Mathematical model of heat and mass transfer in a bidisperse porous material

A model of heat and mass processes in a body with two types of pores is considered. This model describes the initial stage of substance penetration into the porous system (or the inverse process, namely, substance extraction from the system) and takes into account convective transport in large channels. A kinetic function of impregnation (extraction) of the porous medium and the substance flux density are found for a problem with additional conditions.     

Mathematical simulation of radial heat transfer in packed beds by pseudohomogeneous modeling

Uniform flow regime and constant effective thermal conductivity inside packed beds are commonly accepted in the evaluation of the fluid dynamics and heat transfer in such systems.However,several authors have confirmed the presence of an oscillatory velocity profile caused by the effective contribution of porosity profile in the fluid dynamic behavior of packed beds,which directly influences the heat transfer inside the beds.This paper describes the application of a pseudo-homogeneous mathematical ...     

Coupled heat transfer in a composite material

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 141–148, July–August, 1991.     

Mathematical modeling of volumetric material growth

Growth (resp. atrophy) describes the physical processes by which a material of solid body increases (resp. decreases) its size by addition (resp. removal) of mass. In the present contribution, we propose a sound mathematical analysis of growth, relying on the decomposition of the geometric deformation tensor into the product of a growth tensor describing the local addition of material and an elastic tensor, which is characterizing the reorganization of the body. The Blatz-Co hyperelastic constitutive model is adopted for an isotropic body, satisfying convexity conditions (resp. concavity conditions) with respect to the transformation gradient (resp. temperature). The evolution law for the transplant is obtained from the natural assumption that the evolution of the material is independent of the reference frame. It involves a modified Eshelby tensor based on the specific free energy density. The heat flux is dependent upon the transplant. The model consists of the constitutive equation, the energy balance, and the evolution law for the transplant. It is completed by suitable boundary conditions for the displacement, temperature and transplant tensor. The existence of locally unique solutions is obtained, for sufficiently smooth data close to the stable equilibrium. The question of the global existence is examined in the simplified situation of quasistatic isothermal equations of linear elasticity under the assumption of isotropic growth.     

Mathematical modeling of polymer film casting under biaxial stretching taking into account heat transfer

Polymer film casting is studied using a modified Vinogradov-Pokrovskii rheologicalmodel with heat transfer taken into account. Dependences of the film temperature, velocity, and width on the distance to the extruder exit was obtained and the effect of model parameters on these dependences was examined.     

Advanced near-wall modeling for engine heat transfer

Recent developments in the engine heat transfer modeling tend to improve existing wall heat transfer models (temperature wall functions) which mostly rely on the standard or low-Re variants of k-ε turbulence model. Presently applied mesh resolutions already allow for first near-wall computational cells reaching the buffer or locally even viscous/conductive sub-layer, thus increasing the importance of more sophisticated modeling approach. As temperature gradient-induced density and fluid property variations become significant, wall heat transfer is strongly influenced by property variations (viscous/conductive sub-layer) and predictive capability of the turbulence model (buffer region), standard wall laws being inadequate anymore, even for attached boundary layers. The present approach relies on the k-ζ-f turbulence model and formulates a compressible wall function of Han and Reitz in the framework of hybrid wall treatment. The model is validated against spark ignition (SI) engine heat transfer measurements. Predicted wall heat flux evolutions on the cylinder head exhibit very good agreement with the experimental data, being superior to similar numerical predictions available in the published literature.     

Mathematical model of heat transfer in a fluid with account for its relaxation properties

Using the terms that take account for the temporal and spatial nonlocality (time variation of the heat flux and the temperature gradient) in the formula of Fourier’s law for the heat flux a differential equation for a fluid in motion is derived that contains the second time derivative and themixed derivative with respect to the spatial and temporal variables. Numerical solution of the problem of heat transfer in the laminar fluid flow in a plane channel demonstrates that, in view of the lag in the time variation of the heat flux from zero to a certain maximum value, the boundary condition of the first kind (thermal shock) cannot be instantaneously realized. The process of its stabilization on the wall is characterized by a certain time interval, whose duration is determined by the relaxation properties of the fluid. At large values of the dimensionless coefficients of the heat flux relaxation and the temperature gradient the boundary condition of the first kind can be realized only as the steady state is attainted, as Fo→∞. In this case, the flow does not contain temperature jumps and negative temperature values.     

Mathematical model of axisymmetric quasi-steady-state heat and mass transfer in a gas hydrate reservoir

Two problems of axisymmetric gas (gas and water) flow through a reservoir which contains a heterogeneous mixture, namely, gas hydrate, ice (water), and gas, are considered. The exact solutions to the corresponding steady-state and quasi-steady-state nonlinear problems are found. The critical diagrams are constructed for various flow regimes. The characteristic distributions of the gas hydrate, ice (water), and gas saturations are shown for various values of the parameters.     

