Effects of thermophoresis on hydromagnetic mixed convection and mass transfer flow past a vertical permeable plate with variable suction and thermal radiation

The present paper deals with the effect of surface mass transfer on MHD mixed convection flow past a heated vertical flat permeable surface in the presence of thermophoresis, radiative heat flux and heat source/sink. Usual similarity transformations are introduced to obtain similarity solution, using regular perturbation technique. To observe physical insight and interesting aspects of the problem in the presence of thermophoresis, the non-dimensional velocity, temperature and concentration field are numerically studied and displayed graphically for pertinent parameters. It is observed that the thermophoresis has dominant effect on mass transfer mechanism in particle deposition process. The model finds applications in studying particulate deposition on turbine blades, removing small particles from gas streams and determining chemical vapor deposition rate in chemical industries.     

Magneto-Compound Reaction of Convective Flow via a Porous Inclined Plate with Heat Energy Absorption

The current study is concerned with the unsteady heat and mass transfer of MHD free convection flow via a porous inclined plate that accelerates exponentially with temperature and concentration. Heat emission, source/sink, radiation absorption, and reaction are taken into account in the energy and species equations. The innovative part of the work is the analysis of the flow phenomenon with a heat source or sink and radiation absorption along the chemical reaction. The governing PDEs are reduced into ODEs via the non-dimensional variables and afterward solved analytically utilizing the perturbation strategy. Graphical representations of liquid temperature, speed, and concentration as well as the Sherwood \& Nusselt quantities and the skin friction factor are displayed in tabular form for different combinations of appropriate stream quantities. The analysis of a resistance quantum grows with the size of the magnetic, whereas the rates of mass and heat transfer decline with increasing radiation, reaction, and Schmidt number. Thermal-velocity and concentration-velocity profiles interact reciprocally with the accelerating radiation, heat source, and compound reaction. The growth of speed and thermal profiles is clearly visible due to the absorption and Prandtl values. The present results are in strongly consistent with the earlier published results. There are numerous applications for this research in many sectors and material processing for understanding drag in seepage flows on heated/cooled and inclined surfaces.     

Effect of dust particles on a layer of micropolar ferromagnetic fluid heated from below saturating a porous medium

The problem of the effect of dust particles on the thermal convection in micropolar ferromagnetic fluid saturating a porous medium subject to a transverse uniform magnetic field has been investigated theoretically. Linear stability analysis and normal mode analysis methods are used to find an exact solution for a flat micropolar ferromagnetic fluid layer contained between two free boundaries. In case of stationary convection, the effect of various parameters like medium permeability, dust particles, non-buoyancy magnetization, coupling parameter, spin-diffusion parameter and micropolar heat conduction parameter are analyzed. For sufficiently large values of magnetic parameter M₁, the critical magnetic thermal Rayleigh number for the onset of instability is determined numerically and results are depicted graphically. It is also observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the micropolar ferromagnetic fluid saturating a porous medium heated from below in the absence of micropolar viscous effect, microinertia and dust particles.     

A nanocomposite based on a styrene-acrylate copolymer and organically modified montmorillonite 2. Barrier and thermal properties

The results of an investigation into the barrier and thermal properties of polymer nanocomposites prepared by blending a styrene-acrylate copolymer solution with a suspension of organically modified montmorillonite are presented. The influence of organomontmorillonite content on the barrier properties of the nanocomposite is investigated with the example of water vapor permeability. The experimental values of the permeability coefficient are compared with those calculated by using a model taking into account the increased path of diffusing water molecules caused by the shielding effect of plate like particles. The thermograms of differential scanning calorimetry in the temperature range from −40 to 130°C are presented. The results of a thermogravimetric analysis for specimens heated in air to 800°C are also reported. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 503–516, July–August, 2006.     

