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In this paper, we propose a new non-linear partial differential equation to describe the heat transfer problems at the extreme excess temperatures. Its exact traveling wave solutions are obtained by using Cornejo-Perez and Rosu method. [ABSTRACT FROM AUTHOR]

Abstract: A multiprocessor computer system suitable for physical, mathematical, and chemical models, as well as an exact method for the solution of a system of differential equations that describe the actual combustion of a pulverized coal flare, are necessary to study the numerically complex, physicochemical processes occurring in the combustion chambers of power plants. The results of numerical simulation can provide quite a high accuracy. However, the task of setting up a physical and mathematical model with the correct initial and boundary conditions has yet to be completed. In this paper, we studied heat and mass transfer in high-temperature reacting flows during the burning of Karaganda coal in the combustion chamber of an actual power boiler of a thermal power plant in Kazakhstan. The optimal conditions for computational experiments that correspond to real combustion processes are determined. [ABSTRACT FROM AUTHOR]

An analytical study of two different models of rectangular porous fins are investigated using a new approximate analytical method, the Ananthaswamy-Sivasankari method. The obtained results are compared with the numerical solution, which results in a very good agreement. The impacts of several physical parameters involved in the problem are interlined graphically. Fin efficiency and the heat transfer rate are also calculated and displayed. The result obtained by this method is in the most explicit and simple form. The convergence of the solution determined is more accurate as compared to various analytical and numerical methods. [ABSTRACT FROM AUTHOR]

In this paper a numerical simulation of upward two-phase flow evaporation in a vertical tube has been studied by considering water as working fluid. To this end, the computational fluid dynamic simulations of this system are performed with heat and mass transfer mechanisms due to energy transfer during the phase change interaction near the heat transfer surface. The volume of fluid model in an available Eulerian-Eulerian approach based on finite volume method is utilized and the mass source term in conservation of mass equation is implemented using a user defined function. The characteristics of water flow boiling such as void fraction and heat transfer coefficient distribution are investigated. The main cause of fluctuations on heat transfer coefficient and volume fraction is velocity increment in the vapor phase rather than the liquid phase. The case study of this research including convective heat transfer coefficient and tube diameter are considered as a parametric study. The operating conditions are considered at high pressure in saturation temperature and the physical properties of water are determined by considering system’s inlet temperature and pressure in saturation conditions. Good agreement is achieved between the numerical and the experimental values of heat transfer coefficients. [ABSTRACT FROM AUTHOR]

Highlights • The optimal pitch ratio of the ribs mounted in a channel is provided based on inverse analysis. • The entransy dissipation was taken as the objective function in the inverse method. • Taking entransy dissipation as objective function leads to a fast and stable convergence process. Abstract The ribbed surface is a widely used convection heat transfer enhancement technology. The geometric parameters of the ribbed surface have great influences on its heat transfer performance. It is crucial to determine the optimum geometric parameters. In the present work, the optimal arrangement of ribs mounted in a rectangular channel is provided by solving the inverse optimization problem with the entransy dissipation as the objective function. The parameter analysis based on the direct solution is firstly carried out to get an approximate range near the optimal pitch ratio which can provide the initial value for the inverse optimization problem; afterwards, the inverse optimization problem is solved by a modified simplified conjugate gradient method, and the accurate optimal pitch ratio is obtained; finally the optimization results are discussed in detail. The results indicate that, (1) the inverse optimization analysis presented in this paper can provide an accurate optimal value of the pitch ratio; (2) taking the entransy dissipation as the objective function could lead to a faster converge process and give a more stable result than taking the temperature data as the objective function; (3) the optimal value under the fixed heat flux boundary condition is slightly larger than that under the fixed temperature boundary condition. [ABSTRACT FROM AUTHOR]

The paper presents key assumptions of the mathematical model which describes heat and mass transfer phenomena in a solar sewage drying process, as well as techniques used for solving this model with the Fluent computational fluid dynamics (CFD) software. Special attention was paid to implementation of boundary conditions on the sludge surface, which is a physical boundary between the gaseous phase -- air, and solid phase -- dried matter. Those conditions allow to model heat and mass transfer between the media during first and second drying stages. Selection of the computational geometry is also discussed -- it is a fragment of the entire drying facility. Selected modelling results are presented in the final part of the paper. [ABSTRACT FROM AUTHOR]

