Third Level Of Truncation Research Articles

Local Non-Similar Solutions for Boundary Layer Flow over a Nonlinear Stretching Surface with Uniform Lateral Mass Flux: Utilization of Third Level of Truncation

The present study aims to examine the effects of uniform lateral mass flux on the boundary layer flow induced by a non-linearly stretching surface. For uniform mass flux, the boundary layer flow does not conform to a similarity solution. The problem may be resolved by the similarity solution only when the transverse velocity at the boundary of the porous stretching surface is of the form vw∼xp−12. In other words, the flow becomes non-similar; to date, this has not been reported in the literature. That is why, in the current study, the local-similarity approximation up to the third level of truncation is utilized to solve the problem. The pseudo-similarity variable, stream function and transformed streamwise coordinate are defined such that the continuity equation is identically satisfied, and the momentum equation reduces to a non-similar dimensionless boundary layer equation. We derived the non-similar equations of the first, second and third levels of truncations and compared the numerical results obtained from different levels of truncations. In order to find numerical solutions to these equations, the built-in MATLAB routine, known as bvp4c, is used. Further, all non-similar terms that appear in the momentum equations are retained without any approximations. The approximations are introduced only in the subsidiary equations and relative boundary conditions. For the case of suction, the rate of increase in the numerical values of skin friction coefficient obtained from the first level of truncation with increasing velocity index parameter is found to be underestimated, while overestimation is found in the case of injection. The numerical results that were obtained from the third level of truncations are plotted against the embedding physical parameters and are then discussed.

Local non-similarity solution to impact of chemical reaction on MHD mixed convection heat and mass transfer flow over porous wedge in the presence of suction / injection

Combined heat and mass transfer on free, forced, and mixed convection flow along a porous wedge with magnetic effect in the presence of chemical reaction is investigated. The flow field characteristics are analyzed by the Runge-Kutta-Gill scheme with the shooting method as well as the local non-similarity method up to the third level of truncation, which are used to reduce the governing partial differential equations into nine ordinary differential equations. The governing boundary layer equations are converted to a dimensionless form by Falkner-Skan transformations. Because of the effect of suction/injection on the wall of the wedge with buoyancy force and variable wall temperature, the flow field is locally non-similar. Numerical calculations up to the third order level of truncation are carried out as a special case for different values of dimensionless parameters. Effects of the magnetic field strength in the presence of chemical reaction with variable wall temperature and concentration on the dimensionless velocity, temperature and concentration profiles are shown graphically.

Effects of Chemical Reactions, Heat, and Mass Transfer on Nonlinear Magnetohydrodynamic Boundary Layer Flow over a Wedge with a Porous Medium in the Presence of Ohmic Heating and Viscous Dissipation

An analysis is carried out to study the effects of chemical reactions, heat, and mass transfer on nonlinear magnetohydrodynamic (MHD) boundary layer flow over a wedge with a porous medium in the presence of Ohmic heating and viscous dissipation. The fluid is assumed to be incompressible, viscous, electrically conducting, and Boussinesq. A magnetic field is applied transversely to the direction of the flow. A numerical solution for the steady MHD laminar boundary layer flow over a wall of the wedge with suction in the presence of species concentration and mass diffusion has been obtained by transforming the governing equations to nonlinear ordinary differential equations through similarity transformations and further utilizing the R. K. Gill method. Numerical calculations up to the third level of truncation are carried out for different values of dimensionless parameters of the problem under consideration. An analysis of the results obtained shows that the flow field is influenced appreciably by the strength of the magnetic field, chemical reactions, and suction at the wall of the wedge.

Effects of chemical reaction, heat and mass transfer along a wedge with heat source and concentration in the presence of suction or injection

An approximate numerical solution for the steady laminar boundary-layer flow over a wall of the wedge with suction or injection in the presence of species concentration and mass diffusion has been obtained by solving the governing equations using numerical technique. The fluid is assumed to be viscous and incompressible. Numerical calculations up to third level of truncation are carried out for different values of dimensionless parameters and an analysis of the results obtained shows that the flow field is influenced appreciably by the chemical reaction, heat source and suction or injection at the wall of the wedge.

