Solution Of Transfer Equation Research Articles

Physics‐based numerical simulation of heat and moisture transport in red chili subjected to mix‐mode solar drying with phase change energy storage

AbstractIn this study, a coupled heat and mass transfer model was developed using a finite element (FE) simulation approach to describe solar drying of red chili integrated with Na2SO4∙10H2O as phase change material thermal storage. The coupled heat and mass transfer equation solution was achieved by using COMSOL multiphysics with three‐dimensional (3D) axisymmetric geometry mesh generation. The Lagrange triangular FEs of very fine size were employed in obtaining the geometry of the mesh. This study adopts a time‐dependent study that shows the variation of time within 0, 2, 3, 4, and 5 hours, respectively, for continuous drying of red chili in the solar dryer. The effect of air temperature and thermal storage on temperature and moisture distribution on drying of red chili was investigated. The temperature distribution was not uniform and heat transfer at the base was higher than the tip while there is a clear moisture gradient for different drying times, though this moisture moves from the base to the tip and more uniform distribution was obtained after 4 hours of drying. Drying temperature increased from a side to the core of the sample as the drying progresses. Although thermal storage accelerated the drying process, solar radiation showed a greater influence on the drying process. The developed numerical model with the experimental results showed the same trend with the values of MAE and SE for temperature found to be 0.48132 and 0.000842 for the without thermal storage (NTS) sample, 0.2266 and 30.000551 for thermal storage (TS). Also, the values of MAE and SE are 0.0051 and 0.006048 for NTS, 0.00212 and 0.00538 for TS, respectively for moisture profile. The lower values of these errors specify a better prediction capability of the model code.

Assessing the local temperature of human cornea exposed to surface ablation by different laser refractive-surgery devices: a numerical comparative study.

To evaluate the local temperature at corneal tissue after applying single laser pulse from six commercial devices; Medilex™, Katana laser-soft, MEL90, Technolas-Teneo317, Alcon EX500, and PulzarTMZ1. The temperature distribution is simulated using finite element solution of the Penne's bio-heat transfer equation on a 3-D model of human cornea using the manufacturer's assigning parameters. The obtained results showed that the heating effect of Katana laser soft is 40% lower than MEL90 and Pulzar™ Z1, while the broad beam Medilex™ showed the minimum temperature rise especially at 248-nm laser radiation. The change in laser parameters selected for ablation has significant effect on the corneal local temperature. The broad beam-based device produces lower local corneal temperature than other flying spot types.

Exact solution for heat transport of Newtonian fluid with quadratic order thermal slip in a porous medium

In this communication, an analytical solution for the thermal transfer of Newtonian fluid flow with quadratic order thermal and velocity slips is presented for the first time. The flow of a Newtonian fluid over a stretching sheet which is embedded in a porous medium is considered. Karniadakis and Beskok’s quadratic order slip boundary conditions are taking into account. A closed form of analytical solution of momentum equation is used to derive the analytical solution of heat transfer equation in terms of confluent hyper-geometric function with quadratic order thermal slip boundary condition. Accuracy of present results is assured with the numerical solution obtained by Iterative Power Series method with shooting technique. The impacts of porous medium parameter, tangential momentum accommodation coefficient, energy accommodation coefficient on velocity and temperature profiles, skin friction coefficient and reduced Nusselt number are discussed. The Nusselt number increases with the higher estimations of tangential momentum and energy accommodation coefficients.

Numerical solution of stochastic time fractional heat transfer equation with additive noise

In the present paper, we developed an explicit finite difference scheme for stochastic time fractional heat transfer equation. Furthermore, we proved the conditional stability of the solution of the scheme and analyze the effect of the multiplier of the random noise in mean square stability. Also, we discuss the convergence of the explicit scheme in the mean square sense. The approximate solution of the practical problem is obtain by developed scheme and it is represented graphically by Mathematica software.

Computational study of plasma-induced flow instabilities in power modulated atmospheric-pressure microwave plasma jet

This work presents a combined experimental and simulation-based investigation of gas flow perturbations caused by atmospheric-pressure microwave plasma jet with modulated power. These plasma-induced flow instabilities are observed experimentally by schlieren imaging and the mechanism of their formation is explained using a numerical model. The model offers a time-resolved self-consistent solution of plasma dynamics, gas flow, and heat transfer equations. The simulation results are in good agreement with the experimental observations and we conclude that the key mechanism behind the flow perturbations is rapid gas heating at the end of the discharge tube.

