a stretching surface in a rotating viscoelastic fluid is considered. By applying a similarity transformation, the governing partial differ- ential equations are converted into a system of nonlinear ordinary differential equations before being solved numerically by the Keller-box method. The effects of the viscoelastic and rotation parameters on the skin friction coefficients and the velocity profiles are thor- oughly examined. The analysis reveals that the skin friction coefficients and the velocity in the x-direction increase as the viscoelastic parameter and the rotation parameter in- crease. Moreover, the velocity in the y-direction decreases as the viscoelastic parameter and the rotation parameter increase.

Entropy Generation for Flow and Heat Transfer of Sisko-Fluid Over an Exponentially Stretching Surface

In the present study,the effects of the magnetic field on the entropy generation during fluid flow and heat transfer of a Sisko-fluid over an exponentially stretching surface are considered.The similarity transformations are used to transfer the governing partial differential equations into a set of nonlinear-coupled ordinary differential equations.Runge-Kutta-Fehlberg method is used to solve the governing problem.The effects of magnetic field parameter,local slip parameterλ,generalized Biot numberγ,Sisko fluid material parameter,Eckert number Ec,Prandtl number Pr and Brinkman number Br at two values of power law index on the velocity,temperature,local entropy generation number N_(G) and Bejan number Be are inspected.Moreover,the tabular forms for local skin friction coefficient and local Nusselt number under the effects of the physical parameters are exhibited.The current results are helpful in checking the entropy generation for Sisko-fluid.It is found that,an extra magnetic field parameter makes higher Lorentz force that suppresses the velocity.For shear thinning fluids(n<1),the temperature dominates and the velocity rises.Local entropy generation number is more for larger generalized Biot number,magnetic field parameter and Brinkman number.The local skin friction coefficient increases as magnetic field parameter and material parameter are increase and it decreases as local slip parameter increases.The local Nusselt number decreases as magnetic field parameter,local slip parameter and Eckert number are increase,while it increases as material parameter,generalized Biot number and Prandtl number are increase.

MHD effect of mixed convection boundary-layer flow of Powell-Eyring fluid past nonlinear stretching surface

Sufficient conditions are found for the existence of similar solutions of the mixed convection flow of a Powell-Eyring fluid over a nonlinear stretching permeable sur- face in the presence of magnetic field. To achieve this, one parameter linear group trans- formation is applied. The governing momentum and energy equations are transformed to nonlinear ordinary differential equations by use of a similarity transformation. These equations are solved by the homotopy analysis method （HAM） to obtain the approximate solutions. The effects of magnetic field, suction, and buoyancy on the Powell-Eyring fluid flow with heat transfer inside the boundary layer are analyzed. The effects of the non- Newtonian fluid （Powell-Eyring model） parameters ε and δon the skin friction and local heat transfer coefficients for the cases of aiding and opposite flows are investigated and discussed. It is observed that the momentum boundary layer thickness increases and the thermal boundary layer thickness decreases with the increase in ε whereas the momentum boundary layer thickness decreases and thermal boundary layer thickness increases with the increase in δ for both the aiding and opposing mixed convection flows.

Jeffrey fluid flow due to curved stretching surface with Cattaneo-Christov heat flux

The two-dimensional(2D) motion of the Jeffrey fluid by the curved stretching sheet coiled in a circle is investigated. The non-Fourier heat flux model is used for the heat transfer analysis. Feasible similarity variables are used to transform the highly nonlinear ordinary equations to partial differential equations(PDEs). The homotopy technique is used for the convergence of the velocity and temperature equations. The effects of the involved parameters on the physical properties of the fluid are described graphically.The results show that the curvature parameter is an increasing function of velocity and temperature, and the temperature is a decreasing function of the thermal relaxation time.Besides, the Deborah number has a reverse effect on the pressure and surface drag force.

Effects of transpiration on unsteady MHD flow of an upper convected Maxwell (UCM) fluid passing through a stretching surface in the presence of a first order chemical reaction

The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell （UCM） model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration （suction） and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration （suction） and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case.

