Wedge Angle Parameter Research Articles

Soret and Dufour Effects on Mixed Convection Heat and Mass Transfer from a Vertical Wedge in a Porous Medium with Constant Wall Temperature and Concentration

This work studies the Soret and Dufour effects on the boundary layer flow due to mixed convection heat and mass transfer over a downward-pointing vertical wedge in a porous medium saturated with Newtonian fluids with constant wall temperature and concentration. A suitable coordinate transformation is performed, and the obtained nonsimilar equations are solved by cubic spline collocation method. The effects of the Dufour parameter, Soret parameter, wedge angle parameter, mixed convection variable, and buoyancy ratio on the heat and mass transfer characteristics has been studied. The local Nusselt number is found to decrease when the Dufour parameter is increased. Moreover, an increase in the Soret number leads to a decrease in the local Sherwood number. For natural-convection-dominated regime, an increase in the Soret number leads to an increase in the local Nusselt number for buoyancy assisting flows and a decrease for buoyancy opposing flows. As the wedge angle parameter is increased, the local Nusselt number and the local Sherwood number increases for forced convection and forced-convection-dominated mixed convection. The wedge angle parameter is insignificant for natural convection or natural-convection-dominated mixed convection.

Numerical Study of Boundary Layers With Reverse Wedge Flows Over a Semi-Infinite Flat Plate

This paper presents the classical approximation scheme to investigate the velocity profile associated with the Falkner–Skan boundary-layer problem. Solution of the boundary-layer equation is obtained for a model problem in which the flow field contains a substantial region of strongly reversed flow. The problem investigates the flow of a viscous liquid past a semi-infinite flat plate against an adverse pressure gradient. Optimized results for the dimensionless velocity profiles of reverse wedge flow are presented graphically for different values of wedge angle parameter β taken from 0≤β≤2.5. Weighted residual method (WRM) is used for determining the solution of nonlinear boundary-layer problem. Finally, for β=0 the results of WRM are compared with the results of homotopy perturbation method.

Analytic study of magnetohydrodynamic flow and boundary layer control over a wedge

A genuine variational principle developed by Gyarmati, in the field of thermodynamics of irreversible processes unifying the theoretical requirements of technical, environmental and biological sciences is employed to study the effects of uniform suction and injection on MHD flow adjacent to an isothermal wedge with pressure gradient in the presence of a transverse magnetic field. The velocity distribution inside the boundary layer has been considered as a simple polynomial function and the variational principle is formulated. The Euler-Lagrange equation is reduced to a simple polynomial equation in terms of momentum boundary layer thickness. The velocity profiles, displacement thickness and the coefficient of skin friction are calculated for various values of wedge angle parameter m, magnetic parameter 5m and suction/injection parameter H. The present results are compared with known available results and the comparison is found to be satisfactory. The present study establishes high accuracy of results obtained by this variational technique.

Thermodynamical modeling of viscous dissipation in magnetohydrodynamic flow

A genuine variational principle developed by Gyarmati, in the field of thermodynamics of irreversible processes unifying the theoretical requirements of technical, environmental and biological sciences is employed to study the effects of viscous dissipation and stress work on MHD forced convection flow adjacent to a non-isothermal wedge. The velocity and temperature distributions inside the boundary layer are considered as simple polynomial functions and the variational principle is formulated. The Euler-Lagrange equations are reduced to simple polynomial equations in terms of bound?ary layer thicknesses. The values of skin friction coefficient and the Nusselt number are presented for various values of wedge angle parameter m, wall temperature exponent 2m, magnetic parameter ?, Prandtl number (Pr) and Eckert number (Ec). The present results are compared with known available results and the comparison is found to be satisfactory and the present study establishes the fact that the accuracy is remarkable.

Modelling and Analytical Solution to Heat Transfer and Boundary Layer Flow with Suction and Injection

A genuine variational principle developed by Gyarmati in the field of thermodynamics of irreversible processes unifying the theoretical requirements of technical, environmental, and biological sciences is employed to study the effects of uniform suction and injection in the heat transfer and boundary layer flow with power function main stream velocity and surface temperature variations, over a wedge. The velocity and temperature distributions inside the boundary layer are considered as simple polynomial functions and the variational principle is formulated. The Euler–Lagrange equations are reduced to simple polynomial equations in terms of boundary layer thicknesses. The values of skin friction and heat transfer are calculated for any given values of Prandtl number Pr , wedge angle parameter m , wall temperature exponent n , and suction/injection parameter H . The obtained analytic results are compared with known numerical solutions and the comparison establishes the fact that the accuracy is remarkable.

