Mixed Convection Stagnation Point Flow Research Articles

Viscous dissipation effects on unsteady mixed convective stagnation point flow using Tiwari-Das nanofluid model

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.

Steady laminar mixed convection stagnation-point flow of a nanofluid over a vertical permeable surface in the presence of a magnetic field

A similarity solution for a steady laminar mixed convection boundary layer flow of a nanofluid near the stagnation point on a vertical permeable plate with a magnetic field and a buoyancy force is obtained by solving a system of nonlinear ordinary differential equations. These equations are solved analytically by using a new kind of a powerful analytic technique for nonlinear problems, namely, the homotopy analysis method (HAM). Three different types of nanoparticles, namely, copper (Cu), alumina (Al2O3), and titanium oxide (TiO2), with water as the base fluid are considered. The influence of the volume fraction of nanoparticles, permeability parameter, magnetic parameter, and mixed convection parameter on the surface shear stress and surface heat transfer, as well as on the velocity and temperature profiles, is considered. It is observed that the skin friction coefficient and the local Nusselt number increase with the nanoparticle volume fraction for all types of nanoparticles considered in this study. The greatest values of the skin friction coefficient and the local Nusselt number are obtained for Cu nanoparticles.

Nonlinear thermal radiation aspects in stagnation point flow of tangent hyperbolic nanofluid with double diffusive convection

The objective of present study is to examine the nonlinear thermal radiation behavior in the mixed convection stagnation point flow of tangent hyperbolic nanofluid towards a stretching surface. Flow analysis is presented by considering the chemical reaction and heat generation/absorption effects. The convective type conditions are imposed to make the analysis of heat and mass transfer. Nanoparticles effects are encountered due to consideration of thermophoresis and Brownian motion. The governing nonlinear partial differential systems are transform into nonlinear ordinary differential systems by adequate similarity variables. Convergence of the series solutions are obtained for velocity, temperature and concentration. The behavior of significant physical quantities on the velocity, temperature and concentration distributions are analyzed through plots. Graphical results of the skin friction coefficient, local Nusselt and Sherwood numbers are also plotted and examined.

Effects of Second-Order Slip and Magnetic Field on Mixed Convection Stagnation-Point Flow of a Maxwellian Fluid: Multiple Solutions

In this paper, we investigate the effects of second-order slip and magnetic field on the nonlinear mixed convection stagnation-point flow toward a vertical permeable stretching/shrinking sheet in an upper convected Maxwell (UCM) fluid with variable surface temperature. Numerical results are obtained using the bvp4c function from matlab for the reduced skin-friction coefficient, the rate of heat transfer, the velocity, and the temperature profiles. The results indicate that multiple (dual) solutions exist for a buoyancy opposing flow for certain values of the parameter space irrespective to the types of surfaces whether it is stretched or shrinked. It is found that an applied magnetic field compensates the suction velocity for the existence of the dual solutions. Depending on the parametric conditions; elastic parameter, magnetic field parameter, first- and second-order slip parameters significantly controls the flow and heat transfer characteristics. The illustrated streamlines show that for upper branch solutions, the effects of stretching and suction are direct and obvious as the flow near the surface is seen to suck through the permeable sheet and drag away from the origin of the sheet. However, aligned but reverse flow occurs for the case of lower branch solutions when the mixed convection effect is less significant.

Mixed Convection Stagnation-Point Flow of Powell-Eyring Fluid with Newtonian Heating, Thermal Radiation, and Heat Generation/Absorption

AbstractThis article explores the steady mixed convection stagnation-point flow of Powell-Eyring fluid in the presence of thermal radiation, heat generation/absorption, and chemical reaction. Suitable transformations are considered to reduce nonlinear boundary layer partial differential equations into ordinary differential equations. Convergent series solutions of the resulting dimensionless problems are obtained. The effects of emerging physical parameters on the velocity, temperature, and concentration profiles are examined. Numerical values of skin-friction coefficient and local Nusselt and Sherwood numbers are tabulated and analyzed for different values of emerging parameters. A comparative analysis with existing solutions in a limiting sense is made.

Effect of partial slip on an unsteady MHD mixed convection stagnation-point flow of a micropolar fluid towards a permeable shrinking sheet

The objective of the present study was to investigate the partial slip effect on an unsteady two-dimensional mixed convection stagnation point flow towards a permeable shrinking sheet. The governing equations are reduced to a system of non-dimensional partial differential equations using a semi-similarity transformation, before being solved numerically by using Keller-box method. The features of the flow characteristics for different values of the governing parameters are analysed and discussed. The results indicate that the momentum, thermal and concentration boundary layer thicknesses increase with increasing mixed convection parameter for opposing flow, whereas the opposite effect is observed for assisting flow. The results also show that the surface velocity is higher when there is slip at a sheet compared to its absent. Further, the study indicates that the boundary layer thicknesses become thicker and thicker with increasing shrinking parameter, while the opposite effect is observed with increasing Hartmann number. Comparison with previously published work for special cases is performed and found to be in excellent agreement.

