Semi-infinite Horizontal Plate Research Articles

ANALYTICAL STUDY FOR THE BOUNDARY LAYER FLOW IN THE PRESENCE OF HEAT TRANSFER THROUGH A POROUS MEDIUM

In this paper we study a problem of the boundary layer flow through a porous media in the presence of heat transfer. Here we consider high porosity bounded by a semi-infinite horizontal plate. The main aim of this study is to point out local similarity transformations for the boundary layer flow, through a homogeneous porous medium. Here we applying finite difference schemes to find out the numerical solutions of the problem. The free stream velocity and the temperature far away from the plate are exponential function of variables.

Impact of Electrification and Particle Loading on Velocity Profile of Dusty Fluid Flow Over a Stretching Sheet

The performance of incompressible, laminar, boundary- layer flows over a semi-infinite horizontal stretchable plate is considered. The dusty fluid flow problems are modelled and solved in agreement with two-way coupling model. The particle phase momentum equation in the vertical direction is considered where as that for fluid phase is neglected. Here the electrification term added in not from the supply from outside rather it is the generation due to collision of particles So the effects of particle loading and electrification on velocity profile have been studied. From the result analysis it is concluded that electrification and particle density have significant effect on particle phase velocity, whereas carrier fluid phase has negligible effect. The particle phase velocity increases with increasing of electrification parameter and decreases with increase of loading ratio.

New Integral Solutions for Magnetohydrodynamic Free Convection of Power-Law Fluids Over a Horizontal Plate

An integral analysis has been performed to theoretically investigate the magnetohydrodynamic natural convection flow of non-Newtonian power-law fluids over a semi-infinite horizontal plate with constant surface heat flux. The governing boundary layer equations are transformed into a set of coupled ordinary differential equations using stretching transformation. The resultant equations are solved analytically using the integral method. A set of new infinite polynomial series are introduced for presenting the velocity and pressure profiles, providing more accurate results compared with traditional solutions. Implicit expressions for the Nusselt number and friction coefficient are presented for wide ranges of the generalized Prandtl number (Pr*), the non-Newtonian power-law viscosity index (n), and the generalized Hartmann number (Ha*).

Heat transfer effect on MHD flow of a micropolar fluid through porous medium with uniform heat source and radiation

Abstract The present study examines the effect of heat transfer on electrically conducting MHD micropolar fluid flow along a semi-infinite horizontal plate with radiation and heat source. The uniform magnetic field has applied along the principal flow direction. The obtained governing equations have been converted into a set of dimensionless differential equations and then numerically solved by using a well-known Runge-Kutta method with shooting technique. The velocity, microrotation, and temperature distribution are presented for various physical parameters. The numerical values of skin friction and Nusselt numbers at the plates are shown in tabular form, and the obtained results are compared with the results of a previous study. It has been found that the magnetic parameter increases the velocity profile whereas the boundary layer thickness reduces due to the inclusion of coupling parameter and inertia effect. The presence/absence of magnetic parameter and coupling parameter enable to enhance the angular velocity profile while it is worth to note that the backflow has generated in the vicinity of the plate.

Solution of the boundary layer flow of various nanofluids over a moving semi-infinite plate using HPM

Two-dimensional steady boundary layer flow of nanofluids over a moving impermeable semi-infinite hori-zontal plate is studied. The plate moves with constant ve-locity. Similarity transformation is used to transform gov-erning equations to a nonlinear ODE, which is then solved using the semi-analytical homotopy perturbation method (HPM) for various types of nanoparticles: Cu, Al2O3, TiO2, CuO, Ag and SiO2 in water based fluid. The effect of nanoparticle volume fraction and nanoparticle type on flow characteristics is studied and compared with numerical solution. HPM results agree within 2% error with numerical solution. Analyses show that skin friction coefficient increases with nanoparticle volume fraction increase. DOI: http://dx.doi.org/10.5755/j01.mech.20.1.3406

Closed-Form Analytical Solutions for Laminar Natural Convection on Horizontal Plates