Time–space dependent fractional boundary layer flow of Maxwell fluid over an unsteady stretching surface

Fractional boundary layer flow of Maxwell fluid on an unsteady stretching surface was investigated. Time-space dependent fractional derivatives are introduced into the constitutive equations of the fluid. We developed and solved the governing equations using explicit finite difference method and the L1- algorithm as well as shifted Grunwald-Letnikov formula. The effects of fractional parameters, relaxation parameter, Reynolds number, and unsteadiness parameter on the velocity behavior and characteristics of boundary layer thickness and skin friction were analyzed. Results obtained indicate that the behavior of boundary layer of viscoelastic fluid strongly depends on time-space fractional parameters. Increases of time fractional derivative parameter and relaxation parameter cause a decrease of velocity while boundary layer thickness increase, but the space fractional derivative parameter and fractional Reynolds number have the opposite effects.

Dual solutions of time-dependent magnetohydrodynamic stagnation point boundary layer micropolar nanofluid flow over shrinking/stretching surface

Time-dependent,two-dimensional(2 D)magnetohydrodynamic(MHD)micropolar nanomaterial flow over a shrinking/stretching surface near the stagnant point is considered.Mass and heat transfer characteristics are incorporated in the problem.A model of the partial differential expressions is altered into the forms of the ordinary differential equations via similarity transformations.The obtained equations are numerically solved by a shooting scheme in the MAPLE software.Dual solutions are observed at different values of the specified physical parameters.The stability of first and second solutions is examined through the stability analysis process.This analysis interprets that the first solution is stabilized and physically feasible while the second one is un-stable and not feasible.Furthermore,the natures of various physical factors on the drag force,skin-friction factor,and rate of mass and heat transfer are determined and interpreted.The micropolar nanofluid velocity declines with a rise in the suction and magnetic parameters,whereas it increases by increasing the unsteadiness parameter.The temperature of the micropolar nanofluid rises with increase in the Brownian motion,radiation,thermophoresis,unsteady and magnetic parameters,but it decreases against an increment in the thermal slip constraint and Prandtl number.The concentration of nanoparticles reduces against the augmented Schmidt number and Brownian movement values but rises for incremented thermophoresis parameter values.

Radiation efects on MHD stagnation point flow of nano fluid towards a stretching surface with convective boundary condition

The aim of the present paper is to study the numerical solutions of the steady MHD two dimensional stagnation point flow of an incompressible nano fluid towards a stretching cylinder.The effects of radiation and convective boundary condition are also taken into account.The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis.The resulting nonlinear momentum,energy and nano particle equations are simplifed using similarity transformations.Numerical solutions have been obtained for the velocity,temperature and nanoparticle fraction profles.The influence of physical parameters on the velocity,temperature,nanoparticle fraction,rates of heat transfer and nanoparticle fraction are shown graphically.

Convection of Maxwell fluid over stretching porous surface with heat source/sink in presence of nanoparticles:Lie group analysis

The convection of a Maxwell fluid over a stretching porous surface with a heat source/sink in the presence of nanoparticles is investigated. The Lie symmetry group transformations are used to convert the boundary layer equations into coupled nonlinear ordinary differential equations. The ordinary differential equations are solved numerically by the Bvp4c with MATLAB, which is a collocation method equivalent to the fourth-order mono-implicit Runge-Kutta method. Furthermore, more attention is paid to the effects of the physical parameters, especially the parameters related to nanoparticles, on the temperature and concentration distributions with consideration of permeability and the heat source/sink.

Unsteady flow of a Maxwell nanofluid over a stretching surface in the presence of magnetohydrodynamie and thermal radiation effects

The problem of unsteady magnetohydrodynamic(MHD)boundary layer flow of a non-Newtonian Maxwell nanofluid over a stretching surface with thennal radiation is considered.The Maxwell model is used to characterize the non-Newtonian fluid behaviour.An appropriate similarity transformation Is employed to transform the governing partial differential equations of mass,momentum,energy and nanoparticle concentration into ordinary differential equations.Tbe coupled non-linear ordinary differential equations are solved by using the variational finite element method.The flow features and the heat transfer characteristics and nanoparticle volume fraction are analyzed and discussed in detail for several sets of values of the governing flow parameters.Tbe results for the skin-friction coefficient,local Nusselt number and the local Sherwood number are presented in tables for various values of the flow controlling parameters.