Soret and Dufour Effects on MHD Mixed Convection Heat and Mass Transfer of a Stagnation Point Flow towards a Vertical Plate in a Porous Medium with Chemical Reaction, Radiation and Heat Generation

The objective of this paper is to analyze the effects of heat and mass transfer in the presence of thermal radiation, internal heat generation and Dufour effect on an unsteady magneto-hydrodynamic mixed convection stagnation point flow towards a vertical plate embedded in a porous medium. The non-linear partial differential equations governing the flow are transformed into a set of ordinary differential equations using suitable similarity variables and then solved numerically using shooting method together with Runge- Kutta algorithm. The effects of the various parameters on the velocity, temperature and concentration profiles are depicted graphically and values of skin- friction coefficient, Nusselt number and Sherwood number for various values of physical parameters are tabulated and discussed. It is observed that the temperature increases for increasing values of the internal heat generation, thermal radiation and the Dufour number and hence thermal boundary layer thickness increases.

Non-linear Radiation Effects in Mixed Convection Stagnation Point Flow along a Vertically Stretching Surface

Abstract Present phenomenon is dedicated to analyze the combine effects of linear and non-linear Rosseland thermal radiations for stagnation point flow along a vertically stretching surface. For better variation in fluid flow and heat transfer, mixed convection is also considered to sustain this mechanism for significant influence. After incorporating these effects, the pertinent mathematical model is constructed in the form of non-linear partial differential equations and then be transformed into the system of coupled ordinary differential equations with the help of similarity transformation to be further solved numerically. Significant difference in the heat transfer enhancement can be observed through temperature profiles and tables of Nusselt number. Though histogram and isotherms plots, finally it is concluded that non-linear radiation provides better heat transfer rate at the surface of sheet as compare to the linear or absence of radiation effects.

Homotopy analysis method for unsteady mixed convective stagnation-point flow of a nanofluid using Tiwari-Das nanofluid model

Purpose – The current study is mainly motivated by the need to the development of the transient MHD mixed convection stagnation-point flow and heat transfer of an electrically conducting nanofluid over a vertical permeable stretching/shrinking sheet by means of Tiwari-Das nanofluid model. The purpose of this paper is to investigate the effects of the parameters governing the flow i.e. the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter and the velocity ratio parameter on dimensionless velocity and temperature distributions, skin friction coefficient and local Nusselt number. Design/methodology/approach – The mathematical model has been formulated based on Tiwari-Das nanofluid model. Three different types of water-based nanofluid with copper, aluminum oxide (alumina) and titanium dioxide (titania) as nanoparticles are considered in this investigation. Using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved analytically by the well-know homotopy analysis method. The present simulations agree closely with the previous studies in the especial cases. Findings – The results show that by increasing the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter or reducing the velocity ratio parameter, the skin friction coefficient enhances. Furthermore, the local Nusselt number enhances with different rates by increasing the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter and the velocity ratio parameter. Besides, the skin friction coefficient and the local Nusselt number are highest for copper-water nanofluid compared to the alumina-water and titania-water nanofluids. Originality/value – Tiwari-Das nanofluid model has not been applied for the flow with these characteristics as mentioned in the paper. A comprehensive survey on boundary layer behavior has been presented. There are few studies regarding as analysis on thermal and hydrodynamics boundary layer. All plots presented in the paper are new and did not report in any other study. The effects of the parameters governing the flow on skin friction coefficient and local Nusselt number have been illustrated in the paper while there are some conflicts with previous published article that have been interpreted in details in the paper.

Mixed Convection MHD Stagnation Point Flow over a Stretching Surface with the Effects of Heat Source or Sink and Viscous Dissipation

The present study deals with MHD mixed convection stagnation point flow over a stretching sheet with the effects of heat source/sink and viscous dissipation including convective boundary conditions. The governing partial differential equations are transformed into ordinary differential equations by applying similarity transformations. These equations are then solved numerically by using finite difference scheme known as the Keller Box method. The effects of various parameters on velocity and temperature profiles are presented graphically interpreted and the results are discussed.

Effects of chemical reaction on MHD mixed convection stagnation point flow toward a vertical plate in a porous medium with radiation and heat generation

The aim of the present study is to analyze the effects of chemical reaction on MHD mixed convection with the stagnation point flow towards a vertical plate embedded in a porous medium with radiation and internal heat generation. The governing boundary layer equations are transformed into a set of ordinary differential equations using similarity transformations. Then they are solved by shooting technique with Runge-Kutta fourth order iteration. The obtained numerical results are illustrated graphically and the heat and mass transfer rates are given in tabular form. The velocity and temperature profiles overshoot near the plate on increasing the chemical reaction parameter, Richardson number and magnetic field parameter.