An Efficient Acceleration of Solving Heat and Mass Transfer Equations with the Second Kind Boundary Conditions in Capillary Porous Radially Composite Cylinder Using Programmable Graphics Hardware

With the recent developments in computing technology, increased efforts have gone into the simulation of various scientific methods and phenomenon in engineering fields. One such case is the simulation of heat and mass transfer equations which is becoming more and more important in analyzing various scenarios in engineering applications. Analysing the heat and mass transfer phenomenon under various environmental conditions require us to simulate it. However, this process of numerical solution of heat and mass transfer equations is very time consuming. Therefore, this paper aims at utilizing one of the acceleration techniques developed in the graphics community that exploits a graphics processing unit (GPU) which is applied to the numerical solutions of heat and mass transfer equations. The nVidia Compute Unified Device Architecture (CUDA) programming model can be a good method of applying parallel computing to program the graphical processing unit. This paper shows a good improvement in the performance, while solving the heat and mass transfer equations for a capillary porous radially composite cylinder with the second kind of boundary conditions, numerically running on GPU. This heat and mass transfer simulation is implemented using CUDA platform on nVidia Quadro FX 4800 graphics card. Our experimental results depict the drastic performance improvement when GPU is used to perform heat and mass transfer simulation. GPU can significantly accelerate the performance with a maximum observed speedup of more than 8 fold times. Therefore, the GPU is a good approach to accelerate the heat and mass transfer simulation.

Numerical Solution of the 2D Radiative Heat Transfer Equation Using SPH Method

Numerical Solution of the 2D Radiative Heat Transfer Equation Using SPH Method

Thermoelastic study of a functionally graded annular fin with variable thermal parameters using semiexact solution

In this paper, the thermoelastic behavior of a functionally graded material (FGM) annular fin is investigated. The material properties of the annular fin are assumed to vary radially. The heat transfer coefficient and internal heat generation are considered to be functions of temperature. A closed form solution of nonlinear heat transfer equation for the FGM fin is obtained using the homotopy perturbation method (HPM) which leads to nonuniform temperature distributions within the fin. The temperature field is then coupled with the classical theory of elasticity and the associated thermal stresses are derived analytically. For the correctness of the present closed form solution for the stress field, the results are compared with the ANSYS-based finite element method (FEM) solution. The present HPM-based closed form solution of the stress field exhibits a good agreement with the FEM results. The effect of various thermal parameters such as the thermogeometric parameter, conduction-radiation parameter, internal heat generation parameter, coefficient of variation of thermal conductivity, and the coefficient of thermal expansion on the thermal stresses are discussed. The results are presented in both nondimensional and dimensional form. The dimensional stress analysis discloses the suitability of FGM as the fin material in practical applications.

Meta-models for building energy loads at an arbitrary location

Meta-model-based optimization eases the burden of large time and computational costs by replacing the entire simulation process (which requires solutions of transient transfer equations) with the evaluation of simple meta-model functions (such as polynomials) while preserving the accuracy of dynamic simulations. The objective of this study is to present the development of meta-models to predict the cooling and heating load change of a building with variations in building envelope design factors under arbitrary climate conditions. The meta-models were developed using the results of building energy simulations for eight representative cities of climate conditions in the U.S. and were validated by comparing the predictions with simulation results for other cities in the US and Europe. The comparison showed that good accuracy was achieved with the developed unified single model.

