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.

Series Solution of Non-Similarity Boundary-Layer Flow in Porous Medium

This paper aims to present complete series solution of non-similarity boundary-layer flow of an incompressible viscous fluid over a porous wedge. The corresponding nonlinear partial differential equations are solved analytically by means of the homotopy analysis method (HAM). An auxiliary parameter is introduced to ensure the convergence of solution series. As a result, series solutions valid for all physical parameters in the whole domain are given. Then, the effects of physical parameters γ and Prandtl number Pr on the local Nusselt number and momentum thickness are investigated. To the best of our knowledge, it is the first time that the series solutions of this kind of non-similarity boundary-layer flows are reported.

Series solution of non-similarity natural convection boundary-layer flows over permeable vertical surface

The non-similarity solution for natural convection from a permeable isothermal vertical wall is considered. The governing boundary-layer equations for non-similarity flow and temperature fields are solved using the homotopy analysis method. The homotopy-Pade’ technique is applied to accelerate the convergence of the homotopy-series solution. The influence of physical parameters on the non-similarity flows is investigated in detail. Different from the previous analytic results,the homotopy-series solutions are convergent and valid for all physical parameters in the whole domain 0 x 【 ∞ and 0 y 【 ∞.

Flow and heat transfer over hyperbolic stretching sheets

The boundary layer flow and heat transfer analysis of an incompressible viscous fluid for a hyperbolically stretching sheet is presented. The analytical and numer- ical results are obtained by a series expansion method and a local non-similarity （LNS） method, respectively. The analytical and numerical results for the skin friction and the Nusselt number are calculated and compared with each other. The significant observation is that the momentum and the thermal boundary layer thickness decrease as the distance from the leading edge increases. The well-known solution of linear stretching is found as the leading order solution for the hyperbolic stretching.

Unsteady Mixed Convection Flow along Symmetric Wedge with Variable Surface Temperature Embedded in a Porous Medium Saturated with a Nanofluid

Laminar two-dimensional unsteady mixed-convection boundary-layer flow of a viscous incompressible fluid past asymmetric wedge with variable surface temperature embedded in a porous medium saturated with a nanofluid has been studied. The employed mathematical model for the nanofluid takes into account the effects of Brownian motion and thermophoresis. The velocity in the potential flow is assumed to vary arbitrary with time. The non-Darcy effects including convective, boundary and inertial effects will be included in the analysis. The unsteadiness is due to the time-dependent free stream velocity. The governing boundary layer equations along with the boundary conditions are converted into dimensionless form by a non-similar transformation, and then resulting system of coupled non-linear partial differential equations are solved by perturbation solutions for small dimensionless time until the second order. Numerical solutions of the governing equations are obtained employing the implicit finite-difference scheme in combination with the quasi-linearization technique. To validating the method used, we compared our results with previous results in earlier papers on special cases of the problem and are found to be in agreement. Effects of various parameters on velocity, temperature and nanoparticle volume fraction profiles are graphically presented.

Natural Convection Flow and Heat Transfer Enhancement of a Nanofluid past a Truncated Cone with Magnetic Field Effect

A nonsimilarity analysis is performed to investigate the laminar, free convection boundary layer flow over a permeable isothermal truncated cone in the presence of a transverse magnetic field effect. A suitable set of dimensionless variables is used and non-similar equations governing the problem are obtained. Fourth order Runge-Kutta with shooting technique is employed for the numerical solution of the obtained equations. Different water-based nanofluids containing Cu, Ag, CuO, Al2O3, and TiO2 are taken into consideration. The effects of pertinent parameters such as the solid volume fraction of nanoparticles, and magnetic field parameter have been investigated. Furthermore, different models of nanofluid based on different formulas for thermal conductivity and dynamic viscosity on the flow and heat transfer characteristics are discussed. Various comparisons with previously published work for the case of a vertical plate are performed and the results are found to be in excellent agreement.

