Forced Convection Boundary Layer Flow Research Articles

Axisymmetric radiative titanium dioxide magnetic nanofluid flow on a stretching cylinder with homogeneous/heterogeneous reactions in Darcy-Forchheimer porous media: Intelligent nanocoating simulation

Modern nanomaterials coating processes feature high temperature environments and complex chemical reactions required for the precise synthesis of bespoke designs. Such flow processes are extremely complex and feature both heat and mass transfer in addition to viscous behaviour. Intelligent nano-coatings exploit magnetic nanoparticles and can be manipulated by external magnetic fields. Mathematical models provide an inexpensive insight into the inherent characteristics of such coating dynamics processes. Motivated by this, in the current work, a novel mathematical model is developed for dual catalytic reactive species diffusion in axisymmetric coating enrobing forced convection boundary layer flow from a linearly axially stretching horizontal cylinder immersed in a homogenous non-Darcy porous medium saturated withmagnetic nanofluid. Homogeneous and heterogeneous reactions, heat source (e.g. laser source) and non-linear radiative transfer are included. The Tiwari-Das nanoscale model is deployed. A Darcy-Forchheimerdrag force formulation is utilized to simulate both bulk porous drag and second order inertial drag of the porous medium fibres. The magnetic nanofluid is an aqueous electroconductive polymer comprising base fluid water and magnetic TiO2 nanoparticles. The TiO2 nanoparticles are one chemically reacting species (A) and a second species (B) is also present (e.g. oxygen) which also reacts chemically. Viscous heating and Ohmic dissipation are also included to produce a more physically realistic thermal analysis. The non-linear conservation equations proposed here with species diffusion (species A and B) are transformed via an appropriate stream function and scaling variables into a set of non-linear united multi-degree ODEs. The rising nonlinear ordinary differential boundary value problem is solved with four-point Gauss-Lobotto formulae in the MATLAB bvp5c routine. Validation is conducted with an Adams-Moulton predictor–corrector numerical scheme (AM2 coded in Unix). The widespread visualization of velocity, temperature, species A concentration, species B concentration, skin friction, local Nusselt number and species A and B local Sherwood numbers is included. For the higher Schmidt number the momentum diffusion rate exceeds the species diffusion rate and this will produce a depression in concentration values. Further, increasing Darcian parameter retards the local Nusselt number magnitudes since higher permeability corresponds to sparsity in the solid fibres, reduction in thermal conduction and a concomitant cooling of the cylinder surface.

Numerical solution of free stream MHD flow with the effect of velocity slip condition from an inclined porous plate

This article is concerned with Magnetohydrodynamic forced convective boundary layer flow past an inclined plate in a porous medium. Additionally, the effect of heat generation and velocity parameters are considered. The velocity slip and thermal slip effects on velocity and temperature profiles are taken into the account to address the phenomenon of heat transfer. The fundamental system of partial differential equations with necessary boundary conditions are converted into nonlinear ordinary differential equations. The reduced ordinary differential equations are solved numerically by the Finite difference method. It is observed that the results are significantly influenced by the various dimensionless parameters such as magnetic parameter, grashof number, Heat generation parameter, Prandtl number, velocity slip parameter. The impact of pertinent physical quantities on velocity and temperature profile is presented through graphs and tables. The results depicted that Magnetic parameter and permeability parameter have propensity to decrease the velocity profile.