Variable viscosity and thermal conductivity effects on combined heat and mass transfer in mixed convection over a UHF/UMF wedge in porous media: the entire regime

Mixed convection along a wedge embedded in a fluid-saturated porous media incorporating the variation of viscosity and thermal conductivity has been investigated for the case of uniform heat flux (UHF) and uniform mass flux (UMF). The governing equations, reduced to local nonsimilarity boundary layer equations using suitable transformations, have been solved numerically employing finite difference method. The entire regime of the mixed convection is included, as the mixed convection parameter χ varies from 0 (pure free convection) to 1 (pure forced convection). The numerical results for the dimensionless temperature, dimensionless concentration, local Nusselt (Sherwood) number are obtained. The decay of the dimensionless temperature and concentration profiles has been observed. The local Nusselt (Sherwood) number increase for the increase in buoyancy ratio N and for the decrease in wedge angle parameter λ. Also the local Nusselt number decreases for the increase of ε or γ and the local Sherwood number increases for the increase of γ and decreases for the increase of ε. The variations of the local Nusselt (Sherwood) number with the increase of χ have the phenomenon of minimum. It is observed that the Lewis number has a more pronounced effect on the local Sherwood number than it has on the local Nusselt number.

Analytical study of heat transfer and boundary layer flow with suction and injection

The Governing Principle of Dissipative Processes (GPDP) formulated by Gyarmati into non-equilibrium thermodynamics is employed to study the effects of heat transfer, two dimensional, laminar and constant property fluid flow in the boundary layer with suction and injection. The flow and temperature fields inside the boundary layer are approximated by simple third degree polynomial functions and the variational principle is formulated over the region of the boundary layer. The Euler–Lagrange equations of the principle are obtained as polynomial equations in terms of momentum and thermal layer thicknesses. These equations are solvable for any given values of Prandtl number Pr, wedge angle parameter m and suction/injection parameter H. The obtained analytical solutions are compared with known numerical solutions and the comparison shows the fact that the accuracy is remarkable.

Radiation Effect on Mixed Convection over an Isothermal Wedge in Porous Media: The Entire Regime

Numerical solutions are presented for the effect of radiation on mixed-convection flow of optically dense viscous fluids about an isothermal wedge embedded in a saturated porous medium. The partial differential equations are transformed into the nonsimilar boundary-layer equations, which are solved by the Keller box method. Numerical results for the dimensionless temperature profiles and the local Nusselt number parameter are presented for the combined convection parameter X, the wedge angle parameter A, the radiation-conduction parameter R d , and the surface temperature parameter H. The entire regime of the mixed convection is included, when X varies from 0 (pure free convection) to 1 (pure forced convection). As X varies from 0 to 1, the variation of the local Nusselt number parameter has the phenomenon of minimum. As the wedge angle parameter λ increases, the local Nusselt number parameter increases. When the radiation effect becomes significant (for the case of large values of R d and H), the local Nusselt number parameter is also greatly increased

The falkner-skan wedge flows of power-law fluids embedded in a porous medium

The non-Darcy flow characteristics of power-law non-Newtonian fluids past a wedge embedded in a porous medium have been studied. The governing equations are converted to a system of first-order ordinary differential equations by means of a local similarity transformation and have been solved numerically, for a number of parameter combinations of wedge angle parameter m, power-law index of the non-Newtonian fluids n, first-order resistance A and second-order resistance B, using a fourth-order Runge–Kutta integration scheme with the Newton–Raphson shooting method. Velocity and shear stress at the body surface are presented for a range of the above parameters. These results are also compared with the corresponding flow problems for a Newtonian fluid. Numerical results show that for the case of the constant wedge angle and material parameter A, the local skin friction coefficient is lower for a dilatant fluid as compared with the pseudo-plastic or Newtonian fluids.

Coupled heat and mass transfer in mixed convection over a VHF/VMF wedge in porous media: The entire regime

Coupled heat and mass transfer in mixed convection about a wedge embedded in saturated porous media has been analyzed by nonsimilar solutions for the case of variable heat flux (VHF) and variable mass flux (VMF). The entire regime of the mixed convection is included, as the mixed convection parameter χ* varies from 0 (pure free convection) to 1 (pure forced convection). The transformed nonlinear system of equations is solved by using an implicit finite difference method. The dimensionless temperature profiles, the dimensionless concentration profiles, the local Nusselt number and the local Sherwood number are presented. The decay of the dimensionless temperature profiles and the dimensionless concentration profiles has been observed in all cases. The local Nusselt number and the local Sherwood number increase for the increase in buoyancy ratioN*, wall heat/mass flux exponents and for the decrease in wedge angle parameter λ. The variations of the local Nusselt number and the local Sherwood number with the increase of χ* have the phenomenon of minimum. For a positive (negative)N*, increasing the Lewis number decreases (increases) the local Nusselt number. On the other hand, the local Sherwood number enhances as the Lewis number increases. Moreover, it is observed that the Lewis number has a more pronounced effect on the local Sherwood number than it has on the local Nusselt number.

