Numerical study for micropolar flow over a stretching sheet

The paper presents a numerical study of the steady flow of a micropolar fluid flow from a stretching sheet. Approximate analytical solution of high nonlinear momentum, angular momentum and confluent hypergeometric similarity solution of the heat transfer equation are obtained for a particular case when the vortex viscosity is neglected. Accuracy of the analytical solution is verified by numerical solutions obtained by employing finite element and Chebyshev finite difference methods. The good agreement between the numerical results of both methods, together with an excellent agreement with the analytical solutions for the special case, ensures the reliability of the obtained results. The velocity, microrotation and temperature functions are shown graphically and the effect of the permeability parameter is studied.     

Nonlinear mass transfer between a gas and a falling liquid film. 1. Numerical analysis

A numerical analysis is carried out of the kinetics of nonlinear mass transfer between a gas and a falling liquid film. The nonlinear effect which is considered is the result of intensive mass transfer. Under these conditions the large mass flux induces a secondary flow at the phase interface. The mass transport in both phases takes into account the influence of the intensive mass transfer on the hydrodynamic behavior. An equation is obtained for the rate of absorption is greater than the rate of desorption under conditions of intensive mass transfer.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 59, No. 1, pp. 92–98, July, 1990.     

Invariant solutions to the equations of sorption equilibrium dynamics and kinetics

The theory of continuous Lie groups is used for finding invariant solutions to the equation of Sorption kinetics, which describe the mass transfer in a porous symmetrical sorbent grain corresponding to a nonlinear isotherm, and invariant solutions which describe the mass transfer in a porous column with longitudinal stirring.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 2, pp. 298–309, February, 1972.     

Analytical Solution for Convective–Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity

In this article, heat transfer in a moving fin with variable thermal conductivity, which is losing heat by simultaneous convection and radiation to its surroundings is analyzed. The calculations are carried out by using the differential transformation method (DTM) which is an analytical solution technique that can be applied to various types of differential equations. The effects of parameters such as the Peclet number, Pe, thermal conductivity parameter, a, convection–conduction parameter, N _c, radiation–conduction parameter, N _r, dimensionless convection sink temperature, θ _a, and dimensionless radiation sink temperature, θ _s, on the temperature distribution are illustrated and explained. The analytical solution is found to be in good agreement with the direct numerical solution. Moreover, the results demonstrate that the DTM is very effective in generating analytical solutions for even highly nonlinear problems.     

Chemically reactive solute transfer in a moving fluid over a moving surface

The distribution of a solute, undergoing a chemical reaction, between a moving surface and a moving stream is analyzed in this paper: uniform concentration at the boundary is assumed. The governing nonlinear partial differential equations are first transformed into nonlinear ordinary differential equations (ODEs) by a similarity transform, and then the ODEs are solved numerically by a shooting method. The obtained numerical results are compared with the known results in the literature in order to demonstrate the validity of the solutions. Furthermore, analytical results are provided for some parameter regimes. The effects of the governing parameters on the flow and chemical fields are examined. The numerical results indicate that dual solutions exist when the sheet and the free stream move in the opposite directions. These results are in agreement with Ishak et al. (Chem Eng J 148:63–67, 2009), where the results were obtained without chemical reaction. The concentration boundary layer thickness decreases with an increase in the Schmidt number and reaction rate parameter. Moreover, mass absorption at the plate is noted in the case of a constructive chemical reaction.     

On nonlinear problems of heat and mass transfer

A system of nonlinear equations for steady one-dimensional heat and mass transfer problems is considered. Analytical solutions are obtained for certain special cases.     

Choice of optimal parameters of radioisotopic devices used in thermophysical studies

A nonlinear system of differential equations of heat and mass transfer is examined under steady-state conditions. Exact analytical solutions are found to five boundary problems for this system.     

Homogenization of transient heat transfer problems for some composite materials

The article presented is devoted to the homogenization of transient heat transfer problems in some composite materials. The mathematical model used in the FEM computation is based on the effective modules method introduced for periodic composites. The effective heat conductivity is calculated in the closed form; effective heat capacity and mass density for the composite are obtained by simple spatial averaging. Such a homogenization scheme makes it possible to significantly simplify the numerical analysis of transient heat phenomena in various types of composites. Computational experiments performed using symbolic mathematics show the variability of effective heat conductivity for 2D and 3D composites as a function of the reinforcement volume ratio, of composite components conductivity coefficients as well as of the probabilistic moments of material properties versus volume ratio. Finally, using the Finite Element Method program, the comparison of transient heat transfer problem for the real and homogenized composites models is carried out.     