Analysis of Forced Convection Boundary Layer Flow and Heat Transfer Past a Semi-Infinite Static and Moving Flat Plate Using Nanofluids-by Haar Wavelets

The paper presents, the steady state two-dimensional forced convection boundary layer flow of heat transfer past a semi-infinite static flat plate (Blasius problem) and moving flat plate (Sakiadis problem) in the water based nanofluid with various nanoparticles. The self-similar solution exists for the boundary layer equations and using suitable similarity variables, the governing equations have been converted into coupled nonlinear ordinary differential equations (NODEs) with an infinite domain. The governing problems over an infinite interval were solved using semi-numerical technique which makes the use of power of Haar wavelets coupled with collocation method. The solutions obtained using wavelet methods have been confirmed to be more accurate as compared to other previously published results. The several physical interesting results of the problem are concentrated and verified through numerical schemes. Three different types of nonmetallic or metallic nanoparticles such as alumina (Al2O3), copper (Cu) and titania (TiO2) in the base fluid of water with Prandtl number Pr = 6.2, to study the effect of solid volume fraction parameter Φ of the nanofluids. The effect of local skin friction coefficients, Nusselt number, velocity and temperature profiles are plotted for various values of nanoparticle volume fractions and for different nanoparticles are analyzed in detail, the numerical results are presented in terms of Tables. It predicts that, the solid volume fraction affects the fluid flow and heat transfer characteristics.

Hydromagnetic boundary layer flow with heat transfer past a rotating disc embedded in a porous medium

AbstractIn this study, the effect of Coriolis force along with the Darcy parameter has been analyzed on time‐dependent forced convective boundary layer flow of conducting fluids over a rotating disc embedded in a porous medium. The modeled system is solved by power series approximations in the Mathematica environment shooted values. The significant impact of the rheological properties, such as Darcy parameter and Prandtl number , of water, hydrocarbon, and kerosene‐based conducting fluids for the deviation of parameter (Karman) has been noted and then analyzed qualitatively and quantitatively with graphs and tables.

Dual solutions of nanaofluid forced convective flow with heat transfer and porous media past a moving surface

The paper presents a numerical study to explore the possible similarity solutions as well as dual branch solutions to study the performance evaluation of various nanoparticles associated water as the base fluid in the case of steady two-dimensional forced convection boundary layer flow through a moving flat porous plate under external magnetic fields. We considered water as a base fluid embedded with the three different types of nanoparticles namely copper (Cu), alumina (Al2O3) and titania (TiO2). The governing equations are simplified by similarity approach. The resulting equations are solved numerically and the numerical results are explored through graphs and tables and discussed in detail. The influences of problem parameters are discussed for the steady solution. The paper extends results of previous works by others authors contributing to increase the scientific knowledge on the subject. The skin friction coefficient and local Nusselt number on the plane are studied as functions of the problem parameters. The study reveals that the problem considered admits of upper and lower branch solutions for moving parameter λ, magnetic parameter M, the power law parameter n, convection heat transfer b and nanoparticle volume fraction parameter ϕ.

Exact similarity solutions for forced convection flow over horizontal plate in saturated porous medium with temperature-dependent viscosity

In this paper, we revisit a mathematical model representing a two-dimensional forced convection boundary-layer flow over a horizontal impermeable plate with a variable heat flux and viscosity. It is assumed that the fluid viscosity varies as an inverse linear function of temperature, the free stream velocity varies as an inverse linear of x and the wall heat flux varies with x as $x^{\lambda}$ ; where $\lambda > -1$ and x measures the distance along the surface. Analytical local similarity solutions are presented which reveal that there are two competing effects: $\lambda$ and $\theta_{e}$ ; where $\theta_{e}$ is the variable viscosity parameter. It has been shown that for $\theta_{e} > 0$ dual solutions exist and boundary separation occurs, while a unique local similarity solution exists for any $\theta_{e} < 0$ .