Numerical modeling of fluid flow and heat transfer in a narrow Taylor-Couette-Poiseuille system

We consider turbulent flows in a differentially heated Taylor-Couette system with an axial Poiseuille flow. The numerical approach is based on the Reynolds Stress Modeling (RSM) of [Elena and Schiestel, 1996] and [Schiestel and Elena, 1997] widely validated in various rotor-stator cavities with throughflow ( [Poncet, 2005], [Poncet et al., 2005] and [Haddadi and Poncet, 2008]) and heat transfer (Poncet and Schiestel, 2007). To show the capability of the present code, our numerical predictions are compared very favorably to the velocity measurements of Escudier and Gouldson (1995) in the isothermal case, for both the mean and turbulent fields. The RSM model improves, in particular, the predictions of the k-ε model of Naser (1997). Then, the second order model is applied for a large range of rotational Reynolds (3744 ? Re_i ? 37,443) and Prandtl numbers (0.01 ? Pr ? 12), flow rate coefficient (0 ? C_w ? 30,000) in a very narrow cavity of radius ratio s = R_i/R_o = 0.961 and aspect ratio L = (R_o − R_i)/h = 0.013, where R_i and R_o are the radii of the inner and outer cylinders respectively and h is the cavity height. Temperature gradients are imposed between the incoming fluid and the inner and outer cylinders. The mean hydrodynamic and thermal fields reveal three distinct regions across the radial gap with a central region of almost constant axial and tangential mean velocities and constant mean temperature. Turbulence, which is weakly anisotropic, is mainly concentrated in that region and vanishes towards the cylinders. The mean velocity distributions are not clearly affected by the rotational Reynolds number and the flow rate coefficient. The effects of the flow parameters on the thermal field are more noticeable and considered in details. Correlations for the averaged Nusselt numbers along both cylinders are finally provided according to the flow control parameters Re_i, C_w, and Pr.     

Semi-empirical modeling of pool boiling heat transfer in binary mixtures

Pool boiling heat transfer has been investigated for various binary mixtures, including acetone/isopropanol, water/acetone, water/methanol, water/ethanol, water/isopropanol, water/monoethanolamine, water/diethanolamine and water/triethyleneglycol as test solutions. Many correlations have been developed to predict the pool boiling heat transfer coefficient in mixtures in the past few decades, however the predicted values are not confirming. In addition, the application of many existing correlations requires some individual adjusting parameters that may be not available for every system. In this investigation, a new set of experimental data are presented. These data have been compared to major existing correlations. It is observed that the pool boiling heat transfer coefficients in mixtures are less than the ideal boiling heat transfer coefficient. A new semi-empirical model has been proposed based on the mass transfer resistance to predict the boiling heat transfer coefficient with satisfactory accuracy. The new model does not include any tuning parameter and is applicable to any given binary system. The performance of the proposed model is superior to most existing correlations.     

Mass and heat transfer modeling of bio-substrates during packaging

Perishable bio-substrate behavior can be modeled during packaged storage. Local mass and heattransfer have been coupled to respiration rate and microbial growth. Validating measurements have also been performed, and a multi-objective optimization was employed to tune the model. The model is able to simulate gas composition history and local bacteria spoilage in storage modes commonly adopted by the food industry, depending on product features and temperature. Exploitation of this mathematical tool would allow for informed technical and management decisions.     

一个多孔有机织物热湿传递过程的数学模型

利用多孔介质中的Darcy定律建立了一个多孔有机织物中热湿传递过程的数学模型，并提出了一个描述多孔有机织物中液相水重力与表面张力的对比关系的数H=5gρldcLτlεl1/3/2σcosФε1/3采用Crank—Nicolson方法数值求解了该模型，得到了在相同初始和边界条件下，不同有机材料织物中的热湿传递过程，并给出了多孔有机织物中的水蒸汽的浓度场分布、温度场分布以及纤维中的含水量的分布。计算结果与实验结果是吻合的。     

Computational modeling of heat transfer over an unsteady stretching surface embedded in a porous medium

The present paper deals with the study of heat transfer characteristics in the laminar boundary layer flow of an incompressible viscous fluid over an unsteady stretching sheet which is placed in a porous medium in the presence of viscous dissipation and internal absorption or generation. Similarity transformations are used to convert the governing time dependent nonlinear boundary layer equations into a system of non-linear ordinary differential equations containing Prandtl number, Eckert number, heat source/sink parameter, porous parameter and unsteadiness parameter with appropriate boundary conditions. These equations are solved numerically by applying shooting method using Runge-Kutta-Fehlberg method. Comparison of numerical results is made with the earlier published results under limiting cases. The effects of the parameters which determine the velocity and temperature fields are discussed in detail.     

非均质材料热传导问题的扩展有限元法

针对非均质材料,提出了以导热系数为基本参数的热传导扩展有限元法。划分网格时不需要考虑材料界面的存在,因此网格的形成可以大大地简化,且可以获得高质量的网格。不含材料界面的单元,其温度场函数将退化为常规有限元的函数。含材料界面的单元,采用基于水平集的加强函数加强常规温度的近似,加强函数用于模拟界面。数值算例结果体现了该方法...     

Numerically gas radiation heat transfer modeling in chemically nonequilibrium reactive flow

A numerical method for calculation of strong radiation for 2D reactive air is developed. Governing equations are taken to be 2D, compressible Reynolds-average Navier–Stokes and species transport equations. Also, radiation heat flux is evaluated using a model of discrete ordinate method. A multiband model is used to construct absorption coefficients. Tangent slab approximation is assumed to determine the characteristic parameters needed in the Discrete Ordinates Method.     