Application of MFS for determination of effective thermal conductivity of unidirectional composites with linearly temperature dependent conductivity of constituents

In this paper the problem of the effective conductivity in composite material is considered. It is assumed that the thermal conductivity coefficients of both the matrix and fibres materials are temperature-dependent. It yields the temperature-dependency of the effective thermal conductivity. To determine the effective thermal conductivity a unit-cell approach is used, i.e. heat flow in repeated element, which consists of one fibre in the matrix, is considered. It leads to 2-D nonlinear boundary value problems in matrix and fibre regions. In the paper, it is proposed to solve the given nonlinear boundary value problem by Picard iteration. For every iteration step, the linear boundary value problem with two uncoupled linear partially differential equations and coupled boundary conditions is solved. The method of fundamental solution, supported by radial basis functions approximation, is implemented to obtain the required solutions. The numerical experiment has been performed. The results of the experiment and some conclusions are included as well.     

Finite element solutions of free convective Casson fluid flow past a vertically inclined plate submitted in magnetic field in presence of heat and mass transfer

The aim of this research work is to study the influence of thermal radiation on steady magnetohydrodynamic-free convective Casson fluid flow of an optically thick fluid over an inclined vertical plate with heat and mass transfer. Combined phenomenon of heat and mass transfer is considered. Numerical solutions in general form are obtained by using the finite element method. The sum of thermal and mechanical parts is expressed as velocity of fluid. Corresponding limiting solutions are also reduced from the general solutions. It is found that the obtained numerical solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. Numerical results for the controlling flow parameters are drawn graphically and discussed in detail. In some special cases, the obtained numerical results are compared and found to be in good agreement with the previously published results which are available in literature. Applications of this study includes laminar magneto-aerodynamics, materials processing and magnetohydrodynamic propulsion thermo-fluid dynamics, etc.     

Modeling of frosting behavior on a cold plate

This paper proposes a mathematical model to predict the frost properties and heat and mass transfer within the frost layer formed on a cold plate. Laminar flow equations for moist air and empirical correlations for local frost properties are employed to predict the frost layer growth. Correlations for local frost density and effective thermal conductivity of the frost layer, derived from various experimental data, are expressed as a function of the various frosting parameters: the Reynolds number, frost surface temperature, absolute humidity and temperature of the moist air, cooling plate temperature, and frost density. The numerical results are compared with experimental data to validate the proposed model, and those agree well with the experimental data within a maximum error of 10%. Heat and mass transfer coefficients obtained from the numerical analyses are also presented. The results show that the model for the frost growth using the correlation of the heat transfer coefficient without considering the air flow has a limitation in its application.     

One class of analytical self-similar solutions to the system of radiative transfer and energy equations for a homogeneous medium

The known class of analytical self-similar solutions of the traveling heat wave type for a nonlinear integro-differential system of equations which describes nonstationary spectral transfer of radiant energy in a kinetic model is generalized to a homogeneous medium. The solutions are constructed in three-dimensional Cartesian geometry with specially chosen absorption and scattering coefficients. No additional terms that might distort the essence of the physical phenomena being described are introduced into the original equations, and the solution is almost completely determined by the functional dependence on a self-similar variable. This class of exact solutions is also applicable to the “gray matter” approximation and can be used to test numerical methods for calculating direct and inverse problems of radiative transfer. Examples of test calculations are given.     

Efficiency and optimization of an annular fin with combined heat and mass transfer – An analytical solution

An analysis was carried out to study the efficiency of annular fin when subjected to simultaneous heat and mass transfer mechanisms. The temperature and humidity ratio differences are the driving forces for the heat and mass transfer, respectively. Analytical solutions are obtained for the temperature distribution over the fin surface when the fin is fully wet. The effect of the atmospheric pressure on the fin efficiency was also studied, in addition to fin optimum dimensions. It is demonstrated that the closed-form solutions for a dry-fin case presented in many text books are special cases for the solutions presented in this paper.     

Evaluation of geometrically nonlinear effects due to large cross-sectional deformations of compact and shell-like structures

Abstract

This paper investigates geometrically nonlinear effects due to large deformations over the cross sections of beam-like and shell-like structures. Finite elements are used to provide numerical solutions along with the Newton–Raphson technique and the arc-length method. Refined theories able to capture cross-sectional deformation are constructed by referring to the Carrera unified formulation. Full nonlinear Green-Lagrange strains and second Piola-Kirchoff stresses are employed in a total Lagrangian scenario. The numerical results demonstrate that geometrical nonlinearities play a fundamental role when cross-sectional deformations become significant and theories of structures with nonlinear kinematics are utilized. In other words, this means that the use of refined beam models may be ineffective if geometrical nonlinear relations are not employed. These phenomena become particularly evident in thin-walled/shell-like type structures.     