In this paper, a solution to heat equation in a spherical model is proposed. The model takes into account conjointly the boundary conditions and the transfer equations in a spray device. The deposited layer is supposed to be Gaussian and not uniform like most recent studies. The solution, using Legendre, Bessel and Boubaker polynomials expansions, presents the advantage of being continuous and indefinitely derivable. These features make the resolution connectable to any heat transfer similar model. [ABSTRACT FROM AUTHOR]

Abstract: The main objectives of this paper are to present a procedure of how to create and set up a model for the physical processes that take place within an infant radiant warmer and to validate that Computational Fluid Dynamics (CFD) can be used to resolve such problems. In this study, the results are obtained for a simplified model, both in terms of the geometry employed and the prescribed boundary conditions. The results were numerically verified in terms of the convergence history, monitor data and the physical correctness. This study shows that the physical situation is unsteady and the results tend to oscillate, almost periodically, around a mean value. The results presented in the paper are found to be in qualitative agreement with the experimental data. This gives us confidence that the techniques employed in this paper are appropriate and form the starting point for the inclusion of more realistic effects, e.g. real shape of the newborn and radiant lamp, heat generated inside the newborn, moisture transport, etc. [Copyright &y& Elsevier]

This paper describes the procedure of computational determination of the temperature field of a prismatic workpiece heated in a continuous furnace with account for the temperature dependence of the thermal diffusivity. For a numerical solution of the two-dimensional heat conduction equation with boundary conditions of the 3rd kind, an implicit scheme has been used. The calculated time dependences of the temperature for three characteristic points of the cross-section of the prismatic steel workpiece have been compared to the experimental data. The heat transfer coefficients at which the experimental data and the calculated values have a minimum discrepancy have been determined. [ABSTRACT FROM AUTHOR]

One of the promising approaches to the description of many physical processes is the use of the fractional derivative mathematical apparatus. Fractional dimensions very often arise when modeling various processes in fractal (multi-scale and self-similar) environments. In a fractal medium, in contrast to an ordinary continuous medium, a randomly wandering particle moves away from the reference point more slowly since not all directions of motion become available to it. The slowdown of the diffusion process in fractal media is so significant that physical quantities begin to change more slowly than in ordinary media.This effect can only be taken into account with the help of integral and differential equations containing a fractional derivative with respect to time. Here, the problem of heat and mass transfer in media with a fractal structure was posed and analytically solved when a heat flux was specified on one of the boundaries. The second initial boundary value problem for the heat equation with a fractional Caputo derivative with respect to time and the Riesz derivative with respect to the spatial variable was studied. A theorem on the semigroup property of the fractional Riesz derivative was proved. To find a solution, the problem was reduced to a boundary value problem with boundary conditions of the first kind. The solution to the problem was found by applying the Fourier transform in the spatial variable and the Laplace transform in time. A computational experiment was carried out to analyze the obtained solutions. Graphs of the temperature distribution dependent on the coordinate and time were constructed. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model describing the process of non-Fourier heat transfer in biological tissues for generalized coordinate system during thermal ablation by electromagnetic radiation with Gaussian external heat source is studied. The boundary value problem governing this process has been solved using hybrid numerical method taking Legendre wavelet basis function. The result obtained from finite element Legendre wavelet Galerkin method (FELWGM) is compared with exact analytical solution and shows a good agreement. The effect of variability of time, generalized coordinate system, location of tumor or cancer, relaxation time and external heat source coefficient on temperature distribution is discussed in detail. It has been observed that treatment of tumor or cancerous cell is independent of the generalized coordinate system at the thermal ablation position. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the boundary stabilization of a one-dimensional unstable heat equation with the external disturbance flowing into the control end. The active disturbance rejection control (ADRC) and the sliding mode control (SMC) are adopted in investigation. By the ADRC approach, the disturbance is estimated through an external observer and cancelled online by the approximated one in the closed-loop. It is shown that the external disturbance can be attenuated in the sense that the resulting closed-loop system under the extended state feedback tends to any arbitrary given vicinity of zero as the time goes to infinity. In the second part, we use the SMC to reject the disturbance with the assumption in which the disturbance is supposed to be bounded. The reaching condition, and the existence and uniqueness of the solution for all states in the state space via SMC are established. Simulation examples are presented for both control strategies. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a simple and rapid mathematical model to calculate the non-steady-state startup process and study the isothermal characteristics of a particular heat pipe. The model takes into consideration the special structure and usage conditions, where vapor temperature in the heat pipe changes only over time. This vapor temperature change correlation is calculated numerically and is set as the temperature boundary condition for the working well. The temperature, velocity and pressure distribution in the working well are then solved using FLUENT. The results manifest that the time required for approaching steady condition are 450s, 550s and 600s with water bath temperatures of 330K, 340K and 350K, respectively. The comparison of the calculations and experimental data shows good agreement, and the maximum deviation is 3.7K. [Copyright &y& Elsevier]

