Mixed Convection Boundary Layer Flow Research Articles

Chemical reaction effect on MHD boundary-layer flow of two-phase nanofluid model over an exponentially stretching sheet with a heat generation

An analysis has been carried out to study a problem of the chemical reaction and heat generation or absorption effects on MHD mixed convective boundary layer flow of a nanofluid through a porous medium due to an exponentially stretching sheet. Nonlinear partial differential equations are converted into a set of ordinary differential equations by similarity transformations. The transformed equations are solved numerically by using an efficient numerical shooting technique with a fourth–fifth order Runge–Kutta method scheme. The results corresponding to the dimensionless the velocity, temperature, concentration profiles and the reduced Nusselt number, Sherwood number and skin friction coefficient are displayed graphically for various pertinent parameters. It was found that Nusselt number Rex−1/2Nux is a decreasing function of the heat generation or absorption parameter Q and the chemical reaction parameter χ, but Sherwood number Rex−1/2Shx is an increasing function of the heat generation or absorption parameter Q and chemical reaction parameter χ. The skin friction coefficient Rex−1/2Cf is an increasing function of heat generation or absorption parameter Q while decreasing function of the chemical reaction parameter χ. Comparison with previously published work is performed and excellent agreement is observed.

Mixed convection boundary layer flow past a vertical cone embedded in a porous medium subjected to a convective boundary condition

In the present analysis, we study the steady mixed convection boundary layer flow past a vertical cone embedded in a porous medium subjected to a convective boundary condition. The governing partial differential equations are reduced to the coupled nonlinear ordinary differential equations using a similarity transformation before being solved numerically by a shooting method. Both assisting and opposing flows are considered. The influence of the convective heat transfer parameter is analysed and discussed through graphs. Dual solutions are found to exist for the case of opposing flow.

Thermal diffusion and diffusion-thermo effects on mixed convection from an exponentially impermeable stretching surface

The objective of the present article is to investigate the Dufour (diffusion-thermo) and Soret (thermal diffusion) effects on the steady double diffusive mixed convection boundary layer flows over an impermeable exponentially stretching sheet in an exponentially moving free stream under the influence of chemically reactive species. The nonlinear partial differential equations governing the flow, temperature and species concentration fields are expressed in non-dimensional form with the help of suitable non-similar transformations. The resulting final non-dimensional set of coupled nonlinear partial differential equations is solved by using an implicit finite difference scheme in conjunction with the Newton’s linearization technique. The effects of various governing parameters involved in the velocity, temperature and species concentration fields are discussed in this article. The results display that the streamwise co-ordinate ξ (non-similarity variable) profoundly influences the flow, thermal and concentration fields which reveal the accountability of non-similar solutions. Results also indicate that the Dufour number Df decreases the heat transfer coefficient while the Soret number Sr decreases the mass transfer coefficient.

Influence of convective conditions on three dimensional mixed convective hydromagnetic boundary layer flow of Casson nanofluid

The present work deals with the steady laminar three-dimensional mixed convective magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid over a bidirectional stretching surface. A uniform magnetic field is applied normal to the flow direction. Similarity variables are implemented to convert the non-linear partial differential equations into ordinary ones. Convective boundary conditions are utilized at surface of the sheet. A numerical technique of Runge–Kutta–Fehlberg (RFK45) is used to obtain the results of velocity, temperature and concentration fields. The physical dimensionless parameters are discussed through tables and graphs.

Hydromagnetic Mixed Convective Nanofluid Slip Flow past an Inclined Stretching Plate in the Presence of Internal Heat Absorption and Suction

The steady two-dimensional mixed convective boundary layer flow of nanofluid over an inclined stretching plate with the effects of magnetic field, slip boundary conditions, suction and internal heat absorption have been investigated numerically. Two different types of nanoparticles, namely copper and alumina with water as the base fluid are considered. Similarity transformations are employed to transform the governing nonlinear partial differential equations into coupled non-linear ordinary differential equations. The influence of pertinent parameters such as magnetic interaction parameter, angle of inclination, volume fraction, suction parameter, velocity slip parameter, thermal jump parameter, heat absorption parameter, mixed convection parameter and Prandtl number on the flow and heat transfer characteristics are discussed. A representative set of results are displayed graphically to illustrate the issue of governing parameters on the dimensionless velocity and temperature. Numerical values of skin friction coefficient and the Nusselt number are shown in tabular form. A comparative study between the previously published work and the present results in a limiting sense reveals excellent agreement between them.