Coupled heat and mass transfer in mixed convection over a wedge with variable wall temperature and concentration in porous media: The entire regime

A boundary layer analysis is used to investigate both heat and mass transfer characteristics of mixed convection about a wedge in saturated porous media under the coupled effects of thermal and mass diffusion. The surface of the wedge is maintained at a variable wall temperature (VWT) and variable wall concentration (VWC). The nonsimilar governing equations are obtained by using a suitable transformation and solved by Keller box method. Numerical results are presented for the local Nusselt number and the local Sherwood number. Increasing the buoyancy ratio N, the exponent of wall temperature/concentration n and the wedge angle parameter λ increases the local Nusselt number and the local Sherwood number. As mixed convection parameter χ varies from 0 to 1, the local Nusselt number and the local Sherwood number decrease initially, reach a minimum in the intermediate value of χ and then increase gradually. It is apparent that the Lewis number has a pronounced effect on the local Sherwood number than it does on the local Nusselt number. Furthermore, increasing the Lewis number decreases (increases) the local heat (mass) transfer rate.

Thermodynamical Modeling of Boundary Layer Flow With Suction and Injection

The variational principle developed by Gyarmati embodying the principles of non-equilibrium thermodynamics is employed to investigate the laminar boundary layer effect on wedge flows with suction and injection. The velocity function is assumed as a simple third-degree polynomial and the variational principle is formulated. The hydrodynamical boundary layer thickness is derived as the Euler-Lagrange equation of the variational principle. The velocity profiles and skin friction values were computed for various values of suction and injection parameter and wedge angle parameter. The comparison of the present solution with an available exact solution establishes the fact that the accuracy is remarkable.

Stability of Free-Convection Boundary Layer over a Wedge.

Laminar free convection boundary layer flow along a porous wedge which is maintained at a uniform heat-flux have been studied theoretically. Boundary layer equations for the basic steady flow are solved numerically using an efficient finite-difference method in combination with an iterative method. The temporal neutral stability theory for wavelike disturbance of Tollmien-Schrichying type are then presented for the velocity and temperature functions. The corresponding eigenvalue problem for the disturbance amplitude functions is also solved numerically. The neutral stability curves and the disturbance amplitude of the velocity or temperature are given for some values of wedge angle parameter m, suction/injection parameter ξ and modified Grashof number G. The Prandtl number Pγ is taken to 0.73 throughout this paper.

Magnetohydrodynamic free convection flow over a wedge in the presence of a transverse magnetic field

This paper presents the main results of a theoretical study focusing on the effects of a uniform magnetic field on the free convection flow of an electrically conducting fluid past an isothermal wedge. A very efficient numerical method has been used to solve the non-similar boundary layer equations. A range of values for the magnetic field parameter, wedge angle parameter and Prandtl number were considered. Flow and heat transfer characteristics are presented and discussed.

Shooting Method for Third Order Simultaneous Ordinary Differential Equations with Application to Magnetohydrodynamic Boundary Layer

An algorithm based on the shooting method has been developed for the solution of a two-point boundary value problem consisting of a system of third order simultaneous ordinary differential equations. The Falkner-Skan equations for electrically conducting viscous fluid with applied magnetic field has been solved by using this algorithm for various values of the wedge angle and magnetic parameters. The shooting method seems to be well convergent for a system as our results are in good agreement with those obtained by other methods. It is observed that both viscous boundary layer and magnetic boundary layer decrease while velocity as well as magnetic field increase with the increase of the wedge angle.

Plane Solutions for the Displacement and Traction-Displacement Problems for Anisotropic Elastic Wedges

The plane displacement and traction-displacement problems for anisotropic elastic wedges are solved by use of the complex function representation of the plane solution in conjunction with the Mellin transform. The special forms of the solutions pertinent to orthotropic wedges with a material symmetry axis along the wedge bisector is also presented and the dependence of the order of the stress singularities at the apex on the wedge angle and material parameters is shown graphically for this case.