Convective heat transfer characteristics of microencapsulated phase change material suspensions in minichannels

A comparative experimental study was conducted in order to investigate the convective heat transfer characteristics of water-based suspensions of microencapsulated phase change material (MEPCM) flowing through rectangular copper minichannels. The hydraulic diameter of the channels was 2.71 mm. MEPCM particles with an average size of 4.97 μm were used to form suspensions with mass concentrations ranging from 0 to 20%. The comparative experiments were performed for varying mass flow rates in the laminar region and varying thermal conditions. The cooling performance of the MEPCM suspensions strongly depended on the mass flow rate and the MEPCM mass concentration. The 5% suspension always showed a better cooling performance than water resulting in lower wall temperatures and enhanced heat transfer coefficients within the whole range of mass flow rates. The suspensions with higher mass concentrations, however, were more effective only at low mass flow rates. At higher mass flow rates they showed a less effective cooling performance than water.     

Computational modeling of biomagnetic micropolar blood flow and heat transfer in a two-dimensional non-Darcian porous medium

We study theoretically and computationally the incompressible, non-conducting, micropolar, biomagnetic (blood) flow and heat transfer through a two-dimensional square porous medium in an (x,y) coordinate system, bound by impermeable walls. The magnetic field acting on the fluid is generated by an electrical current flowing normal to the x–y plane, at a distance l beneath the base side of the square. The flow regime is affected by the magnetization B ₀ and a linear relation is used to define the relationship between magnetization and magnetic field intensity. The steady governing equations for x-direction translational (linear) momentum, y-direction translational (linear) momentum, angular momentum (micro-rotation) and energy (heat) conservation are presented. The energy equation incorporates a special term designating the thermal power per unit volume due to the magnetocaloric effect. The governing equations are non-dimensionalized into a dimensionless (ξ,η) coordinate system using a set of similarity transformations. The resulting two point boundary value problem is shown to be represented by five dependent non-dimensional variables, f _ξ  (velocity), f _η (velocity), g (micro-rotation), E (magnetic field intensity) and θ (temperature) with appropriate boundary conditions at the walls. The thermophysical parameters controlling the flow are the micropolar parameter (R), biomagnetic parameter (N _H ), Darcy number (Da), Forchheimer (Fs), magnetic field strength parameter (Mn), Eckert number (Ec) and Prandtl number (Pr). Numerical solutions are obtained using the finite element method and also the finite difference method for Ec=2.476×10⁻⁶ and Prandtl number Pr=20, which represent realistic biomagnetic hemodynamic and heat transfer scenarios. Temperatures are shown to be considerably increased with Mn values but depressed by a rise in biomagnetic parameter (N _H ) and also a rise in micropolarity (R). Translational velocity components are found to decrease substantially with micropolarity (R), a trend consistent with Newtonian blood flows. Micro-rotation values are shown to increase considerably with a rise in R values but are reduced with a rise in biomagnetic parameter (N _H ). Both translational velocities are boosted with a rise in Darcy number as is micro-rotation. Forchheimer number is also shown to decrease translational velocities but increase micro-rotation. Excellent agreement is demonstrated between both numerical solutions. The mathematical model finds applications in blood flow control devices, hemodynamics in porous biomaterials and also biomagnetic flows in highly perfused skeletal tissue. Dedicated to Professor Y.C. Fung (1919-), Emeritus Professor of Biomechanics, Bioengineering Department, University of California at San Diego, USA for his seminal contributions to biomechanics and physiological fluid mechanics over four decades and his excellent encouragement to the authors, in particular OAB, with computational biofluid dynamics research.     

Mathematical modeling of natural convection in a vertical cylindrical tank with alternating-sign heat flux distribution on the wall

On the basis of a numerical solution of the two-dimensional nonstationary Navier-Stokes equations in the Boussinesq approximation, mathematical modeling of laminar natural convection is carried out for a sinusoidal heat flux distribution on the side wall. For various values of the governing parameters, the spatial and temporal structure of the convective flow is analyzed in detail.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 66–72, March–April, 1996.     

Thermophysical and heat transfer properties of phase change material candidate for waste heat transportation system

A waste heat transportation system––trans-heat (TH) system––is quite attractive that uses the latent heat of a phase change material (PCM). The purpose of this paper is to study the thermophysical properties of various sugars and sodium acetate trihydrate (SAT) as PCMs for a practical TH system and the heat transfer property between PCM selected and heat transfer oil, by using differential scanning calorimetry (DSC), thermogravimetry-differential thermal analysis (TG-DTA) and a heat storage tube. As a result, erythritol, with a large latent heat of 344 kJ/kg at melting point of 117°C, high decomposition point of 160°C and excellent chemical stability under repeated phase change cycles was found to be the best PCM among them for the practical TH system. In the heat release experiments between liquid erythritol and flowing cold oil, we observed foaming phenomena of encapsulated oil, in which oil droplet was coated by solidification of PCM.