Magnetohydrodynamic (MHD) mixed convection stagnation point flow of a nanofluid over a vertical plate with viscous dissipation

In this study, magnetohydrodynamic effects on the mixed convection flow of nanofluid particles, namely, Cu (copper) and Al2O3 (alumina) near a stagnation region over a vertical plate in the presence of viscous dissipation is investigated. The governing equations of the nanofluid flow model proposed by Tiwari and Das (Int. J. Heat Mass Transfer, 50, 2002 (2007). doi:10.1016/j.ijheatmasstransfer.2006.09.034) are converted into a dimensionless nonlinear system of ordinary differential equations by using the similarity transformation. The solution of the resulting equations is obtained numerically by using a very efficient implicit scheme known as the Keller box method. A comparison with previous studies is shown in tabular form and excellent agreement is found. The effects of pertinent parameters like magnetic parameter M, Eckert number Ec, and volume fraction parameter ϕ on velocity, temperature, skin friction coefficient, and local Nusselt number with fixed value of Prandtl number Pr = 6.2 are shown graphically and discussed. These results show that the skin friction coefficient increases for both nanoparticles in assisting and opposing flow cases because of increasing absolute values of M and Ec, on the other hand heat transfer rate is enhanced in the opposing flow case and reduced in the assisting flow case. The values of skin friction coefficient for both nanoparticles, namely, Cu and Al2O3 increase with the increase in volume fraction parameter ϕ in both assisting and opposing flow cases and Cu has a higher value than Al2O3. The same behavior is observed for local Nusselt number in opposing flow, but in assisting flow the value of local Nusselt number decreases with the increase of ϕ in the presence of magnetic and viscous dissipation effects and Cu has a smaller value than Al2O3.

Finite element analysis of heat and mass transfer by MHD mixed convection stagnation-point flow of a non-Newtonian power-law nanofluid towards a stretching surface with radiation

Abstract Magnetohydrodynamic mixed convection boundary layer flow of heat and mass transfer stagnation-point flow of a non-Newtonian power-law nanofluid towards a stretching surface in the presence of thermal radiation is investigated numerically. The non-Newtonian nanofluid model incorporates the effects of Brownian motion and thermophoresis. The basic transport equations are made dimensionless first and the coupled non linear differential equations are solved by finite element method. The numerical calculations for velocity, temperature and concentration profiles for different values of the physical parameters presented graphically and discussed. As well as for skin friction coefficient, local Nusselt and Sherwood numbers exhibited and examined.

Buongiorno’s model for double-diffusive mixed convective stagnation-point flow of a nanofluid considering diffusiophoresis effect of binary base fluid

The development of double-diffusive mixed convective boundary layer flow of a nanofluid near stagnation point region over a vertical surface has been investigated. Buongiorno’s model is used to incorporate the effects of Brownian motion and thermophoresis for the nanofluid, when the base fluid of the nanofluid is itself a binary fluid such as salty water. In addition the thermal energy equations include regular diffusion and cross-diffusion terms. Using the local similarity method, it is shown that a set of suitable similarity transformations reduces the non-linear coupled PDEs governing on the problem into a set of non-linear coupled ODEs. The analysis shows that velocity, temperature, solutal concentration and nanoparticle concentration profiles in the respective boundary layers depend on ten dimensionless physical parameters, namely the mixed convection parameter λ, the regular double-diffusive buoyancy parameter Nc, the nanofluid buoyancy ratio Nr, the Brownian motion parameter Nb, the thermophoresis parameter Nt, the modified Dufour parameter Nd, the regular Schmidt number Sc, the nanofluid Schmidt number Scn, Prandtl number Pr, and the Dufour-solutal Lewis number Ld. The results are presented in graphical form illustrating the effects of these parameters on boundary layer behavior. A sensitivity analysis of model is tabulated where the difference in each graph can be quantified in terms of root mean square deviation (RMSD) with respect to that with the default parameters. These results are supplemented with the data for the reduced Nusselt number and the two reduced Sherwood numbers, one for the solute and the other for the nanoparticles. It is found that for assisting flow regime the reduced Nusselt number is a decreasing function of each of Nr,NbandNt, and an increasing function of each of λ,NcandNd. The results demonstrate that the highest heat transfer rate is obtained for the situation that the thermophoresis effects are negligible. Moreover, a reduction in the reduced Sherwood number of nanoparticle is observed with increase in each of NcandNt, while this quantity increases with Nb.