Radiation Effect on Mixed Convection Boundary Layer Flow of a Viscoelastic Fluid over a Horizontal Circular Cylinder with Constant Heat Flux

Radiation Effect on Mixed Convection Boundary Layer Flow of a Viscoelastic Fluid over a Horizontal Circular Cylinder with Constant Heat Flux

Mixed Convection Boundary Layer Flow Near the Lower Stagnation Point of a Cylinder Embedded in a Porous Medium Using a Thermal Nonequilibrium Model

The present paper analyzes the problem of two-dimensional mixed convection boundary layer flow near the lower stagnation point of a cylinder embedded in a porous medium. It is assumed that the Darcy's law holds and that the solid and fluid phases of the medium are not in thermal equilibrium. Using an appropriate similarity transformation, the governing system of partial differential equations are transformed into a system of ordinary differential equations, before being solved numerically by a finite-difference method. We investigate the dependence of the Nusselt number on the solid–fluid parameters, thermal conductivity ratio and the mixed convection parameter. The results indicate that dual solutions exist for buoyancy opposing flow, while for the assisting flow, the solution is unique.

THE VISCOUS DISSIPATION EFFECTS ON THE MIXED CONVECTION BOUNDARY LAYER FLOW ON A HORIZONTAL CIRCULAR CYLINDER

Present study consider the mathematical modeling for mixed convection boundary layer flow and heat transfer on a horizontal circular cylinder with viscous dissipation. The transformed partial differential equations are solved numerically by using an implicit finite-difference scheme known as the Keller-box method. Numerical solutions are obtained for the reduced Nusselt number, the local skin friction coefficient, the velocity and temperature profiles. The features of the flow for various values of the Prandtl number, Eckert number and mixed convection parameter are discussed. The results in this paper is original and important for the researchers working in the area of boundary layer flow and this can be used as reference and also as complement comparison purpose in future

Magneto-hydrodynamic mixed convection of a non-Newtonian power-law nanofluid past a moving vertical plate with variable density

Present paper investigates the magnetohydrodynamic boundary layer mixed convection flow over a moving vertical plate in a non-Newtonian power-law nanofluid with variable density. The governing partial differential equations are transformed into a ordinary differential equations by suitable similarity transformations. The system of coupled non-linear ordinary differential equations are solved numerically using variational finite element method. The solutions for the flow and heat transfer characteristics are computed numerically for various values of flow controlling parameters. Investigation predict that an increase in the values of magnetic field parameter and thermophoresis parameter is to enhance the temperature and nanoparticle volume fraction profiles. Increasing power-law index reduces the velocity, temperature and nanoparticle volume fraction profiles. An increase in the Brownian motion and Lewis number is reduces the nanoparticle volume fraction profiles and temperature field is decreases with increasing Pradtl number. An increase in power-law index and thermophoresis is found to be increase in the skin friction co-efficient but decrease in the heat transfer co-efficient.

Mixed convection Jeffrey fluid flow over an exponentially stretching sheet with magnetohydrodynamic effect

The steady two-dimensional MHD mixed convection boundary layer flow and heat transfer of a Jeffrey fluid over an exponentially stretched plate is investigated. The governing partial differential equations are first reduced to nonlinear ordinary differential equations, before being solved numerically using an implicit finite difference scheme. Local similarity solutions are obtained for some embedded parameters, such as Deborah number β, mixed convection parameter λ, Prandtl number Pr and Hartmann number H, are analyzed and discussed.