Thermal stratification effects on non linear MHD laminar boundary—layer flow over a wedge with suction or injection

An approximate numerical solution for thermal stratification on MHD steady laminar boundary-layer flow over a wall of the wedge with suction or injection. The fluid is assumed to be viscous and electrically conducting Boussinesq fluid. A magnetic field is applied transversely to the direction of the flow. The governing partial differential equations of the problem subject to their boundary conditions are solved using R.K.Gill numerical method. Numerical calculations up to third level of truncation are carried out for different values of dimensionless parameters in the problem

EFFECTS OF CHEMICAL REACTION, HEAT AND MASS TRANSFER ON NON-LINEAR MHD LAMINAR BOUNDARY-LAYER FLOW OVER A WEDGE WITH SUCTION OR INJECTION

An approximate numerical solution for the steady MHD laminar boundary-layer flow over a wall of the wedge with suction or injection in the presence of species concentration and mass diffusion has been obtained by solving the governing equations using R.K.Gill method.The fluid is assumed to be viscous and electrically conducting Boussinesq fluid. A magnetic field is applied transversely to the direction of the flow. Numerical calculations up to third level of truncation are carried out for different values of dimensionless parameters and an analysis of the results obtained shows that the flow field is influenced appreciably by the magnetic field,chemical reaction and suction or injection at the wall of the wedge

Local Non-similarity Solutions for Mixed Convection Flow with Lateral Mass Flux over an Inclined Flat Plate Embedded in a Saturated Porous Medium

The problem of mixed convection along an inclined wall, acting as a source or sink with lateral mass flux, embedded in a porous medium is solved by the local non similarity method. The wall surface temperature, the flow free stream velocity and lateral surface velocity vary in a power law along the wall. The two components of buoyancy force are retained. The inclination of the plate ranges from horizontal to vertical. Numerical solutions are carried out up to the third level of truncation and results are presented for a wide range of mass flux parameter at different wall temperature distributions and inclination angles.

Boundary and inertia effects on conjugate mixed convection heat transfer from a vertical plate fin in a high-porosity porous medium

Conjugate mixed convection heat transfer along a vertical plate fin embedded in a saturated high-porosity porous medium has been studied. A local non-similarity solution, up to the third level of truncation, has been obtained for convective flow in the porous medium. The effects of solid boundary and inertia forces which have been neglected in the Darcy flow model were taken into account. Results were obtained for Pr = 7, 20, 50, and other parameters in the range of 0 ⩽ Ω ⩽ 2.0 and 0 ⩽ Ncc ⩽ 2.0. For pure forced convection and low Ncc (nearly isothermal), the error resulting from omitting the boundary and inertia forces decreases with increasing downstream distance. For mixed convection flow the effects of boundary and inertia on local heat transfer coefficient and local heat flux become very significant at large values of Ncc, especially downstream.

Conjugate natural convection about a vertical cylindrical fin with lateral mass flux in a saturated porous medium

The problem of conjugate natural convection about a vertical cylindrical fin with uniform lateral mass flux in a fluid-saturated porous medium has been studied numerically. Solutions based on the third level of truncation are obtained by the local nonsimilarity method. The effects of the surface mass flux, the conjugate convection-conduction parameter, and the surface curvature on fin temperature distribution, local heat transfer coefficient, local heat flux, average heat transfer coefficient, and total heat transfer rate are presented. A comparison with finite-difference solutions for the case of constant wall temperature was made, and found in a good agreement.

THE INFLUENCE OF LATERAL MASS FLUX ON CONJUGATE NATURAL CONVECTION FROM A VERTICAL PLATE FIN IN A SATURATED POROUS MEDIUM

The effects of lateral surface mass transfer on the natural convection boundary layer about a vertical plate fin with solution-determined thermal boundary conditions (or fin temperature distributions) in a fluid-saturated porous medium were studied numerically. It was found that the governing parameters far the problem are the convection-conduction parameter Ncc and the lateral mass flux parameter fw. The non-similar solutions were obtained by the local nonsimilarity method and were carried out up to the third level of truncation. The effects of mass flux on fin temperature distribution, boundary-layer thickness, local heat transfer coefficient, local heat flux, and total heat transfer rate are presented and discussed.