Dual solutions for MHD stagnation-point flow of a nanofluid over a stretching surface with induced magneticfield

Present study deals with the buoyancy-driven MHD mixed convection stagnation-point flow, heat and mass transfer of a nanofluid over a non-isothermal stretching sheet in presence of induced magneticfield, radiation, chemical reaction, suction/injection and heat source/sink. The basic governing partial differential equations are reduced to a set of ordinary differential equations by using appropriate similarity transformation. The resulting system is solved numerically by bvp5c Matlab package. Numerical results are validated by comparing with the published results. The influence of non-dimensional governing parameters on velocity, induced magneticfield, temperature and concentration profiles along with coefficient of skin friction, local Nusselt and Sherwood numbers are discussed and presented with the help of graphs and tables. Comparisons are made with the existed studies. Results indicate that dual solutions exists only for certain range of suction/ injection parameter and injection parameter have tendency to enhance the momentum, thermal and concentration boundary layer thickness.

MHD mixed convection stagnation-point flow of a viscoelastic fluid towards a stretching sheet in a porous medium with heat generation and radiation

An analysis was carried out to study the effect of thermal radiation on magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid near the stagnation point of a vertical stretching sheet in a porous medium with internal heat generation–absorption. The flow is generated because of linear stretching of the sheet and influenced by the uniform magnetic field that is applied horizontally in the flow region. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically using an accurate implicit finite difference scheme. A comparison of the obtained results with previously published numerical results is done and the results are found to be in good agreement. The effects of the viscoelastic fluid parameter, magnetic field parameter, nonuniform heat source–sink, and the thermal radiation parameter on the heat transfer characteristics are presented graphically and discussed. The values of the skin friction coefficient and the local Nusselt number are tabulated for both cases of assisting and opposing flows.

Inclined Magnetic Field Effect in Stratified Stagnation Point Flow Over an Inclined Cylinder

Abstract The present work addresses the double stratified mixed convection stagnation point flow induced by an impermeable inclined stretching cylinder. The fluid is electrically conducting in the presence of an inclined magnetic field. Viscous dissipation is considered. Temperature and concentration at and away from the boundary are assumed variable. Series solutions of momentum, energy, and concentration equations are computed. The characteristics of various physical parameters on the distributions of velocity, temperature, and concentration are analyzed graphically. Behaviours of skin friction coefficient, Nusselt, and Sherwood numbers are discussed numerically. Comparison of the skin friciton coefficient is also examined in the limiting case.

MHD convective stagnation-point flow of nanofluids over a non-isothermal stretching sheet with induced magnetic field

This paper is concern with the investigation of buoyancy-driven hydromagnetic mixed convection stagnation-point flow of nanofluids over a stretching sheet in the presence of induced magnetic field. Three types of nanofluids namely, Cu–water, \(\hbox {Al}_2\hbox {O}_3\)–water, \(\hbox {TiO}_2\)–water are considered. The resulting system is solved numerically by a fifth-order Runge–Kutta–Fehlberg scheme with shooting technique. Numerical results are validated by comparing the present results with previously published results. Investigations predict that the effects of magnetic field is to increase induced magnetic field, whereas reverse effects is seen by increasing the volume fraction of the nanoparticles.

Magnetohydrodynamic Mixed Convection Stagnation-Point Flow of a Power-Law Non-Newtonian Nanofluid towards a Stretching Surface with Radiation and Heat Source/Sink

Two-dimensional MHD mixed convection boundary layer flow of heat and mass transfer stagnation-point flow of a non-Newtonian power-law nanofluid towards a stretching surface in the presence of thermal radiation and heat source/sink is investigated numerically. The non-Newtonian nanofluid model incorporates the effects of Brownian motion and thermophoresis. The basic transport equations are made dimensionless first and the complete nonlinear differential equations with associated boundary conditions are solved numerically by finite element method (FEM). The numerical calculations for velocity, temperature, and nanoparticles volume fraction profiles for different values of the physical parameters to display the interesting aspects of the solutions are presented graphically and discussed. The skin friction coefficient, the local Nusslet number and the Sherwood number are exhibited and examined. Our results are compatible with the existing results for a special case.

Mixed convection stagnation-point flow of nanofluids over a stretching/shrinking sheet in a porous medium with internal heat generation/absorption

In this paper, we analyzed the buoyancy-driven radiative non-isothermal heat transfer in a nanofluid stagnation-point flow over a stretching/shrinking sheet embedded in a porous medium.The effects of thermal radiation and internal heat generation/absorption along with suction/injection at the boundary are also considered. Three different types of nanofluids, namely the Copper-water, the Alumina-water and the Titanium dioxide water are considered. The resulting coupled nonlinear differential equations are solved numerically by a fifth-order Runge-Kutta-Fehlberg integration scheme with a shooting technique. A good agreement is found between the present numerical results and the available results in the literature for some special cases. The effects of the physical parameters on the flow and temperature characteristics are presented through tables and graphs, and the salient features are discussed. The results obtained reveal many interesting behaviors that warrant further study on the heat transfer enhancement due to the nanofluids.