MINIMIZATION OF THE CHEMICAL POLLUTION LEVEL AT THE WORKING ZONES IN OPEN AREAS USING SCREENS

Purpose. The scientific work aims to develop a new method for assessing the level of chemical air pollution in working zones located in open areas near highways using screens of different heights. Methodology. The analytical method for calculating the airflow velocity field near protective screens is based on the mathematical apparatus of the theory of complex variable functions, which allows obtaining the value of the velocity potential and the flow function, to calculate the velocity value at any point of the plane with a screen of different height. The obtained velocity field is used to calculate the level of carbon monoxide concentration in the numerical solution of the two-dimensional mass transfer equation. Findings. The developed program of numerical calculation allows conducting computational experiments on the effectiveness of the use of protective screens, taking into account changes in their geometry and meteorological conditions. The developed method based on the obtained concentration field makes it possible to carry out an assessment of the risk of chronic intoxication for the employees of the take-out trade, who are within the zone of the emission source (highway) for a long time. Originality. The regularities of changes in the concentration of carbon monoxide are established depending on the distance to the emission source at a height of 2 m from the ground in the presence of a screen of a certain height and in its absence. A risk assessment of chronic carbon monoxide intoxication has been carried out for take-out trade workers near the highway. It is shown that the presence of the screen reduces the risk of chronic CO intoxication by 10% as compared to its absence. Increasing the screen height to 1.8 m reduces the risk of chronic intoxication by 6% relatively to the situation when the screen height is 1.2 m. Practical value. The developed numerical-analytical method for calculating the level of chemical pollution in working zones in open areas and the program «Screen» created on its basis allow us to carry out a prompt forecast of atmospheric air pollution level with carbon monoxide taking into account the effectiveness of the screens. Quantitative results are necessary at the planning stage of trading places near highways, during the architectural-planned reorganization of adjacent developments.

DETERMINING ZONES OF CHEMICAL POLLUTION IN THE CITIES AND ASSESMENT OF CHRONIC DISEASES RISKS

Purpose. The scientific paper is aimed at creating a methodology of chemical pollution zones in the territories of industrial cities and accounting the possibility of assessing the risks of chronic diseases. Methodology. The method of numerical calculation of nitrogen dioxide concentration in atmospheric air is based on the solution of three-dimensional impurity transfer equations, which directly comes from a permanently stationary source (industrial enterprise) and a linearly distributed source (highway). The method takes into account the process of chemical transformation of impurities and photolysis in the atmosphere. The numerical model is based on the splitting of model equations and their solution using an implicit difference scheme. Findings. The created software allows conducting computational experiments to calculate the areas of atmospheric air pollution with nitrogen dioxide, taking into account the interaction of impurities coming from various types of pollution sources and meteorological parameters. On the basis of the obtained field of nitrogen dioxide concentration, an assessment of the change in the risk of chronic intoxication associated with atmospheric air pollution with nitrogen dioxide over 50 years was carried out. Originalitys. For the first time the regularities of changes in the level of atmospheric air pollution with nitrogen dioxide have been established with due regard to the mutual influence of emissions from the industrial enterprise and highway and their chemical transformation in the atmosphere. The risk of chronic intoxication has been calculated and its changes have been analyzed with due regard to the interaction of emissions from the industrial enterprise and highway, it leads up to 10% of risk increasing. Practical value. Authors developed a mathematical model and method of numerical calculation. Software created on their base allows obtaining quickly quantitative results necessary in developing the system for monitoring the man-made loaded regions of the city. The obtained patterns of impurities dispersion allow us to estimate the levels of pollution in urban areas of the city by emissions from industrial enterprises and highways. Accounting of the mutual impact of emissions and the calculation of risks of intoxication allows solving environmental problems arising in the development of transport strategy in cities.

Numerical modeling and comparative study of different membrane-based liquid desiccant dehumidifiers

A numerical model for membrane-based liquid desiccant dehumidifiers is presented. The model uses the conjugate method and calculates a more realistic boundary condition on the membrane, and the separating walls. This boundary condition is calculated by the simultaneous solution of momentum, energy, and mass transfer equations of flows. To increase accuracy, flows are considered hydrodynamically, thermally, and in concentration to be developing. The validation results showed that the model can accurately predict the humidity ratio change of the supply air with less than 3.22% error. Afterward, four membrane-based liquid desiccant dehumidifiers including cross-flow, counter-flow, internally cooled and developed internally cooled are modeled and investigated. The dehumidifiers performances are compared at different inlet air conditions, and the results indicate that the developed internally cooled dehumidifier has the highest effectiveness.