Partial slip effect on non-aligned stagnation point nanofluid over a stretching convective surface

The present study inspects the non-aligned stagnation point nano fluid over a convective surface in the presence of partial slip. Two types of base fluids namely water and kerosene are selected with Cu nanoparticles. The governing physical problem is presented and transformed into a system of coupled nonlinear differential equations using suitable similarity transformations. These equations are then solved numerically using midpoint integration scheme along with Richardson extrapolation via Maple. Impact of relevant physical parameters on the dimensionless velocity and temperature profiles are portrayed through graphs. Physical quantities such as local skin frictions co-efficient and Nusselt numbers are tabularized.It is detected from numerical computations that kerosene-based nano fluids have better heat transfer capability compared with water-based nanofluids. Moreover it is found that water-based nanofluids offer less resistance in terms of skin friction than kerosene-based fluid. In order to authenticate our present study, the calculated results are compared with the prevailing literature and a considerable agreement is perceived for the limiting case.

Unsteady flow of a Maxwell hybrid nanofluid past a stretching/shrinking surface with thermal radiation effect

The non-Newtonian fluid model reflects the behavior of the fluid flow in global manufacturing progress and increases product performance.Therefore,the present work strives to analyze the unsteady Maxwell hybrid nanofluid toward a stretching/shrinking surface with thermal radiation effect and heat transfer.The partial derivatives of the multivariable differential equations are transformed into ordinary differential equations in a specified form by applying appropriate transformations.The resulting mathematical model is clarified by utilizing the bvp4c technique.Different control parameters are investigated to see how they affect the outcomes.The results reveal that the skin friction coefficient increases by adding nanoparticles and suction parameters.The inclusion of the Maxwell parameter and thermal radiation effect both show a declining tendency in the local Nusselt number,and as a result,the thermal flow efficacy is reduced.The reduction of the unsteadiness characteristic,on the other hand,considerably promotes the improvement of heat transfer performance.The existence of more than one solution is proven,and this invariably leads to an analysis of solution stability,which validates the first solution viability.

Effect of viscous dissipation and heat source on flow and heat transfer of dusty fluid over unsteady stretching sheet

This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface. The study considers the effects of frictional heating （viscous dissipation） and internal heat generation or ab- sorption. The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method. An analysis is carried out for two different cases of heating processes, namely, variable wall temperature （VWT） and variable heat flux （VHF）. The effects of various physical parameters such as the magnetic parameter, the fluid-particle interaction pa- rameter, the unsteady parameter, the Prandtl number, the Eckert number, the number density of dust particles, and the heat source/sink parameter on velocity and temperature profiles are shown in several plots. The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.

Analytical solution of magnetohydrodynamic sink flow

An analytical solution to the famous Falkner-Skan equation for the magnetohydrodynamic （MHD） flow is obtained for a special case, namely, the sink flow with a velocity power index of-1. The solution is given in a closed form. Multiple solution branches are obtained. The effects of the magnetic parameter and the wall stretching parameter are analyzed. Interesting velocity profiles are observed with reversal flow regions even for a stationary wall. These solutions provide a rare case of the Falkner-Skan MHD flow with an analytical closed form formula. They greatly enrich the analytical solution for the celebrated Falkner-Skan equation and provide better understanding of this equation.

Impact of Joule heating and multiple slips on a Maxwell nanofluid flow past a slendering surface

This manuscript presents a study of three-dimensional magnetohydrodynamic Maxwell nanofluid flow across a slendering stretched surface with Joule heating.The impact of binary chemical reactions,heat generation,thermal radiation,and thermophoretic effect is also taken into consideration.The multiple slip boundary conditions are utilized at the boundary of the surface.The appropriate similarity variable is used to transfer the flow modeled equations into ODEs,which are numerically solved by the utilization of the MATLAB bvp4c algorithm.The involved parameter's impact on the concentration,velocity,and temperature distribution are scrutinized with graphs.The transport rates(mass,heat)are also investigated using the same variables,with the results reported in tabulated form.It is seen that the fluid relaxation,magnetic,and wall thickness characteristics diminish the velocities of fluid.Further,the velocity,concentration,and temperature slip parameters reduce the velocities of fluid,temperature,and concentration distribution.The results are compared to existing studies and shown to be in dependable agreement.