Effect of Radiation and Heat Generation on Unsteady MHD Flow of Non-Newtonian Fluid Along a Stretching Vertical Surface

In this paper, the unsteady forced convection boundary-layer flow of a non-Newtonian fluid along a continuously moving stretching sheet with thermal radiation and heat generation or absorption in the presence of magnetic field has been studied. First, the governing equations have been nondimensionalized by usual transformations to obtain the similar solutions. Then, the obtained equations have been solved by an implicit finite difference method. The convergency of explicit and implicit finite difference method has also been discussed. The results are presented for the effect of various parameters such as magnetic parameter (M), radiation parameter (N), heat source parameter (Q), Prandtl number (Pr) and power-law fluid index (n). The effects of these parameters on skin-friction coefficient (Cf) and the local Nusselt number (NuL) which are of physical and engineering interest have also been studied and presented graphically.GANIT J. Bangladesh Math. Soc.Vol. 36 (2016) 7-17

Similarity Solution of Forced Convection Flow of Powell-Eyring &amp; Prandtl-Eyring Fluids by Group-Theoretic Method

Generalized one parameter group theoretical method is applied to study Powell-Eyring and Prandtl-Eyring fluid models for heat transfer in forced convection boundary layer flow. The velocity and the temperature variations for two dimensional steady incompressible, laminar forced convection flow of both fluid modelspast a flat plate is considered. Velocity and temperature variation for different values offluid index and physical parameter A,B,α,β and Pr are presented graphically. Also, comparison for both fluid models is done graphically.

Boundary layer flow past a continuously moving thin needle in a nanofluid

A steady two-dimensional laminar forced convection boundary layer flow along a horizontal thin needle immersed in a nanofluid is considered. The governing partial differential equations are first reduced to a system of nonlinear ordinary differential equations, before being solved numerically using the boundary value problem solver (bvp4c) in Matlab, for copper-water nanofluid with Prandtl number Pr=6.2 (water). The physical quantities of interest such as the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented. Dual solutions are found when the needle and the free stream move in the opposite directions. It is seen that the solution domain decreases with increasing values of the solid volume fraction parameter. The influences of the needle size and the solid volume fraction parameter on the flow and heat transfer characteristics as well as on the velocity and temperature profiles are investigated.

Effects of Hydromagnetic and Thermophoresis of Unsteady Forced Convection Boundary Layer Flow over Flat Plates

In this paper, we analyze unsteady two dimensional hydromagnetic forced convection boundary layer flow of a viscous incompressible fluid along flat plates with thermophoresis. The potential flow velocity has been taken as a function of the distance x and time t. The governing partial differential equations are transformed to ordinary differential equation by applying local similarity transformation. The resulting similarity equations are then solved numerically for unsteady case, applying Nachtsheim-Swigert shooting iteration technique with six order Runge-Kutta method. The variations in fluid velocity, fluid temperature and species concentration are displayed graphically and discussed for different material parameters entering into the analysis. The effects of the pertinent parameters on the skin-friction coefficient, wall heat transfer coefficient and wall deposition flux rate are also displayed in tabulated form and discussed them from the physical point of view. An analysis of the obtained results shows that the flow field is influenced appreciably by the magnetic field parameter and the thermophoresis particle deposition.

Analytical solution of conjugate turbulent forced convection boundary layer flow over plates

A conjugate (coupled) forced convection heat transfer from a heated conducting plate under turbulent boundary layer flow is considered. A heated plate of finite thickness is cooled under turbulent forced convection boundary layer flow. Because the conduction and convection boundary layer flow is coupled (conjugated) in the problem, a semi-analytical solution based on Differential Transform Method (DTM) is presented for solving the non-linear integro-differential equation occurring in the problem. The main conclusion is that in the conjugate heat transfer case the temperature distribution of the plate is flatter than the one in the non-conjugate case. This feature is more pronounced under turbulent flow when compared with the laminar flow.