Flow and heat transfer of a micropolar fluid in an axisymmetric stagnation flow on a cylinder with variable properties and suction (numerical study)

Summary. In this paper, an analysis is presented to study the effects of variable properties, density, viscosity and thermal conductivity of a micropolar fluid flow and heat transfer in an axisymmetric stagnation flow on a horizontal cylinder with suction, numerically. The fluid density and the thermal conductivity are assumed to vary linearly with temperature. However, the fluid viscosity is assumed to vary as a reciprocal of a linear function of temperature. The similarity solution is used to transform the problem under consideration into a boundary value problem of nonlinear coupled ordinary differential equations which are solved numerically by using the Chebyshev finite difference method (ChFD). Numerical results are carried out for various values of the dimensionless parameters of the problem. The numerical results show variable density, variable viscosity, variable thermal conductivity and micropolar parameters, which have significant influences on the azimuthal and the angular velocities and temperature profiles, shear stress, couple stress and the Nusselt number. The numerical results have demonstrated that with increasing temperature ratio parameter the azimuthal velocity decreases. With increasing variable viscosity parameter the temperature increases, whereas the azimuthal and the angular velocities decrease. Also, the azimuthal and the angular velocities increase and the temperature decreases as the variable conductivity parameter increases. Finally, the pressure increases as the suction parameter increases.     

Application of Differential Transform Method to Thermoelastic Problem for Annular Disks of Variable Thickness with Temperature-Dependent Parameters

This article analyzes the one-dimensional steady temperature field and related thermal stresses in an annular disk of variable thickness that has a temperature-dependent heat transfer coefficient and is capable of temperature-dependent internal heat generation. The temperature dependencies of the thermal conductivity, Young’s modulus, and the coefficient of linear thermal expansion of the disk are considered, whereas Poisson’s ratio is assumed to be constant. The differential transform method (DTM) is employed to analyze not only the nonlinear heat conduction but also the resulting thermal stresses. Analytical solutions are developed for the temperature and thermal stresses in the form of simple power series. Numerical calculations are performed for an annular cooling/heating fin of variable thickness. Numerical results show that the sufficiently converged analytical solutions are in good agreement with the solutions obtained by the Adomian decomposition method and give the effects of the temperature-dependent parameters on the temperature and thermal stress profiles in the disk. The DTM is useful as a new analytical method for solving thermoelastic problems for a body with temperature-dependent parameters including material properties.     

三重介质油藏有限导流垂直裂缝井的流-固耦合模型

考虑了三重介质油藏介质变形与垂直裂缝井闭合的影响,推广了Cinco-Ley H的有限导流垂直裂缝井的双线性渗流理论,将流体在垂直裂缝井与地层中形成的渗流划分为两个区域:三重介质油藏中的非线性流动区域和垂直裂缝井内的非线性流动区域;由此建立了三重介质油藏有限导流垂直裂缝井的流-固耦合模型。鉴于该模型的强非线性,采用稳定的有限差分格式求得其数值解,并将数值结果绘制成试井样板曲线。将数值结果与不考虑介质变形或垂直裂缝闭合的模型进行对比验证了该文模型研究的必要性。另外,还讨论了垂直裂缝井渗透率模量、窜流系数、基岩弹性储容比、井筒储集系数对无因次井底压力及压力导数的敏感性影响。     

Non-Darcian flow and heat transfer along a permeable vertical surface with nonlinear density temperature variation

The non-Darcy free convection flow on a vertical flat plate embedded in a fluid-saturated porous medium in the presence of the lateral mass flux with prescribed constant surface temperature is considered. The coupled nonlinearities generated by the density variation with temperature, inertia, and viscous dissipation are included in the present study. In particular, we analyze a system of nonlinear ODEs describing self-similar solutions to the flow and heat transfer problem. These transformed equations are integrated numerically by a second-order finite difference scheme known as the Keller box method. Furthermore, some analytical results are provided to establish relationships between the physical invariants in the problem, and also to validate the numerical method. One of the important findings of our study is that an increase in the Rayleigh number increases the velocity boundary layer thickness, while the opposite is true for the thermal boundary layer thickness.     

Effective Medium Approximation for Nonlinear Composite Media

We build the perturbation expansion method for nonlinear composite media and extend the EMA fornonlinear effective conductivity. Using the solutions of boundary-value problems of a cylindrical in-clusion, we derive formulae for nonlinear effective conductivity.     

Mathematical model of drying of deformable materials and numerical calculation method

A further development of numerical methods for calculating the nonlinear interdependent processes of heat and mass transfer in capillary-porous materials with account for their stressed-strained state is given.