ГЕОТЕРМИЯ И ОЦЕНКА НЕФТЕГАЗОВОГО ПОТЕНЦИАЛА БУРЕИНСКОГО БАССЕЙНА (ДАЛЬНИЙ ВОСТОК РОССИИ)

Актуальность. Буреинский осадочный бассейн – наиболее интересная в нефтегазоносном отношении межгорная впадина слабоизученной материковой части Дальнего Востока России. Положительная оценка в отношении перспектив обнаружения в отложениях бассейна месторождений нефти и газа обоснована результатами ранее проведённых производственных и научных работ. Цель: дальнейшая аргументация перспектив нефтегазоносности верхнеюрско-нижнемеловых отложений Буреинского бассейна на основе применения отечественного программного обеспечения бассейнового моделирования TeploDialog, обладающего оригинальными особенностями. Объект: осадочные комплексы средне-верхнеюрский, верхнеюрско-нижнемеловой и меловой Кындалского грабена, наиболее хорошо изученной структуры в составе Буреинского краевого прогиба. Ранее проведенные исследования показали, что в процесс нефтегазообразования вовлечён весь юрско-меловой разрез Буреинского бассейна. Методы. В комплексе ТeploDialog реализован метод палеотемпературного моделирования, основанный на численном решении уравнения теплопроводности горизонтально-слоистого твердого тела с подвижной верхней границей. В математическую модель непосредственно включены климатический вековой ход температур на земной поверхности, как краевое условие, и палеотемпературы из определений отражательной способности витринита, как «наблюденные». Метод не требует априорных сведений о природе и величинах глубинного теплового потока, поток определяется решением обратной задачи геотермии в рамках параметрического описания седиментационной истории и истории теплофизических свойств осадочной толщи. Результаты. Установлено, что геотермия грабена, начиная с юрского времени, благоприятствовала процессам генерации жидких углеводородов в породах осадочного чехла, которые могли начаться около 107 млн лет назад, в середине альба. Наиболее интенсивно нефтегенерация происходила в период 107–40 млн лет назад, до середины эоцена. Температурные условия генерации жидких углеводородов сохраняются для талынджанского очага. Наибольшая продолжительность температурных периодов, благоприятных для газообразования, наблюдается в чемчукинском очаге. Условия генерации газа сохраняются для ургальского и чагдомынского очагов. Результаты, полученные с использованием отечественной системы TeploDialog и ранее полученные в системе PetroMod, во многом совпадают. Названные системы характеризуются разными подходами к рассмотрению тектоно-седиментационных и термических условий генерации УВ. Поэтому результаты настоящих исследований являются дополнительной аргументацией положительных перспектив нефтегазоносности верхнеюрско-нижнемеловых отложений Буреинского бассейна.

Semi-Analytic Monte Carlo Model for Oceanographic Lidar Systems: Lookup Table Method Used for Randomly Choosing Scattering Angles

Monte Carlo (MC) is a significant technique for finding the radiative transfer equation (RTE) solution. Nowadays, the Henyey-Greenstein (HG) scattering phase function (spf) has been widely used in most studies during the core procedure of randomly choosing scattering angles in oceanographic lidar MC simulations. However, the HG phase function does not work well at small or large scattering angles. Other spfs work well, e.g., Fournier-Forand phase function (FF); however, solving the cumulative distribution function (cdf) of the scattering phase function (even if possible) would result in a complicated formula. To avoid the above-mentioned problems, we present a semi-analytic MC radiative transfer model in this paper, which uses the cdf equation to build up a lookup table (LUT) of ψ vs. P Ψ ( ψ ) to determine scattering angles for various spfs (e.g., FF, Petzold measured particle phase function, and so on). Moreover, a lidar geometric model for analytically estimating the probability of photon scatter back to a remote receiver was developed; in particular, inhomogeneous layers are divided into voxels with different optical properties; therefore, it is useful for inhomogeneous water. First, the simulations between the inverse function method for HG cdf and the LUT method for FF cdf were compared. Then, multiple scattering and wind-driven sea surface condition effects were studied. Finally, we compared our simulation results with measurements of airborne lidar. The mean relative errors between simulation and measurements in inhomogeneous water are within 14% for the LUT method and within 22% for the inverse cdf (ICDF) method. The results suggest feasibility and effectiveness of our simulation model.