A boundary layer based integral analysis has been performed to investigate laminar natural convection heat transfer characteristics for fluids with arbitrary Prandtl number over a semi-infinite horizontal plate subjected either to a variable wall temperature or variable heat flux. The wall temperature is assumed to vary in the form T¯w(x¯)-T¯∞=ax¯n whereas the heat flux is assumed to vary according to qw(x¯)=bx¯m. Analytical closed-form solutions for local and average Nusselt number valid for arbitrary values of Prandtl number and nonuniform heating conditions are mathematically derived here. The effects of various values of Prandtl number and the index n or m on the heat transfer coefficients are presented. The results of the integral analysis compare well with that of previously published similarity theory, numerical computations and experiments. A study is presented on how the choice for velocity and temperature profiles affects the results of the integral theory. The theory has been generalized for arbitrary orders of the polynomials representing the velocity and temperature profiles. The subtle role of Prandtl number in determining the relative thicknesses of the velocity and temperature boundary layers for natural convection is elucidated and contrasted with that in forced convection. It is found that, in natural convection, the two boundary layers are of comparable thickness if Pr ≤ 1 or Pr ≈ 1. It is only when the Prandtl number is large (Pr > 1) that the velocity boundary layer is thicker than the thermal boundary layer.

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.

Magnetohydrodynamic free convection flow above an isothermal horizontal plate

In the present study a new similarity theory is developed to study the fluid flow and heat transfer characteristics for the steady laminar natural convection boundary layer flow of an incompressible and electrically conducting fluid past a semi-infinite horizontal plate subjected to a constant wall temperature under the action of transverse magnetic field. The governing parabolic boundary layer PDEs are transformed to ordinary differential equations using similarity transformation. This results in a set of three coupled, non-linear ordinary differential equations with variable coefficients (representing the interaction of the temperature and velocity fields) which are then solved by the shooting method. Asymptotic analyses and series solutions are also constructed to explore the mathematical behaviour of the solutions. The numerical results are obtained for various values of Prandtl number and magnetic field parameter ζ. The effects of various values of Prandtl number and magnetic field parameter ζ on the velocity profiles, temperature profiles, wall shear stress and heat transfer coefficients are presented. The results indicate that the wall shear stress τw decreases whereas the local Nusselt number Nux increases with increase in Prandtl number if the magnetic field parameter ζ is held constant at a particular value. On the other hand, both the wall shear stress and Nusselt number decrease with increase in the magnetic field parameter ζ for a fluid with constant Prandtl number. Generic correlations for Nux and τw have been developed in terms of the fluid Prandtl number Pr and magnetic field parameter ζ. A generic relation for free convection flow with magnetohydrodynamic effects, that is equivalent to the well-known Reynolds analogy for forced convection flow, has also been formulated in the present work.

Forced Flow of Vapor Condensing Over a Horizontal Plate (Problem of Cess and Koh): Steady and Unsteady Solutions of the Full 2D Problem

Accurate steady and unsteady numerical solutions of the full 2D governing equations—which model the forced film condensation flow of saturated vapor over a semi-infinite horizontal plate (the problem of Cess and Koh)—are obtained over a range of flow parameters. The results presented here are used to better understand the limitations of the well-known similarity solutions given by Koh. It is found that steady/quasisteady filmwise solution exists only if the inlet speed is above a certain threshold value. Above this threshold speed, steady/quasisteady film condensation solutions exist and their film thickness variations are approximately the same as the similarity solution given by Koh. However, these steady solutions differ from the Koh solution regarding pressure variations and associated effects in the leading part of the plate. Besides results based on the solutions of the full steady governing equations, this paper also presents unsteady solutions that characterize the steady solutions’ attainability, stability (response to initial disturbances), and their response to ever-present minuscule noise on the condensing-surface. For this shear-driven flow, the paper finds that if the uniform vapor speed is above a threshold value, an unsteady solution that begins with any reasonable initial-guess is attracted in time to a steady solution. This long time limiting solution is the same—within computational errors—as the solution of the steady problem. The reported unsteady solutions that yield the steady solution in the long time limit also yield “attraction rates” for nonlinear stability analysis of the steady solutions. The attraction rates are found to diminish gradually with increasing distance from the leading edge and with decreasing inlet vapor speed. These steady solutions are generally found to be stable to initial disturbances on the interface as well as in any flow variable in the interior of the flow domain. The results for low vapor speeds below the threshold value indicate that the unsteady solutions exhibit nonexistence of any steady limit of filmwise flow in the aft portion of the solution. Even when a steady solution exists, the flow attainability is also shown to be difficult (because of waviness and other sensitivities) at large downstream distances.

