Influence of chemical reaction on heat and mass transfer of non-Newtonian fluid with yield stress by free convection from vertical surface in porous medium considering Soret effect

The effect of chemical reaction on free convection heat and mass transfer for a non-Newtonian power law fluid over a vertical flat plate embedded in a fluid-saturated porous medium has been studied in the presence of the yield stress and the Soret effect. The governing boundary layer equations and boundary conditions are cast into a dimen- sionless form by similarity transformations, and the resulting system of equations is solved by a finite difference method. The results are preSented and discussed for concentration profiles, as well as the Nusselt number and the Sherwood number for various values of the parameters, which govern the problem. The results obtained show that the flow field is influenced appreciably by the presence of the chemical reaction parameter γ the order of.the chemical reaction parameter m, the Soret number St, the buoyancy ratio N, the Lewis number Le, and the dimensionless rheological parameter Ω.

The patterns of high-degree thermal free convection and its features in a spherical shell

A high-degree (degree l = 6 and order m = 0, 1, 2, [midline ellipsis] , l. High-order model for short) and steady thermal free convective motion of an infinite Prandtl number and Boussinesq fluid in a spherical shell is calculated by a Galerkin method. Convection is driven by an imposed temperature drop across top rigid and bottom stress-free isothermal boundaries only heated from below of the shell. In this paper, the scalar poloidal and fluctuating temperature fields are expanded into associated Legendre polynomials with degree l = 6 and order m = 0, 1, 2, [midline ellipsis] , l. Compared with zero-order model (degree l = 6 and order m = 0), from which 2-D longitudinal (r-θ) profiles can be obtained, high-order model can provide a series of southerly (r-θ), easterly (r-φ) and radial (θ-φ) velocity profiles, which probably reveal more detail features of mass motion in the mantle. It is found that Rayleigh number has great effects on the patterns and velocities of thermal free convection and controls the relative ratio of hot and cold plume in the shell. Probably, the present results mainly reveal the mass motion in the lower mantle, while the striking differences of convection patterns from velocities at different positions have important geodynamical significances.

A Study of Two Dimensional Unsteady MHD Free Convection Flow over a Vertical Plate

In this paper, unsteady free convection heat transfer flow over a vertical plate in the presence of a magnetic field is discussed in detail. The dimensionless partial differential equations of continuity, momentum along energy are analyzed with suitable transformations. For numerical calculation, an implicit finite difference method is applied to solve a set of nonlinear dimensionless partial differential equations. Dimensionless velocity and temperature profile are also investigated due to the effects of assumed parameters in the concerned problem. An explicit finite difference technique is used to compute velocity and temperature profiles. The stability conditions are also examined.

Unsteady Electromagnetic Free Convection Micropolar Fluid Flow through a Porous Medium along a Vertical Porous Plate

Unsteady electromagnetic free convection flows of two-dimensional micropolar fluid through in a porous medium parallel to a vertical porous plate have been investigated numerically. Similarity analysis has been used to transform the governing equations into its non-dimensional form by using the explicit finite difference method to obtain numerical solutions. Estimated results have been gained for various values of Prandtl number, Grashof number, material parameters, micropolar parameter, electric conductivity, electric permeability, thermal relaxation time and the permeability of the porous medium. The effects of pertinent parameters on the velocity, electric induction, magnetic induction, microrotation and temperature distributions have been investigated briefly and illustrated graphically.

Three dimensional free convection couette flow with transpiration cooling

Free convection flow between two vertical parallel plates with transverse sinusoidal injection of the fluid at the stationary plate and its corresponding removal by constant suction through the plate in uniform motion has been analyzed. Due to this type of injection velocity, the flow becomes three-dimensional. Analytical expressions for the velocity, temperature, skin friction and rate of heat transfer were obtained. The important characteristics of the problem, namely the skin friction and the rate of heat transfer are discussed in detail with the help of graphs.