Perturbation analysis of unsteady magnetohydrodynamic convective heat and mass transfer in a boundary layer slip flow past a vertical permeable plate with thermal radiation and chemical reaction

An analytical study for the problem of unsteady mixed convection with thermal radiation and first-order chemical reaction on magnetohydrodynamics boundary layer flow of viscous, electrically conducting fluid past a vertical permeable plate has been presented. Slip boundary condition is applied at the porous interface. The classical model is used for studying the effect of radiation for optically thin media. The non-linear coupled partial differential equations are solved by perturbation technique. The results obtained show that the velocity, temperature and concentration fields are appreciably influenced by the presence of chemical reaction, thermal stratification and magnetic field. It is observed that the effect of thermal radiation and magnetic field decreases the velocity, temperature and concentration profiles in the boundary layer. Also, the effects of the various parameters on the skin-friction coefficient and the rate of heat transfer at the surface are discussed.     

Effect of magnetic field dependent viscosity on ferroconvection in the presence of dust particles

This paper deals with the theoretical investigation of the effect of magnetic field dependent (MFD) viscosity on the thermal convection in a ferromagnetic fluid in the presence of dust particles. For a flat ferromagnetic fluid layer contained between two free boundaries, the exact solution is obtained using a linear stability analysis and a normal mode analysis method. For the case of stationary convection, dust particles always have a destabilizing effect, whereas the MFD viscosity has a stabilizing effect on the onset of convection. In the absence of MFD viscosity, the destabilizing effect of magnetization is depicted but in the presence of MFD viscosity, non-buoyancy magnetization may have a destabilizing or a stabilizing effect on the onset of convection. The critical wave number and critical magnetic thermal Rayleigh number for the onset of stationary convection are also determined numerically for sufficiently large values of buoyancy magnetization parameter M ₁. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. It is observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid heated from below in the absence of dust particles. The oscillatory modes are introduced due to the presence of the dust particles, which were non-existent in their absence. A sufficient condition for the non-existence of overstability is also obtained.     

Spatial Stability for Mixed Convection Boundary Layer over a Heated Horizontal Plate

The spatial stability properties of a mixed convection boundary layer developing over a heated horizontal plate is studied here under linear and quasi-parallel flow assumption. The main aim of the present work is to find out if there is a critical buoyancy parameter that would indicate the importance of heat transfer in destabilizing mixed convection boundary layers, when the buoyancy effect is given by Boussinesq approximation. The undisturbed flow used here is that given by the similarity solution of [ 1 ] that implies the wall temperature to vary as the inverse square root of the distance from the leading edge of the plate. The stability of this flow has been investigated by using the compound matrix method (CMM)—that allows finding all the modes in the chosen range in the complex wave number plane for spatial stability analysis. Presented neutral curves for mixed convection boundary layer show the existence of two types of disturbances present simultaneously, for large buoyancy parameter. One notices very unstable high-frequency mode when the buoyancy parameter exceeds the above-mentioned critical value. This unstable thermal mode is in addition to the hydrodynamic mode of isothermal flow given by corresponding similarity profile. The calculated critical buoyancy parameter is shown to qualitatively match with experimental results.     

Stagnation point flow of dusty Casson fluid with thermal radiation and buoyancy effects

The aim of the study is to examine the stagnation point flow of a dusty Casson fluid over a stretching sheet with thermal radiation and buoyancy effects. The governing boundary layer equations are represented by a system of partial differential equation. After applying suitable similarity transformations, the resulting boundary layer equations are solved numerically using the Runge Kutta Fehlberg fourth-fifth order method (RKF-45 method). The behaviors of velocity, temperature and concentration profiles of fluid and dusty particles with respect to change in fluid particle interaction parameter, Casson paramter, Grashof number, radiation parameter, Prandtl number, number density, thermal equilibrium time, relaxation time, specific heat of fluid and dusty particles, ratio of diffusion coefficients, Schmidt number and Eckert number are analysed graphically and discussed. Our computed results interpret that velocity distribution decays for higher estimation of Casson parameter while temperature distribution shows increasing behavior for larger radiation parameter.     

On the Existence and Parameter Dependence of Similarity Solutions for Free Convection on a Vertical Plate

The free convection on a heated vertical plate is considered, both for the case of prescribed plate temperature and the case of prescribed heat flux. The parameter dependence of the similarity solutions are investigated, and the existence proofs given for a range of the parameter values.     