Unsteady laminar mixed convection boundary layer flow near a vertical wedge due to oscillations in the free-stream and surface temperature

The unsteady laminar boundary layer characteristics of mixed convection flow past a vertical wedge have been investigated numerically. The free-stream velocity and surface temperature are assumed to be oscillating in the magnitude but not in the direction of the oncoming flow velocity. The governing equations have been solved by two distinct methods, namely, the straightforward finite difference method for the entire frequency range, and the extended series solution for low frequency range and the asymptotic series expansion method for high frequency range. The results demonstrate the effects of the Richardson number, Ri, introduced to quantify the influence of mixed convection and the Prandtl number, Pr, on the amplitudes and phase angles of the skin friction and heat transfer. In addition, the effects of these parameters are examined in terms of the transient skin friction and heat transfer.

Axisymmetric mixed convective MHD flow over a slender cylinder in the presence of chemically reaction

The present analysis is focused on the study of the magnetic effect on coupled heat and mass transfer by mixed convection boundary layer flow over a slender cylinder in the presence of a chemical reaction. The buoyancy effect due to thermal diffusion and species diffusion is investigated. Employing suitable similarity transformations, the governing equations are transformed into a system of coupled non-linear ordinary differential equations and are solved numerically via the implicit, iterative, second order finite difference method. The numerical results obtained are compared with the available results in the literature for some special cases and the results are found to be in excellent agreement. The velocity, temperature, and the concentration profiles are presented graphically and analyzed for several sets of the pertinent parameters. The pooled effect of the thermal and mass Grashof number is to enhance the velocity and is quite the opposite for temperature and the concentration fields.

Similarity Solutions of Unsteady Mixed Convective Boundary Layer Flow of Viscous Incompressible Fluid along Isothermal Horizontal Plate

Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.

STEADY DOUBLE-DIFFUSIVE MIXED CONVECTION BOUNDARY LAYER FLOW PAST A VERTICAL FLAT PLATE EMBEDDED IN A POROUS MEDIUM FILLED BY A NANOFLUID USING BUONGIORNO'S MODEL

The steady double-diffusive mixed convection boundary layer flow past a vertical flat plate embedded in a porous medium filled by a nanofluid is investigated numerically. Using a similarity transformation, the partial differential equations are transformed into ordinary differential equations before being solved numerically by a shooting method and Maple software. The effects of the mixed convection parameter on the flow and heat transfer characteristics are investigated. The results show that it is possible to obtain dual solutions for the opposing flow, while for the assisting flow, the solution is unique. The local Nusselt number, the local Sherwood number, and the local nanoparticle mass flux increase as the mixed convection parameter increases.

Transient Combined Convective Heat Transfer over a Stretching Surface in a Non-Newtonian Nanofluid Using Buongiorno’s Model

The present paper investigates the transient mixed convective boundary layer flow of an incompressible non-Newtonian quiescent nanofluid adjacent to a vertical stretching surface. The effects of the Brownian motion and thermophoresis are included for the nanofluid. Using appropriate non-similarity transformations the non-dimensional, coupled and highly non-linear system of equations is solved numerically using the efficient Keller-box implicit finite difference method for the whole transient from t=0 (initial state) to (final steady-state flow). The box method is unconditionally stable. Numerical results for dimensionless velocity (f’), micro-rotation (g), temperature (θ), nanoparticle volume fraction (Φ) at final steady state flow, skin friction function (), Nusselt number function () and Sherwood number function () have been presented on various parameters inform of tables and graphs. The results indicate that as Nb and Nt increase, the Nusselt number decreases whereas Sherwood number increases at initial and early state time but decreases at the final steady state time. As the K increases, the friction factor decreases whereas surface mass transfer rate and the surface heat transfer rates slightly increase. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work. The study has many practical applications such as extrusion of plastic sheets, paper production, glass blowing, metal spinning and drawing plastic films.

Mixed convection flow over a horizontal circular cylinder in a viscous fluid at the lower stagnation point with convective boundary conditions

In this paper, we study the steady mixed convection boundary layer flow over a horizontal circular cylinder in a viscous fluid with the bottom surface of the cylinder heated by convection from a hot fluid. The resulting system of nonlinear partial differential equations is solved numerically using an efficient implicit finite-difference scheme known as the Keller box method along with Newton’s linearization techniques. The special case at the lower stagnation point of the cylinder is considered. The solutions for the flow and heat transfer characteristics are obtained and presented for various values of the governing parameters, namely, the mixed convection parameter, the Prandtl number, and the conjugate parameter. The effects of these parameters on the flow and heat transfer characteristic are thoroughly examined in this study.