Comparison of Different Generation Mechanisms of Free Convection between Two Stations on the Tibetan Plateau

Based on high-quality data from eddy covariance measurements at the Qomolangma Monitoring and Research Station for Atmosphere and Environment（QOMS） and the Southeast Tibet Monitoring and Research Station for Environment（SETS）,near-ground free convection conditions（FCCs） and their characteristics are investigated. At QOMS, strong thermal effects accompanied by lower wind speeds can easily trigger the occurrence of FCCs. The change of circulation from prevailing katabatic glacier winds to prevailing upslope winds and the oscillation of upslope winds due to cloud cover are the two main causes of decreases in wind speed at QOMS. The analysis of results from SETS shows that the most important trigger mechanism of FCCs is strong solar heating. Turbulence structural analysis using wavelet transform indicates that lowerfrequency turbulence near the ground emerges from the detected FCCs both at QOMS and at SETS. It should be noted that the heterogeneous underlying surface at SETS creates large-scale turbulence during periods without the occurrence of FCCs. Regarding datasets of all seasons, the distribution of FCCs presents different characteristics during monsoonal and non-monsoonal periods.

Transient free convection flow of a viscoelastic fluid over vertical surface

In this paper, the viscoelsatic boundary layer flow and the heat transfer near a vertical isothermal impermeable surface and in a quiescent fluid are examined. The governing equations are formulated and solved numerically using MackCormak＇s technique. The results show excellent agreement with previously published results by a comparision. Representative results for the velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers, and local skin friction coefficients are shown graphically for different values of viscoelsatic parameters. In general, it is found that the velocities increase inside the hydrodynamic boundary layers and the temperatures decrease inside the thermal boundary layers for the viscoelsatic fluid as compared with the Newtonian fluid due to favorable tensile stresses. Consequently, the coefficients of friction and heat transfer enhance for higher viscoelsatic parameters.

Transient Free Convection and Heat Transfer in a Partitioned Attic-Shaped Space under Diurnal Thermal Forcing

One primordial consideration in residential ventilation standards is the comfort of provided to people living in those habitations.This is highly dependent on the thermal and fluid flow conditions,the space geometry and so on.Efficient designs may reduce the energy usage,making the buildings more sustainable over a longer period of time.This study aims to investigate the impact of whole day thermal conditions on the fluid flow structure and heat transfer phenomena,mainly natural convection,inside a partitioned attic-shaped configuration.The Finite Volume Method is applied to solve the governing equations.Sinusoidal thermal boundary condition is applied on the sloping walls to illustrate the characteristics of primary flow through daily cycles.A highly thermal conductive partition was placed vertically at the middle of the cavity.Note that through the partition,only heat could freely transfer between two fluid zones.Results show that,during day time,a stratified fluid flow structure is obtained,which originates from the prevailing conduction heat transfer mechanism,while,for the night-time it changed into a strong convection mechanism which significantly affects the flow structure.These results are particularly important for understanding the fluid dynamics inside the attic shaped building and also designing new residential building.

Magnetohydrodynamic Effect on Free Convection of Three Dimensional Laminar Flow in Porous Annulus

A numerical study has been carried out to investigate heat transfer by free convection under the effect of MHD （magnetohydrodynamic） for steady state three-dimensional laminar flow in horizontal and vertical cylindrical annulus filled with saturated porous media （sand silica） with fins attached to the inner cylinder. A single electric coil placed around the inner cylinder to generate a magnetic field. The governing equations which used are continuity, momentum （using Darcy＇s law） and energy equations which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using Fortran 90 program. The parameters affected on the system are Rayleigh number ranging within （102 ~ Ra＊ 〈 104）, and MHD （Mn） （0 〈_ Mn 〈_ 100） and radius ratio Rr （0.225, 0.338 and 0.435）. The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that heat transfer decrease with the increase of magnetohydrodynamic. It was found that the average Nusselt number increase with Ra＊ and decrease with H~ Mn and Rr. A correlation for the average Nusselt number in terms of Ra＊ and Mn, has been developed for the inner cylinder.

Soret and Dufour Effects on Unsteady Free Convection Fluid Flow in the Presence of Hall Current and Heat Flux

Unsteady MHD natural convective heat and mass transfer flow through a semi-infinite vertical porous plate in a rotating system have been investigated with the combined Soret and Dufour effects in the presence of Hall current and constant heat flux. It is considered that the porous plate is subjected to constant heat flux. The obtained non-dimensional, non-similar coupled non-linear and partial differential equations have been solved by explicit finite difference technique. Numerical solutions for velocities, temperature and concentration distributions are obtained for various parameters by the above mentioned technique. The local and average shear stresses, Nusselt number as well as Sherwood number are also investigated. The stability conditions and convergence criteria of the explicit finite difference scheme are established for finding the restriction of the values of various parameters to get more accuracy. The obtained results are illustrated with the help of graphs to observe the effects of various legitimate parameters.