Abstract: Nowadays, consumers look for minimally processed, additive-free food products that maintain their organoleptic properties. This has led to the development of new technologies for food processing. One emerging technology is high hydrostatic pressure, as it proves to be very effective in prolonging the shelf life of foods without losing its properties. Recent research has involved modelling and simulating the effect of combining thermal and high pressure processes (see Denys et al. (2000) [3], Infante et al. (2009) [5], Knoerzer et al. (2007) [6], Otero et al. (2007) [9]). The focus is mainly on the inactivation of certain enzymes and microorganisms that are harmful to food. Various mathematical models that study the behaviour of these enzymes and microorganisms during a high pressure process have been proposed (see Infante et al. (2009) [5], Knoerzer et al. (2007) [6]). Such models need the temperature and pressure profiles of the whole process as an input. In this paper we present two dimensional models, with different types of boundary conditions, to calculate the temperature profile for solid type foods. We give an exact solution and propose several simplifications, in both two and one dimensions. The temperature profile of these simplified two and one dimensional models is calculated both numerically and analytically, and the solutions are compared. Our results show a very good agreement for all the approximations proposed, and so we can conclude that the simplifications and dimensional reduction are reasonable for certain parameter values, which are specified in this work. [Copyright &y& Elsevier]

A finite difference approach to a one-dimensional Stefan problem with periodic boundary conditions is studied. The evolution of the moving boundary and the temperature field are simulated numerically, and the effects of the Stefan number and the periodical boundary condition on the temperature distribution and the evolution of the moving boundary are analyzed. [ABSTRACT FROM AUTHOR]

This article deals with mathematical modeling and simulation of heat transfer in tissue under periodic boundary condition using nonlinear dual‐phase‐lag‐bioheat‐transfer (DPLBHT). We have taken the temperature dependent blood perfusion and metabolic heat source as exponent variation in nonlinear DPLBHT model, both are experimentally validated function of temperature. In this article we applied finite difference method and Runge–Kutta (4,5) scheme to solve nonlinear problem. In particular case the exact solution is obtained and compared with numerical scheme and both are in good agreement. Effect of different parameters are discussed in detail such as blood perfusion rate, dimensionless heat source parameters, relaxation, and thermalization time on dimensionless temperature. The whole article is analyzed in dimensionless form. [ABSTRACT FROM AUTHOR]

Abstract: In order to study the influence of moisture transfer on the wall internal surface temperature, a coupled heat and moisture transfer transient model was proposed in this paper. Relative humidity and temperature were chosen as the driving potentials. The accuracy of the proposed model was verified by comparing the simulated results with the experimental data. By employing the developed model, the internal surface temperature of walls made of different materials was evaluated under the constant and variable boundary conditions. The results show that the effect of moisture transfer on the wall internal surface temperature is significant. When the moisture transfer is taken into account, the internal surface temperature has cooling effect on the indoor air and is beneficial to improve the indoor thermal environment during the working hours in summer, which lays a scientific basis for low energy building design. [Copyright &y& Elsevier]

Abstract: The paper deals with modeling the convective drying process. A relevant and reliable mathematical model that captures the history and distribution of temperature is presented. The attention is focused on the simultaneous heat and mass transfer occurring during drying where dry and hot air flows about the food. In the present study, external resistance to mass transfer is considered negligible. As a result, the drying curve is almost independent of the boundary conditions, which means that drying is diffusion-controlled. The main connotation of present study regards to undertake analytical procedure to establish the novel model for practical applications. The results show that the temperature evolution can be evaluated from an advanced analytical solution in a quick and efficient manner. The model is validated with the literature experimental data obtained for carrot and mango slabs. A good agreement is obtained between the model predictions and the available experimental results. [Copyright &y& Elsevier]

