Numerical study of flow around flat plate using higher-order accuracy scheme

In this paper, the control volume method is used to establish the general expression of entropy generation due to combined convective heat and mass transfer in internal and external fluid streams. The expression accounts for irreversibilities due to the presence of heat transfer across a finite temperature difference, mass transfer across a finite difference in the chemical potential of a species, and due to flow friction. Based on the assumption of local thermodynamic equilibrium, the generalized form of the Gibbs equation is used in this analysis. The results are applied to two fundamental problems of forced convection heat and mass transfer in internal and external flows. After minimizing the entropy generation, useful conclusions are derived that are typical of the second law viewpoint for the definition of the optimum operation conditions for the specified applications, which is a valuable criterion for optimum design of heat and fluid flow devices.

Simultaneous heat and mass transfer in free convection

Preface to the classics edition Preface Acknowledgments Part I. The Method of Weighted Residuals: 1. Introduction 2. Boundary-value problems in heat and mass transfer 3. Eigenvalue and initial-value problems in heat and mass transfer 4. Applications to fluid mechanics 5. Chemical reaction systems 6. Convective instability problems Part II. Variational Principles: 7. Introduction to variational principles 8. Variational principles in fluid mechanics 9. Variational principles for heat and mass transfer problems 10. On the search for variational principles 11. Convergence and error bounds Author index Subject index.

The solution of the conjugate problem of convective-conductive heat transfer in the channels of power plants is presented. The problem of convective heat transfer in the gas phase is solved by the integral theory of heat transfer. A one-dimensional problem of conductive heat transfer in the material of the wall is solved by the finite-difference method. Relative laws of heat and mass transfer and friction are obtained by numerical integration with respect to the boundary-layer thickness. The effect of the material and geometry of the wall on the level of problem “conjugation” is studied.

Three types of problems related to problems of heat and mass transfer in the soil are considered. The first class of problems deals with the diagnostics of damage of underground pipelines by thermal fields on the soil surface. The second type studies the dynamics of changes in the temperature of a geothermal reservoir depending on the temperature of the water entering this reservoir and the pressure gap between injection and production wells. The third-type problems consider the propagation of non-stationary thermal fields in the soil from operated engineering systems in the permafrost. The main attention is paid to long-term forecasting of the propagation of non-stationary thermal fields in the frozen soil between operating production wells of northern oil and gas fields. In problems of the first two classes, which served as a basis for the development of problems of the third type, water filtration in the soil is considered, and thermal fields propagate in single-phase media. The third-class problems take into account possible phase transitions in the soil when describing non-stationary thermal fields in permafrost soils, leading to Stefan-type problems. Accounting for water migration for the specific third-type problems on the determination of the radius of frozen soil thawing from production wells in northern oil and gas fields does not significantly affect this process since lateral water migration above the groundwater level is minimal. Therefore, only the latent heat of the initial water content is taken into consideration. This paper discusses a mathematical model containing the most significant physical and climatic data affecting the distribution of thermal fields in permafrost rocks and presents the results of numerical calculations.

Simultaneous mass and heat transfer with reactions in a multicomponent, laminar, falling liquid film

The paper presents the coefficient inverse problem of heat and mass transfer. It is known that the process of moisture and heat transfer in soil is described by a system of partial differential equations. The inverse coefficient problem is solved for finding the thermophysical characteristics of the heat and mass transfer equations. The initial-boundary conditions for the heat and mass transfer system are set. To solve the problem, the measured values of temperature and moisture are additionally set at the accessible boundary of the considered area. To solve the inverse problem, the Dufort- Frankel scheme and Matlab Optimization Toolbox are used. The Jacobian is used to reduce the number of iterations. The results of numerical calculations with and without Jacobian are presented.

Purpose This paper aims to address the problem of double-diffusive magnetohydrodynamics (MHD) non-Darcy convective flow of heat and mass transfer over a stretching sheet embedded in a thermally-stratified porous medium. The controlling parameters such as chemical reaction parameter, permeability parameter, etc., are extensively discussed and illustrated in this paper. Design/methodology/approach With the help of appropriate similarity variables, the governing partial differential equations are converted into ordinary differential equations. The transformed equations are solved using the spectral homotopy analysis method (SHAM). SHAM is a numerical method, which uses Chebyshev pseudospectral and homotopy analysis method in solving science and engineering problems. Findings The effects of all controlling parameters are presented using graphical representations. The results revealed that the applied magnetic field in the transverse direction to the flow gives rise to a resistive force called Lorentz. This force tends to reduce the flow of an electrically conducting fluid in the problem of heat and mass transfer. As a result, the fluid velocity reduces in the boundary layer. Also, the suction increases the velocity, temperature, and concentration of the fluid, respectively. The present results can be used in complex problems dealing with double-diffusive MHD non-Darcy convective flow of heat and mass transfer. Originality/value The uniqueness of this paper is the examination of double-diffusive MHD non-Darcy convective flow of heat and mass transfer. It is considered over a stretching sheet embedded in a thermally-stratified porous medium. To the best of the knowledge, a problem of this type has not been considered in the past. A novel method called SHAM is used to solve this modelled problem. The novelty of this method is its accuracy and fastness in computation.