Unsteady boundary layer flow and heat transfer over an exponentially shrinking sheet with suction in a copper-water nanofluid

An analysis of unsteady boundary layer flow and heat transfer over an exponentially shrinking porous sheet filled with a copper-water nanofluid is presented.Water is treated as a base fluid.In the investigation,non-uniform mass suction through the porous sheet is considered.Using Keller-box method the transformed equations are solved numerically.The results of skin friction coefficient,the local Nusselt number as well as the velocity and temperature profiles are presented for different flow parameters.The results showed that the dual non-similar solutions exist only when certain amount of mass suction is applied through the porous sheet for various unsteady parameters and nanoparticle volume fractions.The ranges of suction where dual non-similar solution exists,become larger when values of unsteady parameter as well as nanoparticle volume fraction increase.So,due to unsteadiness of flow dynamics and the presence of nanoparticles in flow field,the requirement of mass suction for existence of solution of boundary layer flow past an exponentially shrinking sheet is less.Furthermore,the velocity boundary layer thickness decreases and thermal boundary layer thickness increases with increasing of nanoparticle volume fraction in both non-similar solutions.Whereas,for stronger mass suction,the velocity boundary layer thickness becomes thinner for the first solution and the effect is opposite in the case of second solution.The temperature inside the boundary layer increases with nanoparticle volume fraction and decreases with mass suction.So,for the unsteadiness and for the presence of nanoparticles,the flow separation is delayed to some extent.

Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature

This paper discusses the natural convection boundary layer flow of a micropo- lax nanofluid over a vertical permeable cone with variable wall temperatures. Non-similax solutions are obtained. The nonlineaxly coupled differential equations under the boundary layer approximations governing the flow axe solved numerically using an efficient, itera- tive, tri-diagonal, implicit finite difference method. Different experimental correlations for both nanofluid effective viscosity and nanofluid thermal conductivity are considered. It is found that as the vortex-viscosity parameter increases, both the velocity profiles and the local Nusselt number decrease. Also, among all the nanoparticles considered in this investigation, Cu gives a good convection.

Unsteady mixed convection flow over stretching sheet in presence of chemical reaction and heat generation or absorption with non-uniform slot suction or injection

The article examines the unsteady mixed convection flow over a vertical stretching sheet in the presence of chemical reaction and heat generation or absorption with non-uniform mass transfer. The unsteadiness is caused by the time dependent free stream velocity varying arbitrarily with time. Non-similar solutions are obtained nu- merically by solving the coupled nonlinear partial differential equations using the quasi- linearization technique in combination with an implicit finite difference scheme. To reveal the tendency of the solutions, typical results for the local skin friction coefficient and the local Nusselt and Sherwood numbers are presented for different values of parameters. The effects of various parameters on the velocity, temperature, and concentration distributions are discussed here. The present numerical results are compared with the previously published work, and the results are found to be in excellent agreement.

Non-similar mixed convection analysis for magnetic flow of second-grade nanofluid over a vertically stretching sheet

The aspiration of this research is to explore the impact of non-similar modeling for mixed convection in magnetized second-grade nanofluid flow.The flow is initiated by the stretching of a sheet at an exponential rate in the upward vertical direction.The buoyancy effects in terms of temperature and concentration differences are inserted in the x-momentum equation.The aspects of heat and mass transfer are studied using dimensionless thermophoresis,Schmidt and Brownian motion parameters.The governing coupled partial differential system(PDEs)is remodeled into coupled non-similar nonlinear PDEs by introducing non-similar transformations.The numerical analysis for the dimensionless non-similar partial differential system is performed using a local non-similarity method via bvp4c.Finally,the quantitative effects of emerging dimensionless quantities on the nondimensional velocity,temperature and mass concentration in the boundary layer are conferred graphically,and inferences are drawn that important quantities of interest are substantially affected by these parameters.It is concluded that non-similar modeling,in contrast to similar models,is more general and more accurate in convection studies in the presence of buoyancy effects for second-grade non-Newtonian fluids.