Abstract: This paper investigates the numerical simulation of non-Fourier transient heat transfer in a two-dimensional sub-100nm metal-oxide-semiconductor field-effect transistor (MOSFET). The dual-phase-lag (DPL) model with a specific normalization procedure is introduced for the modeling of nanoscale heat transport. The boundary conditions are selected similar to what existed in a real MOSFET device, both uniform and non-uniform heat generations within the transistor are applied, and the end parts of the top boundary which are in contact with the metallic material are left open. A temperature-jump boundary condition is used on all boundaries in order to consider the boundary phonon scattering at micro and nanoscale. A three-level finite difference scheme has been employed to generate the numerical results which are illustrated for a silicon sub-100nm MOSFET corresponding to the Knudsen number of 10. The results are presented at real times less than 50ps to avoid the three-dimensional effects. It is concluded that the combination of the DPL model with mixed-type temperature boundary condition is able to predict the heat flux and temperature distribution obtained from the Boltzmann transport equation (BTE) more accurate than the ballistic-diffusive equations (BDE). After verification of our results, the thermal field and the hotspot temperature within the bulk silicon are presented and the effect of adding a layer of silicon-dioxide to the transistor on its thermal behavior has been investigated. [Copyright &y& Elsevier]

Abstract: In the precision glass moulding process, the heat transfer and the resulting transient temperature distributions of the molten glass are of great importance because they significantly affect the productivity as well as the thermally induced residual stresses in the final product. Thermal modelling of the heating system in the glass moulding process considering detailed heating mechanisms therefore plays an important part in optimizing the heating system and the subsequent pressing stage in the lens manufacturing process. The current paper deals with three-dimensional transient thermal modelling of the multi-stage heating system in a wafer based glass moulding process. In order to investigate the importance of the radiation from the interior and surface of the glass, a simple finite volume code is developed to model one dimensional radiation–conduction heat transfer in the glass wafer for an extreme case with very high temperature difference considering temperature dependant thermal conductivity and heat capacity. Afterwards, by using three-dimensional FEM modelling along with a predefined experimental test, the equivalent glass–mould interface contact resistance is determined for two different pressures. Finally, the three-dimensional modelling of the multi-stage heating system in the wafer based glass moulding process is simulated with the FEM software ABAQUS for a particular industrial application for mobile phone camera lenses to obtain the temperature distribution in the glass wafer. In the numerical modelling, the interface boundary conditions for each heating stage are changed according to the determining heat transfer mechanism(s). Numerical results are compared with experimental data to show the validity of the numerical modelling. The obtained results show that the right thermal modelling is highly dependent on the proper choice of thermal boundary conditions in different stages according to the real physical phenomena behind the process. [Copyright &y& Elsevier]

In this paper, a simple transformation of coordinates is proposed that facilitates the efficient simulation of the non-isothermal lithium-ion pseudo 2-D battery model. The transformed model is then conveniently discretized using orthogonal collocation with the collocation points in the spatial direction. The resulting system of differential algebraic equations (DAEs) is solved using efficient adaptive solvers in time. A series of mathematical operations are performed to reformulate the model to enhance computational efficiency and programming convenience while maintaining accuracy even when non-linear or temperature dependent parameters are used. The transformed coordinate allows for efficient simulation and extension from cell sandwich to stack models. Furthermore, the transformation and reformulation techniques are used to simulate operation of an 8-cell battery stack subject to varying heat transfer coefficients as well as specified temperature boundary conditions. [ABSTRACT FROM AUTHOR]

Abstract: The paper presents a model-based investigation of a metal hydride reactor applied as a solid state hydrogen storage device. The elements of a metal hydride reactor are hydrogen supply duct, internal hydrogen distribution, hydride bed, reactor shell and the flow domain of the heat transfer fluid. Internal hydrogen distribution and hydride bed are porous media. Therefore, hydrogen flows through non-porous and porous regions during its reversible exothermic absorption and endothermic desorption, respectively. The interface between porous and non-porous regions is a discontinuity with respect to energy transport mechanisms. Hence, Danckwerts-type boundary conditions for the energy balance equation are introduced. Application of the first and second law of thermodynamics to the interface reveals that temperature jumps may occur at the hydrogen inlet but are not allowed at the hydrogen outlet. Exemplarily the loading behavior of a metal hydride storage tank based on sodium alanate is analyzed. It is demonstrated and experimentally validated that only Danckwerts-type boundary conditions predict the important cooling effect of the inlet hydrogen on the exothermic absorption process correctly. [Copyright &y& Elsevier]