Effects of variable fluid properties and thermophoresis on unsteady forced convective boundary layer flow along a permeable stretching/shrinking wedge with variable Prandtl and Schmidt numbers

In this paper, the effects of variable fluid properties and thermophoresis on unsteady forced convective boundary layer flow along a permeable stretching/shrinking wedge are studied numerically. The analysis accounts for temperature dependent viscosity and thermal conductivity. The governing time dependent nonlinear partial differential equations are reduced to a set of nonlinear ordinary differential equations by the similarity transformations. The resulting local similarity equations are solved numerically by Nachtsheim–Swigert shooting iteration technique with sixth order Runge–Kutta integration scheme. Comparison with previously published work is performed and the results are found to be in excellent agreement. Numerical results for the non-dimensional velocity, temperature and concentration profiles as well as the variable Prandtl number and the variable Schmidt number are displayed graphically for several sets of material parameters. The effects of the model parameters on the local skin friction coefficient, the rate of heat and mass transfer, and the thermophoretic particle deposition velocity are also tabulated. The results show that for the flow with variable thermal conductivity, the Prandtl number as well as the Schmidt number varies significantly within the boundary layer. Thus, in any physical model where fluid transport properties are temperature dependent, the Prandtl number and the Schmidt number within the boundary layer should be considered as variables rather than constants.

An exact integral method to evaluate wall heat flux in spatially developing two-dimensional wall-bounded flows

An integral method to evaluate wall heat flux in turbulent wall-bounded flows is presented. The method is mathematically exact and has the advantage of having no explicit streamwise gradient terms. Importantly, the mathematical exactness of the method allows for a direct measurement of the wall heat flux without any a priori assumptions regarding the flow or temperature field or invoking flow transport analogies. It is useful in cases when measurements at multiple streamwise locations are not available or feasible, for flows with ill-defined outer boundary conditions, or when the measurement grid does not extend over the whole boundary layer thickness. The method is applied to existing datasets for both forced and natural convection boundary layer flow for which independent estimates of wall heat flux were known, and the different results compare favorably. Complications owing to experimental limitations and measurement error in determining wall heat flux from the proposed method are presented, and mitigating strategies are described.

MHD Flow of Nanofluids over an Exponentially Stretching Sheet Embedded in a Stratified Medium with Suction and Radiation Effects

An analysis has been carried out to investigate the influence of the combined effects of MHD, suction and radiation on the forced convection boundary layer flow of a nanofluid over an exponentially stretching sheet, embedded in a thermally stratified medium. The governing boundary layer equations of the problem are formulated and transformed into ordinary differential equations, using a similarity transformation. The resulting ordinary differential equations are solved numerically, by the shooting method. The effects of the governing parameters on the flow and heat transfer characteristics are studied and discussed in detail. Different types of nanoparticles, namely, Cu, Ag, Al2O3 and TiO2, with water as the base fluid, are studied. It is found that the effects of the radiation parameter, volume fraction and suction are the same on the temperature profiles, in contrast to the effects of thermal stratification. Comparisons with previously published works are performed in some special cases, and found to be in good agreement.

On a Homotopy Perturbation Treatment of Steady Laminar Forced Convection Flow over a Nonlinearly Stretching Porous Sheet

The steady two-dimensional laminar forced convection boundary layer flow of an incompressible viscous Newtonian fluid over a nonlinearly stretching porous (permeable) sheet with suction is considered. The sheet’s permeability is also considered to be nonlinear. The boundary layer equations are transformed by similarity transformations to a nonlinear ordinary differential equation (ODE). Then the homotopy perturbation method (HPM) is used to solve the resultant nonlinear ODE. The dimensionless entrainment parameter and the dimensionless sheet surface shear stress are obtained for various values of the suction parameter and the nonlinearity factor of sheet stretching and permeability. The results indicate that the dimensionless sheet surface shear stress decreases with the increase of suction parameter. The results of present HPM solution are compared to the values obtained in a previous study by the homotopy analysis method (HAM). The HPM results show that they are in good agreement with the HAM results within 2% error.

H212 平板上のナノ流体強制対流境界層流れの解析解と数値解

The problem of forced convective laminar boundary layer flow of alumina water nanofluid over a flat plate is investigated in the present paper. Both analytical solution (i.e. the local similarity solution) and numerical solution based on finite difference method are obtained for the boundary layer problem in nanofluid convection. The results generated from the local similarity method are compared against those from the finite difference method. Comparison reveals that there is only minor difference between the local similarity solution and numerical solution of finite difference method. Thus, the local similarity method can be directly extended to the boundary layer flow of nanofluid convection over a flat plate.