Magnetohydrodynamic Conjugate Free Convective Heat Transfer Analysis of an Isothermal Horizontal Circular Cylinder with Temperature Dependent Viscosity

Heat transfers due to MHD-conjugate free convection from the isothermal horizontal circular cylinder while viscosity is a function of temperature is investigated. The governing equations of the flow and connected boundary conditions are made dimensionless using a set of non-dimensional parameters. The governing equations are solved numerically using the finite difference method. Numerical results are obtained for various values of viscosity variation parameter, Prandtl number, magnetic parameter, and conjugate conduction parameter for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and heat transfer rate along the surface.

Transient Free Convection and Thermal Stratification in Uniformly-Heated Partially-Filled Horizontal Cylindrical and Spherical Vessels

An integral approach has been used to analyze the development of the free convection boundary layer on heated concave surfaces,such as those in horizontal cylinders or a sphere.Based on the non-dimensional laminar and turbulent velocity and temperature profiles closed form expressions for the boundary layer thickness,velocity scale as well as the boundary layer commencement after the point of instability are obtained.In addition,the mass flowrate to the thermal stratified region is given.

Conjugate Heat Transfer for Free Convection along a Vertical Plate Fin

In this study,a new and effective improved Semi-Analytic and Semi-Empirical formula f(Pr)= (0.749999437Pr^(1/2))/((0.609+1.221Pr^(1/2)+1.238Pr)^(1/4))has been proposed to solve a conjugate problem with free convection in the incompressible laminar boundary layer flow and heat conduction in a solid wall for the flow passing a flat plate fin. A combination of flat-plate flow and flat-plate fin heat conduction has been considered in the present study.Finite -difference solutions for the interface temperature profiles and the heat transfer rates have been presented over the entire thermo-fluid-dynamic field for Prandtl numbers from 0.001 to 10000.First,the similar flow field has been solved by the Runge-Kutta method and the shooting methods,then the correlation equation of the local heat transfer coefficient have been obtained.Finally,the empirical formula has been substituted into the fin temperature heat conduction calculation processes to obtain the iterative solutions of the conjugate problems.

General Solutions for Hydromagnetic Free Convection Flow over an Infinite Plate with Newtonian Heating, Mass Diffusion and Chemical Reaction

The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined.Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration,three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution(the steady-state),for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.

Investigation of the Influence of Free Convection on the Heat Transfer of Cylinders with Different Aspect Ratios

The heat transfer from an electrically heated cylinder (wire) of finite length to the surrounding fluid can be divided into heat radiation, conduction and convection. A technical application of these cylinders with typical dimensions of 1-2 mm length and a few micrometers diameter is the Hot-Wire-Anemometry.This systematic study should clarify the influence of the convection to three dimensional heat transfer of cylinders. For this aim it is planned to investigate Reynolds numbers below Re = 1 (creeping flow). For this reason measurements should be done under 1g in the earth laboratory and also under microgravity (μg) conditions. Comparisons of these measurements under otherwise same conditions allows to distinguish between the pure convection heat transfer and the contributions due to conduction and other effects. For measarements under μg the Drop Tower Bremen can be used as research facility. Due to the fast response of convection to changes in the gravity conditions the Drop Tower is an ideal and cost efficient experimental tool. The experimental setup is build to operate at velocity range of 0-l m/s which includes the whole range of convection from pure free convection at 0 m/s over mixed convection up to pure forced convection at velocities above about 0.15 m/s. This velocity region corresponds to a range of the Reynolds number of Re = 0 - 0.18 for a cylinder of 5 μ m diameter at Tf= 140℃ in air at an ambient temperature of about 21℃.