Abstract: This paper focuses on the investigation of the 3D mathematical model to simulate the coupled heat and liquid moisture transfer in hygroscopic porous fibrous media. The flow of the liquid moisture, the water vapor sorption/desorption by fibers and the diffusion of the water vapor are taken into account in this 3D model. Prediction-corrector method is used to solve the 3D governing equations. A series of computational results of the coupled heat and moisture transfer are obtained with the specific initial conditions and boundary conditions. The distribution of the water vapor concentration in the void spaces, the volume fraction of the liquid water in the void spaces, the distribution of the water content in fibers and the changes of the temperature in porous fibrous media are computed. It is shown that the effects of the gravity and capillary actions are significant in hygroscopic porous fibrous media. The comparison with the experimental measurements shows the reasonable agreement between the two. The results illustrate that the 3D model of the coupled heat and liquid moisture transfer in hygroscopic porous fibrous media is satisfactory. [Copyright &y& Elsevier]

Abstract: In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the heat balance and refined integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t >0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions. [Copyright &y& Elsevier]

Abstract: For purposes of an accurate mathematical modeling, it is essential to establish trustworthy boundary conditions. The heat transfer that occurs at the casting/mold interface is one of these important conditions, which is a fundamental task during unsteady solidification in permanent mold casting processes. This paper presents an overview of the inverse analysis technique (IHCP) applied to the determination of interfacial heat transfer coefficients, hi , for a number of alloy solidification situations. A search algorithm is used to find the transient metal/mold interface coefficient during solidification which is reported either as a function of the casting surface temperature or time. Factors affecting hi such as the direction of gravity in relation to the growth interface, the initial melt temperature profile, the wettability of the liquid layer in contact with the mold inner surface, were individually analyzed and experimental laws for hi have been established. [Copyright &y& Elsevier]

Abstract: In the paper, numerical and experimental analyses of heat and mass transfer during frost formation on a fin-and-tube heat exchanger have been presented. Modelling of the frost formation on cold surfaces placed in a humid air stream, requires a complex mathematical approach. A transient two-dimensional mathematical model of frost formation has been developed. The applied mathematical model has been defined using governing equations for the boundary layer that include air and frost sub-domains as well as a boundary condition on the air–frost interface. The mathematical model with initial and boundary conditions has been discretised according to the finite volume method and solved numerically using the SIMPLER algorithm for the velocity–pressure coupling. Results have shown that the frost layer formation significantly influences the heat transfer between air and fins. As a result of numerical calculations, time-wise frost thickness variations for different air humidities, temperatures and velocities have been presented. Using the developed mathematical model, the algorithm and the computer code, which have been experimentally validated, it is possible to predict a decrease of exchanged heat flux in the heat exchanger under frost growth conditions. [Copyright &y& Elsevier]

Abstract: The paper discusses heat transfer enhancement and deterioration phenomena observed in experimental data for fluids at supercritical pressure. The results obtained by the application of various CFD turbulence models in the prediction of experimental data for water and carbon dioxide flowing in circular tubes are firstly described. On this basis, the capabilities of the addressed models in predicting the observed phenomena are shortly discussed. Then, the analysis focuses on further results obtained by a low-Reynolds number k – ε model addressing one of the considered experimental apparatuses by changing the operating conditions. In particular, the usual imposed heat flux boundary condition is changed to assigned wall temperature, in order to highlight effects otherwise impossible to point out. The obtained results, supported by considerations drawn from experimental information, allow comparing the trends observed for heat transfer deterioration at supercritical pressure with those typical of the thermal crisis in boiling systems, clarifying old concepts of similarity among them. [Copyright &y& Elsevier]

This communication presents non-Newtonian fluid flow over a stretching cylinder. Rheological relations of second-grade fluid are employed in the modeling. Heat transfer is characterized by a convectively heated cylinder. Different from the previous classical studies in the literature, the nonlinear thermal radiation contribution is taken into consideration. Resulting nonlinear mathematical problems are computed for the approximate convergent solutions. Impact of different parameters on the velocity and temperature profiles is examined. Computations for heat transfer rate are presented and examined for the influences of pertinent parameters. It is noted that fluid velocity enhances when curvature parameter is increased. Surface heat transfer rate enhances larger Eckert number, radiation parameter and Prandtl number. [ABSTRACT FROM AUTHOR]