Thermal Conduction in Bispherical Systems and its Role in Self-Induced Thermophoresis of Aerosol Particles

Some problems arising in the study of thermal conduction insmall particles are examined. In particular, we investigatethe temperature profile around bispherical bodies which containinternal heat sources due, for example, to radioactive decay,chemical reactions, or radiation. Two special cases have beenexamined in depth: a heated sphere in the neighbourhood of aplane, and two unequal spheres in rigid contact with each other.A solution of the thermal conduction equation for these problemsin bispherical coordinates leads to useful closed-form expressionsfor the temperature profiles, both within and external to thespheres We particularly note the induced temperature gradient over thesurfaces of the spheres since this has important implicationsin the phenomenon of thermophoresis. The magnitude of self-inducedthermophoresis is examined and its practical implications discussed     

微极流体薄膜层通过以滑移速度移动的可渗透无限平板时流体特性变化和热辐射对流动和热传导的影响

微极流体薄膜层通过按滑移速度移动的可渗透无限竖直平板时,研究热辐射对混合对流薄膜层流动和热传导的影响.假定流体粘度和热传导率变化是温度的一个函数.对一些典型的可变参数值,应用Chebyshev谱方法,数值求解流动的控制方程.将所得结果与已发表文献的结果进行比较,结果是一致的.绘出并讨论了可变参数对速度、微旋转速度、温度分布曲线、表面摩擦因数和Nusselt数的影响.     

A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition

This paper considers the classical problem of hydrodynamic and thermal boundary layers over a flat plate in a uniform stream of fluid. It is well known that similarity solutions of the energy equation are possible for the boundary conditions of constant surface temperature and constant heat flux. However, no such solution has been attempted for the convective surface boundary condition. The paper demonstrates that a similarity solution is possible if the convective heat transfer associated with the hot fluid on the lower surface of the plate is proportional to x^?1/2. Numerical solutions of the resulting similarity energy equation are provided for representative Prandtl numbers of 0.1, 0.72, and 10 and a range of values of the parameter characterizing the hot fluid convection process. For the case of constant heat transfer coefficient, the same data provide local similarity solutions.     

Influence of surface mass transfer on mixed convection flows over non-isothermal horizontal flat plates

Non-similar solution of a steady mixed convection flow over a horizontal flat plate in the presence of surface mass transfer (suction or injection) is obtained when there is power-law variation in surface temperature. The surface temperature is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A non-similar mixed convection parameter is considered which covers the whole convection regime, namely from pure free convection to pure forced convection. Numerical results are reported here to account the effects of Prandtl number, surface temperature, surface mass transfer parameter (suction or injection) on velocity and temperature profiles, and skin friction and heat transfer coefficients.     

Buoyancy and chemical reaction effects on MHD mixed convection heat and mass transfer in a porous medium with thermal radiation and Ohmic heating

The combined effect of mixed convection with thermal radiation and chemical reaction on MHD flow of viscous and electrically conducting fluid past a vertical permeable surface embedded in a porous medium is analyzed. The heat equation includes the terms involving the radiative heat flux, Ohmic dissipation, viscous dissipation and the internal absorption whereas the mass transfer equation includes the effects of chemically reactive species of first-order. The non-linear coupled differential equations are solved analytically by perturbation technique. The results obtained show that the velocity, temperature and concentration fields are appreciably influenced by the presence of chemical reaction, thermal stratification and magnetic field. It is observed that the effect of thermal radiation and magnetic field is to decrease the velocity, temperature and concentration profiles in the boundary layer. There is also considerable effect of magnetic field and chemical reaction on skin-friction coefficient and Nusselt number.     

Magnetic effect on the formation of longitudinal vortices in natural convection flow over a rotating heated flat plate

A numerical study of magnetic effect on the formation of longitudinal vortices in natural convection flow over a rotating heated flat plate is presented. The onset position characterized by the local Grashof number, depends on the rotational Reynolds number, the Prandtl number, the Hartmann number, and the wave number. The Coriolis force and the Lonertz force have significant effects on the formation of longitudinal vortices and the associated instability. Positive rotation stabilizes the flow on the rotating flat surface. On the contrary, a negative rotation destabilizes the flow. The flow is found more stable as the value of Hartmann number increases. The numerical data show reasonable agreement with the experimental results with the case of thermal instability in natural convection over a flat plate heated from below.     