HOC Simulation of Double-diffusive Natural Convection in a Rectangular Cavity

In this paper, the problem of heat and mass transfer due to the steady motion of a Rivlin- Ericksen fluid in tubes of varying cross-section is considered. Suction at tube walls is taken into account. Under the assumption that the deformations of the boundaries are small, the equations of motion have been solved by using a perturbation technique. The temperature and concentration distributions are obtained. The effects of various physical parameters are discussed. The Nusselt and Sherwood numbers are obtained. A set of figures for a quantitative illustration is presented.

Subject of research: problems of numerical determination of point sources in inverse heat and mass transfer problems. Purpose of research: description of theoretical results (theorem of existence and uniqueness of solutions of the inverse problem), creation of an algorithm for solving the problem of numerical determination of point sources, study of its properties, numerical implementation of the algorithm and its testing and verification of stability. Objects of research: problems of numerical determination of point sources (right-hand side of a special type) in inverse problems of heat and mass transfer. The sources are specified as a sum of Dirac delta functions with coefficients that depend on time and characterize the power of the corresponding source. They are unknown and are to be determined together with a solution of the equation. The values of the solution at a certain set of points lying inside the domain serve as the overdetermination data. Methods of research: the algorithm is based on the finite element method for spatial variables and the finite difference method for time. The unknown right-hand side is determined at each time layer using the overdetermination condition. Main results of research: description of the algorithm for solving the problem, its properties, results of numerical experiments. In particular, the conditions are described when the algebraic system to which the problem is reduced has a unique solution. The data obtained as a result of the calculations are compared with test examples. The calculations are also carried out with the addition of random noise of various levels to the measurement data. The results show that the solution is stable under random perturbations of the data.

A boundary value problem is considered for the equations of heat and mass transfer when one of the boundary conditions contains normal derivatives of the third order, to which a certain problem of heat and mass transfer in drying processes is reduced. The solution of the boundary value problem is sought in the form of the thermal potential of a double layer. A lemma on finding the limits of the third order normal derivatives is given. Using the boundary conditions, a system of the integro-differential equations (SIDE) with various heat conduction operators is obtained. A characteristic part of SIDE is solved by the method of integrated transformations of Fourier-Laplace when performing a condition of solvability. By the method of regularization of SIDE it is reduced to the system of the integrated equations of Volterra-Fredholm. A theorem of solvability of a boundary value problem is given under the condition of solvability of the heat and mass transfer equations with normal derivatives in the boundary conditions.

This work is devoted to solving the problem of heat and mass transfer in a rectangular cable channel laid in the earth mass, taking into account the electric and magnetic dynamics processes in the metal elements of the power cable. The current load of power cables depends on the temperature field in the cable construction, which in turn the following factors influence: the conditions of heat transfer, thermal characteristics of the materials used, the induced currents in a metal screen of power cables, etc. The proposed mathematical model of the processes of complex heat and mass transfer is based on the laws of conservation of mass, momentum, and energy. For the electrodynamics problem, equations of current density and a magnetic potential vector based on Maxwell equations are used. The problem was solved numerically under conditions of natural convection with taking into account the radiant energy by the finite element method in the Ansys Fluent software package. As a result, the power of heat losses in the metal structural elements of the power cable and the velocity and temperature fields in the cable channel were calculated. The temperature fields in the cable channel are presented and analyzed depending on the location of power cables. The different operating modes of the cable line are discussed. To analyze the heat processes in the cable channel, the nonstationary problem defining the heating time of cable lines to the limit values is solved. The heating curves of the cable lines operating in unsteady mode are obtained. The maximum operating time of the cable line in an overload and short circuit is determined.

The problem of heat and mass transfer in a visco-elastic fluid flow over a stretching sheet in the presence of a uniform magnetic field is examined. The important physical quantities such as the skin friction coefficient, heat transfer co-efficient and the mass transfer co-efficient are determined. It is found that the heat and mass transfer distribution decreases with the increasing values of the visco-elastic parameter k<sub>1</sub>.

A numerical solution of the problem of heat and mass transfer in evaporation of a droplet of water moving in a stream of high-temperature (up to 1200 K) gases is done on the basis of a system of nonlinear nonstationary partial differential equations describing conductive and radiative heat transfer in the droplet, as well as composite heat transfer at the ″liquid–gas″ interface. The values of the water evaporation rate have been determined. It is shown that the dependence of the evaporation rate on the droplet surface temperature has a nonlinear character. Characteristic relationships between the convective and radiative heat fluxes on the droplet surface (the radiative flux substantially exceeds the convective one; on decrease in the difference between the gas and droplet surface temperatures the difference between the radiative and convective heat fluxes decreases), the lifetimes (total evaporation) of droplets, as well as of the temperature and concentration of steam and gases in the vicinity of droplets have been determined. The calculated characteristics of the water droplet evaporation under conditions of high temperatures of the gas medium differ considerably from those obtained within the framework of the "diffusional" model of evaporation. A comparison of the results of numerical simulation with the experimental data obtained with the use of high-velocity panoramic optical methods of visualization by ″tracing particles″ is carried out.