Variants of the differential equation of heat conduction in a solid body, which follow from the Fourier and Cattaneo-Vernotte hypotheses and the Lykov equation, are considered. A boundary value problem describing temperature fields in a body (cylinder) upon cyclic heat transfer with cold and hot media is formulated. An analytical solution to the boundary value problem with a hyperbolic differential equation of heat conduction with allowance for thermal relaxation and temperature damping with cyclic boundary conditions of the third kind is given. The thermal transient processes calculated by the classical heat conductance equation and hyperbolic equation of heat conduction on the axis of the cylinder at different values of factors such as the ratio of the thermal damping time to the thermal relaxation time, the duration of cyclic periods, the Fourier relaxation number, and the Biot number are compared. A conclusion is made that the theory of regenerative air heater should be improved by taking into account thermal relaxation and thermal damping in the nozzle and measurements of the thermal relaxation and thermal damping times of the corresponding materials. [ABSTRACT FROM AUTHOR]

New formulations of the optimal control problem for metal solidification in a furnace are proposed in the case of an object of complex geometry. The underlying mathematical model is based on a three-dimensional two-phase initial-boundary value problem of the Stefan type. The formulated problems are solved numerically with the help of gradient optimization methods. The gradient of the cost function is exactly computed by applying the fast automatic differentiation technique. The research results are described and analyzed. Some of the results are illustrated. [ABSTRACT FROM AUTHOR]

We investigate the influence of different thermal and velocity boundary conditions on numerical geodynamo models. We concentrate on the implications for magnetic field morphology, heat transport scaling laws, force balances and generation mechanisms. The field morphology most strongly depends on the local Rossby number, but there is some variation in the dipolarity of the field with boundary condition. Scaling laws also depend on the boundary conditions, but a diffusivity-free scaling is a good first order approximation for all our dipolar models. Our multipolar models, however, obey different scaling laws from dipolar models implying a different force balance in these models. We find that our dipolar models have a stronger degree of Lorentz–Coriolis balance compared to our multipolar models which have a stronger degree of Lorentz-inertial balance.The models with a stronger Lorentz–Coriolis dominance can be generated by either αω, α2ω or α2 mechanisms whereas the models with a stronger Lorentz-inertial balance are all α2 dynamos. These results imply that some caution is necessary when extrapolating results from dynamo models to Earth-like parameters since the choice of boundary conditions can have important effects. [ABSTRACT FROM PUBLISHER]

We consider a boundary value problem that describes heat propagation in a homogeneous isotropic body in the framework of the hyperbolic heat conduction model. We construct a class of boundary data (controls) depending on a functional parameter and providing a given distribution of the body temperature at a given time. By using the Lagrange method, from the constructed class, we choose a subclass of controls minimizing a given loss function. [ABSTRACT FROM AUTHOR]

The article presents a study which investigates the approximate solution to quasilinear parabolic-hyperbolic problem. The study used an initial-boundary-value problem for quasilinear system in four differential equations to represent the mathematical model of interrelated processes of soil mass and heat and moisture transfer being analyzed. Study has presented an algorithm for the problem's approximate solution.

A numerical model of the anterior chamber of the rabbit eye is presented. The model takes into account both the fluid dynamics of the aqueous humor and the realistic boundary conditions at the interface of the cornea with the environment. The model is used to determine the temperature distribution and velocity field under 60-GHz millimeter wave radiation. The maximum predicted temperature (45.8^\circC for an incident power density of 475 mW/cm^2) is in good agreement with experimental results. Moreover, the model shows that there is a value for the incident power density (about 100 mW/cm^2) for which the direction of aqueous humor flow due to buoyancy is inverted, because of the inversion of the temperature gradient in the anterior chamber of the eye. This phenomenon has already been reported from experimental observations and can be numerically studied, if aqueous humor fluid dynamics are taken into account in the heat-transfer model. [ABSTRACT FROM PUBLISHER]

The results of mathematical modeling of free convective heat exchange near a semiinfinite, impermeable, flat vertical surface have been presented. The features of velocity and temperature fields as functions of the boundary conditions and the Prandtl number have been studied. Tables of numerical solutions have been given. The esults obtained have been compared to the numerical data of other authors. [ABSTRACT FROM AUTHOR]