An optimization of eigenfunction expansion method for the interaction of water waves with an elastic plate

The hydroelastic interaction of an incident wave with a semi-infinite horizontal elastic plate floating on a homogenous fluid of finite depth is analyzed using the eigenfunction expansion method. The fluid is assumed to be inviscid and incompressible and the wave amplitudes are assumed to be small. A two-dimensional problem is formulated within the framework of linear potential theory. The fluid domain is divided into two regions, namely an open water region and a plate-covered region. In this paper, the orthogonality property of eigenfunctions in the open water region is used to obtain the set of simultaneous equations for the expansion coefficients of the velocity potentials and the edge conditions are included as a part of the equation system. The results indicate that the thickness and the density of plate have almost no influence on the reflection and transmission coefficients. Numerical analysis shows that the method proposed here is effective and has higher convergence than the previous results.

Soret effect on mixed convection heat and mass transfer along a semi-infinite horizontal plate in the presence of heat generation and chemical reaction

The aim of this work is to study Soret and chemical reaction effects on laminar mixed convection boundary-layer flow and heat and mass transfer past a semi-infinite horizontal flat plate in the presence of heat generation. A transformation is introduced that reduces the equations governing the flow to a system of nonlinear coupled ordinary differential equations. The transformed equations are solved numerically using the fourth-order Runge–Kutta integration scheme coupled with the shooting method. Graphical results for the velocity, temperature, and concentration profiles for various parametric conditions are presented and studied. The effects of the chemical reaction parameter, Soret parameter, and the heat generation parameter on the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are presented in tabular form and discussed.PACS Nos.: 44.20+b, 44.20+Cb

On the Asymptotic Approach to Thermosolutal Convection in Heated Slow Reactive Boundary Layer Flows

The study sought to investigate thermosolutal convection and stability of two dimensional disturbances imposed on a heated boundary layer flow over a semi-infinite horizontal plate composed of a chemical species using a self-consistent asymptotic method. The chemical species reacts as it diffuses into the nearby fluid causing density stratification and inducing a buoyancy force. The existence of significant temperature gradients near the plate surface results in additional buoyancy and decrease in viscosity. We derive the linear neutral results by analyzing asymptotically the multideck structure of the perturbed flow in the limit of large Reynolds numbers. The study shows that for small Damkohler numbers, increasing buoyancy has a destabilizing effect on the upper branch Tollmien-Schlichting (TS) instability waves. Similarly, increasing the Damkohler numbers (which corresponds to increasing the reaction rate) has a destabilizing effect on the TS wave modes. However, for small Damkohler numbers, negative buoyancy stabilizes the boundary layer flow.

Chebyshev finite difference method for the effects of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate with temperature dependent viscosity

The effect of variable viscosity, chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate has been analyzed. The fluid viscosity is assumed to vary as an inverse linear function of temperature. By means of the similarity solutions, deviation of the velocity, concentration and temperature fields as well as the skin friction and heal transfer results from their constant values are determined numerically by using Chebyshev finite difference method. The effects of variable viscosity, chemical reaction and Schmidt number parameters on the velocity, concentration and temperature profiles have been studied.

Free-surface flows emerging from beneath a semi-infinite plate with constant vorticity

The free-surface flow past a semi-infinite horizontal plate in a finite-depth fluid is considered. It is assumed that the fluid is incompressible and inviscid and that the flow approaches a uniform shear flow downstream. Exact relations are derived using conservation of mass and momentum for the case where the downstream free surface is flat. The complete nonlinear problem is solved numerically using a boundary-integral method and these waveless solutions are shown to exist only when the height of the plate above the bottom is greater than the height of the uniform shear flow. Interesting results are found for various values of the constant vorticity. Solutions with downstream surface waves are also considered, and nonlinear results of this type are compared with linear results found previously. These solutions can be used to model the flow near the stern of a (two-dimensional) ship.

Local similarity transformations for the boundary layer flow through a homogeneous porous medium by the presence of heat transfer

In this paper we point out local similarity transformations for the flow through a medium with high porosity bounded by a semi-infinite horizontal plate and we have the presence of heat transfer. The free stream velocity and the temperature far away from the plate are exponential functions of a variable.