Temperature Dependent Variable Properties on Mixed Convective Unsteady MHD laminar Incompressible fluid Flow with Heat Transfer and Viscous Dissipation

In the present paper we investigated that the numerical solution of mixed convective laminar boundary layer flow with uniform transverse magnetic field for a vertical porous plate. The fluid properties are considered the nonlinear functions of temperature as μ = μ∞(T / T∞)A and κ = κ∞(T / T∞)C For flue gases the values of the exponents A and C are taken as A=0.7, and C=0.83. Also time dependent suction velocity is considered. The governing equations are reduced into ordinary differential equations by introducing the suitable similarity variables and then solved numerically by using sixth ordered Runge-Kutta method and Nachtsheim Swigert iteration technique. The numerical results of our physical interest are shown graphically and tabular form.

Mixed convection boundary-layer flow of a micro polar fluid towards a heated shrinking sheet by homotopy analysis method

A comprehensive study of two dimensional stagnation flow of an incompressible micro polar fluid with heat transfer characteristics towards a heated shrinking sheet is analyzed analytically. The main goal of this paper is to find the analytic solutions using a powerful technique namely the Homotopy Analysis Method (HAM) for the velocity and the temperature distributions and to study the steady mixed convection in two-dimensional stagnation flows of a micro polar fluid around a vertical shrinking sheet. The governing equations of motion together with the associated boundary conditions are first reduced to a set of self-similar nonlinear ordinary differential equations using a similarity transformation and are then solved by the HAM. Some important features of the flow and heat transfer for the different values of the governing parameters are analyzed, discussed and presented through tables and graphs. The heat transfer from the sheet to the fluid decreases with an increase in the shrinking rate. Micro polar fluids exhibit a reduction in shear stresses and heat transfer rate as compared to Newtonian fluids, which may be beneficial in flow and thermal control of polymeric processing.

Unsteady mixed convection of a micropolar fluid past a circular cylinder due to time-dependent free stream velocity and temperature

Unsteady mixed convection boundary-layer flow of an electrically conducting micropolar fluid past a circular cylinder is investigated taking into account the effect of thermal radiation and heat generation or absorption. The reduced non-similar boundary-layer equations are solved using the finite difference method. It is found that the magnitude of the friction factor and the couple stress significantly increases due to the increase of the mixed convection parameter, the conduction-radiation parameter, the surface temperature parameter, the heat absorption parameter and the frequency parameter. However the magnitude of the heat transfer rate decreases with these parameters. The converse characteristics are observed for the Prandtl number. The magnitude of the couple stress and the heat transfer rate is seen to decrease whereas the magnitude of the skin factor increases with increasing the vortex viscosity parameter. The magnetic field parameter reduces the skin factor, couple stress and heat transfer rate. The amplitude of oscillation of the transient skin factor and couple stress gradually increases owing to an increase of $\xi$. But the transient heat transfer rate is found to be oscillating with almost the same amplitude for any value of $\xi$. The amplitude of oscillation of the transient skin factor and couple stress increases with an increase of $S$ and $\xi$ while the amplitude of the transient heat transfer rate increases with increasing Pr and $S$.

Non-similar solutions of mixed convection flow from an exponentially stretching surface

Abstract In this paper we focus on to obtaining non-similar solutions for steady two dimensional double diffusive mixed convection boundary layer flows over an impermeable exponentially stretching sheet in an exponentially moving free stream under the influence of chemically reactive species. The nonlinear partial differential equations governing the flow, temperature and species concentration fields are presented in non-dimensional form with the help of suitable non-similar transformations. The resulting final non-dimensional set of coupled nonlinear partial differential equations is solved by using an implicit finite difference scheme in combination with the Newton’s linearization technique. The effects of various non-dimensional physical parameters on velocity, temperature and species concentration fields are discussed. The results reveal that the streamwise coordinate ξ remarkably influences the flow, thermal and solutal concentration fields which display the existence of non-similar solutions.