Similarity Theory for Forced Convection over Horizontal Plates

A similarity analysis is performed to study the fluid flow and heat transfer characteristics for the steady laminar forced convection boundary-layer flow past a semi-infinite horizontal plate in the presence of mass transfer, i.e., suction or blowing. The plate is subjected either to a nonuniform heat flux or nonuniform wall temperature. The heat flux is assumed to vary in the following form , whereas the wall temperature is assumed to vary as . Numerical results are obtained for various values of Prandtl number, suction or injection parameter , as well as for various levels of heating or . The effects of various values of Prandtl number , suction or injection parameter , and the index or on velocity profiles, temperature profiles, skin-friction coefficients, and local Nusselt number are presented. The results of the present general theory agree well with previously published results for the case of constant wall temperature (the only case with quantitative solutions that were available in the literature). Subtle new flow physics, such as a sharp reduction in the Nusselt number with increasing Prandtl number when mass injection is present and the Prandtl number is large, has been elucidated.

Similarity Solution of Unsteady Combined Free and Force Convective Laminar Boundary Layer Flow about a Vertical Porous Surface with Suction and Blowing

Abstract In this paper the unsteady laminar combined free and forced convective boundary layer flow about a vertical porous plate in viscous incompressible fluid with suction and blowing is considered. The governing non-dimensional boundary layer partial differential equations are simplified first by using Boussinesq approximation. Secondly, similarity transformations are introduced on the basis of detailed analysis in order to transform the simplified coupled partial differential equations into a set of ordinary differential equations. The transformed complete similarity equations are then solved numerically by using Nachtsheim-Swigert shooting iteration technique along with sixth order Runga-Kutta method. The flow phenomenon has been characterized with the help of obtained flow controlling parameters such as suction parameter, buoyancy parameter, Prandtl number and the other driving parameter. The effects of the involved parameters on the velocity and temperature fields across the boundary layer are investigated. Numerical results for the velocity and temperature distributions are presented graphically. It is found that a small suction or blowing can play a significant role on the patterns of flow and temperature fields.

Forced Convection Flow of Nanofluids Past Power Law Stretching Horizontal Plates

In the present work, we studied a nonsimilar solution of steady forced convection boundary layer flow and heat transfer of a nanofluid past a stretching horizontal plate. One-phase model has been used for this study. The nonsimilarity equations are solved numerically. We considered a nanofluid consists of AL2O3 as a nanoparticles and water as a base fluid. The volume fraction of nanoparticles is considered in the range 0 ≤ ? ≤ 0.2. with prandtl number pr = 6.2 for the water working as a regular fluid. The parameters which governing the solution are volume fraction of nanoparticles , stretching plate parameter ξ and power law index N. We investigated the effect of these parameters on the skin friction coefficient, Nusselt number, velocity and temperature profiles. We found that heat transfer rate and skin fraction increased when ? increased. On the other hand, we concluded that the increase in ξ and N made heat transfer rate increases and skin fraction decreases.

The development of forced convection heat transfer near a forward stagnation point with Newtonian heating

A mathematical model for the unsteady forced convection boundary-layer flow near a forward stagna- tion point is considered when there is Newtonian heating on the surface whereby the heat transfer is proportional to the local surface temperature. In a previous paper (Salleh et al. J Eng Math 69:101-110, 2011), a critical value γc, dependent on the Prandtl number σ , of the heat transfer coefficient γ was identified, with solutions for the corresponding steady problem possible only for γ γ c, the solution still continues to large time, now growing exponentially with time. This rate of growth is determined by an eigenvalue problem which we solve numerically for general values of γ and σ and asymptotically for large γ and both large and small σ .