Group method analysis of melting effect on MHD mixed convection flow from radiate vertical plate embedded in a saturated porous media

The linear transformation group approach is developed to simulate problem of hydromagnetic heat transfer by mixed convection along vertical plate in a liquid saturated porous medium in the presence of melting and thermal radiation effects for opposing external flow. The application of a one-parameter transformation group reduces the number of independent variables by one so that the governing partial differential equations with the boundary conditions reduce to an ordinary differential equations with appropriate corresponding conditions. The Runge-Kutta shooting method is used to solve the determining equations of the set of nonlinear ordinary differential equations. are presented in the form of the temperature and flow fields in the melting region within the boundary layer for different parameters entering into the analysis. Also the effects of the pertinent parameters on the rate of the heat transfer in terms of the local Nusselt number at the solid–liquid interface are also discussed.     

传导-辐射对沿垂直平面有热泳的瞬时自然对流的影响

研究存在热辐射时,热泳微粒的沉积,对沿垂直平面瞬态自然对流边界层流动的影响,垂直平面浸没在光密灰色流体中.分析中采用Rosseland扩散近似表示辐射热通量项.将控制方程简化为抛物线型的偏微分方程组,然后在整个时间段0≤τ<∞,利用有限差分法数值求解.还得到了小数值时间和大数值时间的渐近解,发现渐近解和数值解吻合很得好.而且,流体,20℃和1个标准大气压下的空气,即Prandtl数Pr为0.7时,用图形给出了不同物理参数,即热辐射参数Rd、表面温度参数θw和热泳参数λ,对瞬时的表面剪切应力τw、表面热传输率qw和组分浓度扩散率(传质率)mw的影响,以及对瞬时的速度、温度和浓度分布曲线的影响.     

传导-辐射和磁流体组合对磁化可渗透平板自然对流影响的数值解法

研究粘性、不可压缩、导电流体,在磁化可渗透竖直平板上作自然对流时,数值地分析辐射和磁流体组合的影响.采用两种方法数值地求解非相似的控制方程:1)对所有吸入参数值ξ,采用有限差分法;2)为小数值和大数值的吸入参数值ξ,分别建立起级数的渐近解.用图形和列表形式,给出Prandtl数Pr,磁Prandtl数Pm,磁力参数S,辐射参数Rd,壁面温度θw的变化,对壁面摩擦因数、热交换率和电流密度的影响.最后分析上述物理参数对速度分布、温度分布和磁场横向分量的影响.     

应力降低因子和陶瓷材料抗热冲击阻力参数的性质及适用条件

将对流条件下薄板的瞬态导热问题的解析解引入自由弹性薄板的热应力场模型中,给出了相应应力降低因子的具体表达形式．为了便于比较,进一步定义了一个新的应力降低因子．详细讨论了应力降低因子及分别对应于高Biot模数和低Biot模数的第1个和第2个抗热冲击阻力参数及与中间量级的Biot模数相对应的近似表达式的性质及适用条件．将传热学与热弹性力学或断裂力学相结合的方法及有限元方法是该文所推荐的抗热震性能计算方法．研究表明,采用断裂临界温差和断裂临界无量纲时间相结合的方式能够直观简洁地表征陶瓷材料的抗热震性能．     

Influence of radiation on MHD free convection from a vertical flat plate embedded in porous media with thermophoretic deposition of particles

Magneto-hydrodynamics and thermal radiation effects on heat and mass transfer in steady laminar boundary layer flow of a Newtonian, viscous fluid over a vertical flat plate embedded in a fluid saturated porous media in the presence of the thermophoresis particle deposition effect is studied in this paper. The governing equations are transformed by special transformations. Brownian motion of particles and thermophoretic transport are considered in the flow equations. The magnetic field is considered to be applied. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The resulting similarity equations are solved numerically by the fourth-order Runge–Kutta method with shooting technique. Many results are obtained and representative set is displayed graphically to illustrate the influence of the various parameters on the wall thermophoretic deposition velocity, concentration, temperature and velocity profiles.