Conjugated, mixed convection-conduction heat transfer along a cylindrical fin in a porous medium

The problem of mixed convection flow about a vertical, cylindrical fin embedded in a porous medium is studied analytically based on the conjugate convection-conduction theory. A local nonsimilarity solution, up to the third level of truncation, is obtained for the convective flow in the porous medium. The resulting set of ordinary differential equations are coupled with the one-dimensional heat conduction equation in the fin through interfacial conditions. The effects of the conjugate convection-conduction parameter, surface curvature and the mixed convection parameter on the fin temperature distribution, local heat transfer coefficient, local heat flux, total heat transfer and fin efficiency are illustrated. The results of the present analysis are found to have trends similar to those of the classical fluids.

The Influence of Lateral Mass Flux on Conjugate Natural Convection from a Vertical Plate Fin in a Saturated Porous Medium

The effects of lateral surface mass transfer on the natural convection boundary layer about a vertical plate fin with solution-determined thermal boundary conditions (or fin temperature distributions) in a fluid-saturated porous medium were studied numerically. It was found that the governing parameters for the problem are the convection-conduction parameter N/sub cc/ and the lateral mass flux parameter f/sub w/. The nonsimilar solutions were obtained by the local nonsimilarity method and were carried out up to the third level of truncation. The effects of mass flux on fin temperature distribution, boundary-layer thickness, local heat transfer coefficient, local heat flux, and total heat transfer rate are presented and discussed.

MIXED CONVECTION ABOUT A NONISOTHERMAL CYLINDER AND SPHERE IN A POROUS MEDIUM

The problems of mixed convection about a nonisothermai horizontal cytiner and sphere embedded in a porous medium are analyzed based on a curvilinear orthogonal coordinate system together with boundary-layer simplifications. Different transformations were performed for the horizontal cylinder and the sphere, and the resulting equations are identical for the two geometries. Approximate solutions for the problems are obtained based on the nonlocal similarity method. Numerical computations for the temperature distribution and heat flux were carried out up to the third level of truncation. The effects of buoyancy and wall temperature variations on heat transfer characteristics about a heated horizontal cylinder and sphere in a porous medium are examined.

Non-similar boundary layer analysis of mixed convection about a horizontal heated surface in a fluid-saturated porous medium

An analysis has been performed for the study of the buoyancy effects in the parallel and stagnation forced flows in a porous medium adjacent to a heated surface with wall temperature being a power function of distance, i.e., T W ≈ x λ . Local non-similarity methods were used to obtain approximate solutions for the problem. Numerical solutions were carried out to the third level of truncation for parallel aiding flow over a heated horizontal surface with 0 ≤ λ ≤ 2 for a wide range of buoyancy parameters. For wall temperature with λ < 0.5, it is found that the differences between the first and the third level of truncations are very small. The difference is more marked for λ > 0.5, and it accentuates as the value of the buoyancy parameter or λ is increased.

Local non-similar solutions for free convective flow with uniform lateral mass flux in a porous medium

The problem of free convection along a vertical plane source or sink with uniform lateral mass flux in a porous medium is solved by the local non-similarity approximation. Solutions are carried out to the third level of truncation. Results for heat transfer characteristics as obtained from the third level of truncation are found in excellent agreement with a previous investigation using the finite difference method for a wide range of the mass flux parameter.

Local Nonsimilar Solutions for Natural Convection on a Vertical Cylinder

The local nonsimilarity solution method has been applied to solve for natural convection on a vertical cylinder for conditions where there are large deviations from the flat plate results. To assess and insure the accuracy of the results, solutions were obtained for three levels of truncation of the governing equations. The solutions were carried out for Pr = 0.733 and for a range of cases extending from small deviations from the flat plate to a factor-of-four deviation between the local heat fluxes for the cylinder and the flat plate. The results provided by the local similarity solutions were found to be highly accurate over this range. Comparisons were made with available results for the local and surface-integrated heat transfer, and solution methods were identified which appear promising for application beyond the range studied here. A presentation of representative temperature and velocity profiles showed only small deviations between the local similarity solutions and those for the third level of truncation.