Effects of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate

An approximate solution for the steady laminar flow along a semi infinite horizontal plate in the presence of species concentration and chemical reaction has been obtained using Numerical Technique. It has been observed that in the presence of chemical reaction, (i) the velocity and concentration increase with decrease of Schmidt number Sc. (ii) Skin friction and rate of concentration decrease with the increase of chemical reaction parameter.

MIXED CONVECTION BOUNDARY LAYER FLOW OF A MICROPOLAR FLUID ON A HORIZONTAL PLATE

An analysis is performed to study the heat transfer characteristics of laminar mixed convection boundary layer flow of a micropolar fluid past a semi-infinite horizontal fiat plate with variable surface heat flux. A nonsimilar mixed convection parameter £ and a pseudosimilarity variable v are introduced to cast the governing boundary layer equations into a system of dimensionless equations, which are solved numerically using the finite difference method. A single mixed convection parameter is used to cover the entire regime of mixed convection from the pure forced convection limit to the pure free convection limit. The effect of material parameters, the power-law variation of surface heat flux, nonsimilar mixed convection parameter and Prandtl number are considered. The micropolar fluids are observed to display drag reduction and reduced surface heat transfer rate when compared to Newtonian fluids. The effect of the buoyancy force results in the enhancements of friction factor, heat transfer rate and wall couple stress.

A higher-order analysis of natural convection in a corner

A study of natural convection flow in a right angled corner formed by a semi-infinite vertical plate, which is maintained at the ambient temperature, and a semi-infinite horizontal plate, which is prescribed with a uniform heat flux, is carried out for moderately large values of the Grashof number by the method of matched asymptotic expansions. Higher-order corrections are found for the velocity and temperature fields as well as for the heat transfer and skin friction coefficients. The interaction between the two boundary-layers, which form on the vertical and horizontal plates, takes place through an isothermal outer flow. Eigenvalues and their corresponding eigenfunctions which are associated with the inner expansions have been sought. We are able to continue the solution up to the contribution played by the first eigenvalue and to uniquely find the first eigensolution. Numerical results have been obtained for a wide range of values of the Prandtl number, σ, but the results are only presented for σ=0.72 (air) and 6.7 (water). It is found that higher-order corrections to the classical boundary-layer theory are quite significant even for Grashof numbers of order 109.

Natural convection in a right-angle corner: higher-order analysis

Higher-order boundary-layer effects for natural convection flow in a right-angle corner formed by a semi-infinite vertical plate, which is prescribed with a uniform heat flux, and a semi-infinite horizontal plate, which is thermally insulated, is presented. Using the method of asymptotic matched expansions the solution is obtained up to the fourth-order expansion. For the first time the interplay between the two boundary-layer flows, which takes place through the outer inviscid region, has been investigated. Eigen-values and their corresponding eigenfunctions which are associated with the inner expansions have been sought and it has been found that their contribution up to fourth-order correction is identically zero. Numerical results have been obtained for Prandtl numbers of 0.72 (air), 1 and 6.7 (water) and the flow in the outer region and the velocity and temperature profiles in the boundary layers are presented. Also the variation of the local Nusselt number and skin friction coefficients on the plates are presented as functions of the local Grashof numbers. It is found that the presence of the horizontal plate has quite a substantial effect on the higher-order approximations in the vertical boundary layer and the outer region.

Similarity solution for free and forced convection hydromagnetic flow over a horizontal semi-infinite plate through a non-homogeneous porous medium

A similarity analysis for the free and forced convection hydromagnetic flow over a horizontal semi-infinite flat plate through a non-homogeneous porous medium is presented, taking into account the hydrostatic pressure variation normal to the flat plate. The similarity solution of the problem under consideration is obtained under certain valid simplifying assumptions when, (i) the plate temperature is inversely proportional to the square root of the distance from the leading edge, (ii) the intensity of the applied magnetic field, normal to the plate, changes with the inverse square root of the distance from the leading edge, and (iii) the permeability of the porous medium, occupying a semi-infinite region of the space bounded by the flat plate, is proportional to the distance measured in the direction of the flow. A numerical solution of the resulting system of ordinary differential equations of motion and energy is obtained, depending on the Prandtl number Pr, the magnetic parameterMn,the bouyancy parameter λ, and the permeability parameterPm.The variations of the fundamental quantities of the problem are shown graphically followed by a quantitative discussion.