Nonlinear free thermal convection in a spherical shell:A variable viscosity model

In mantle convection models, the mantle viscosity is generally assumed constant or dependent on depth. In this paper, a laterally variable viscosity is introduced into mantle convection model in which the mantle viscosity consists of a constant background and latitude-dependent viscosity with small fluctuations. The features of toroidal field dependent on depth and Rayleigh number are discussed under two boundary conditions, i.e., the top rigid and bottom stress-free boundaries (R-F boundary for short) and both rigid ones (R-R boundary for short), respectively. The results show that the energy of toroidal field mainly concentrates in the middle and upper parts of a spherical shell, and the ratio of toroidal to total velocities amounts to only a few percents and hardly depends on Rayleigh number, while the convection patterns of toroidal field have been strongly affected by Rayleigh number. It is found that the convection patterns and velocities of toroidal field have obvious differences in latitudinal direction, which clearly reflects the effects of lateral mantle viscosity variations on the convection patterns. These preliminary results give us a possible hint to study some global tectonic phenomena, e.g. the asymmetry of the southern and northern hemispheres and the Earth's differential rotation.

THE EFFECT OF LONGITUDINAL OSCILLATIONS ON FREE CONVECTION FROM A VERTICAL PLATE EMBEDDED IN A POROUS MEDIUM

In this paper oscillatory 2-D natural convection from a vertical isothermal wall embedded in a po- rous medium, and originating from the oscillation of longitudinal fluid flow, has been investigated both analytically and numerically. Two asymptotic solutions, valid for large and small values of dimensionless frequency γ respectively, are obtained in the closed form. In the range where the asymptotic solutions break down, numerical results to the governing equations are obtained by local similarity meth- od. Both numerical and analytical results show that pulsatory components of the flow and heat transfer depend only on the parameter γ, and the effect of longitudinal oscillation is to decrease the magnitude or' pulsatory Nusselt number with a phase lag between 0 and 90 deg. A correlation for pulsatory heat trans- fer rates is proposed in the whole range of γ within 3% accuracy compared with the numerical results.

MHD effects on free convective flow over moving semi-infinite vertical cylinder with temperature oscillation

Numerical solutions of magnetodynamics （MHD） effects on the free convective flow of an incompressible viscous fluid past a moving semi-infinite vertical cylinder with temperature oscillation are presented. The dimensionless, unsteady, non-linear, and coupled governing partial differential equations are solved by using an implicit finite difference method of the Crank-Nicolson type. The velocity, temperature, and concentration profiles are studied for various parameters. The local skin-friction, the average skinfriction, the Nusselt number, and the Sherwood number are also analyzed and presented graphically. The results are compared with available results in literature, and are found to be in good agreement.

Natural convection flow of a couple stress fluid between two vertical parallel plates with Hall and ion-slip effects

The Hall and ion-slip effects on fully developed electrically conducting couple stress fluid flow between vertical parallel plates in the presence of a temperature dependent heat source are investigated. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using the homotopy analysis method （HAM）. The effects of the magnetic parameter, Hall parameter, ion-slip parameter and couple stress fluid parameter on velocity and temperature are discussed and shown graphically

Homotopy Analysis of MHD Free Convective Micropolar Fluid Flow along a Vertical Surface Embedded in Non-Darcian Thermally-Stratified Medium

The dynamics of steady, two-dimensional magnetohydrodynamics (MHD) free convective flow of micropolar fluid along a vertical porous surface embedded in a thermally stratified medium is investigated. The ratio of pressure drop caused by liquid-solid interactions to that of pressure drop caused by viscous resistance are equal;hence, the non-Darcy effect is properly accounted for in the momentum equation. The temperature at the wall and at the free stream which best accounts for thermal stratification are adopted. Similarity transformations are used to convert the nonlinear partial differential equation to a system of coupled non-linear ordinary differential equation and also to parameterize the governing equations. The approximate analytical solution of the corresponding BVP are obtained using Homotopy Analysis Method (HAM). The effects of stratification parameter, thermal radiation and other pertinent parameters on velocity, angular velocity and temperature profiles are shown graphically. It is observed that increase in the stratification parameter leads to decrease in both velocity and temperature distribution and also makes the microrotation distribution to increase near the plate and decrease away from the plate. The influence of both thermal stratification and exponential space dependent internal heat source on velocity, micro-rotation and temperature profiles are presented. The comparison of the solutions obtained using analytical techniques (HAM) and MATLAB package (bvp4c) is shown and a good agreement is observed.