Calculation of the numerical benchmark NURISP based on the complex MRNK + KEDR-D

The Kurchatov Institute developed the MRNK software package that provides the solution of the nonstationary neutron transfer equation based on the multipoint kinetics method. Currently, work is underway to improve the MRNK software package - connecting feedback on the thermophysical properties of reactor materials. To determine the thermophysical parameters, the KEDR-D program is used - a modified version of the stationary three-dimensional KEDR program for calculating non-stationary processes. The task was set to verify the MRNK + KEDR-D complex based on published data for the international numerical benchmark NURISP. The report presents the stages of achieving the goal (calculation of the stationary state of the core and comparison with the reference data; investigation of fast transient process and comparison with reference data.) In this paper, the data obtained for the MRNK + KEDR-D complex are compared with the data obtained for the Tripoli4-SubChanFlow and DYN3D-FLICA, DYN3D-SubChanFlow complexes. When calculating the steady state of the active zone, the results are in excellent agreement with the results obtained on foreign complexes. Discrepancies in temperature of the fuel and coolant, density of the coolant and distribution of energy release over the height of the assembly are minimal.When calculating the fast transient process (removal of control rods in the central fuel assembly in 0.1 s), the results are consistent with the reference data satisfactorily. There are discrepancies in the area of the greatest impacts of feedback. A comparison was made of the dependence of the temperature of the fuel and the coolant, the power change over time.

Fundamental solution of steady and transient bio heat transfer equations especially for skin burn and hyperthermia treatments

AbstractIn the field of bio heat transfer, as of now, the main concern of researchers lies in the proper and accurate thermal damage of the diseased tissues without destroying or damaging the neighboring healthy tissues during the tumor treatment. The present work aims to develop a new approach toward solving the bio heat transfer equations for the skin burn and hyperthermia treatments. Both analytical and numerical solutions are proposed. For the analytical study, a differential transform method is used to solve steady and unsteady state heat equations. The finite volume method is adopted to solve these equations numerically, which provides a better scope to solve the highly nonlinear complex equations. To obtain a complete solution, a code is developed in MATLAB and MATHEMATICA. The variation of different parameters, such as perfusion constant, space heating, surface step heating, and thermal conductivity, with time were observed. Apart from the above analysis of temperature distribution during skin burn through the spilling of hot beverage, its numerical solution was also performed for this problem at different boundary conditions. It was observed that with the help of the temperature distribution, depending on the time and the severity of the burn, different ranges of depths of the burn can be determined.

A localized RBF-MLPG method for numerical study of heat and mass transfer equations in elliptic fins

The aim of this paper is to propose a local meshless method for the numerical solutions of heat and mass transfer equations in elliptic fins. The domain and boundary are discretized with arbitrary positioned nodes. Then, around each node a small number of neighboring nodes, called stencil, is considered. By collocating the unknown solution and enforcing the PDE governing operator on each stencil, a small system is obtained. Enforcement of the PDE governing operator on each stencil is done via its local weak formulation on a subdomain contained in the stencil.Using local weak formulation increases the stability of the method and makes it more efficient than the existing Local RBF methods. In addition, the boundary conditions are directly imposed via stencils which contain boundary points. Using the concept of generalized differentiations, an iterative approach based on Newton method is proposed to deal with the nonlinear term. Abenchmark problem with known analytical solution is used to investigate the accuracy of the proposed method and its sensitivity to different parameters. It is observed that the method enjoys exponential convergence and in comparison with existing local methods, the presented method is more stable and accurate. After investigating the validation of the method, the method is successfully used for solving the governing differential equations of the 2-D temperature distribution under the dry and fully wet conditions and the numerical results are obtained and presented on two different computational domains.

Impact of Liquid Medium on Laser Ablation Mechanism: Surface Heating and Cooling

Stainless steel target was ablated under both of Hexane and water to examine the effect of liquid on the ablation mechanism in terms of surface heating and cooling. Experimentally, a narrow, a smooth and a deep ablation is observed under water. In addition, the pit due to the collapse of cavitation bubble under water is insignificant as compared with Hexane. The focused beam on the target under liquid was estimated from measuring the crater’s diameter from the optical image. The difference in focused beam sizes is attributed mainly to the refractive index of the liquid. Heat transfer equation is solved to estimate the temperature profile on the solid surface for a single pulse. By considering the estimated beam size under liquid, the solution of heat transfer equation suggests for the first time rapid heating of the target under water, but doesn’t confirm the rapid cooling rate under Hexane. The smooth ablation in water is attributed to the more confined plasma.

Stresses in radiative annular fin under thermal loading and its inverse modeling using sine cosine algorithm (SCA)

This work presents a novel mathematical model for the analysis of thermal stresses in a radiative annular fin with temperature-dependent thermal conductivity and radiative parameter. An approximate analytical solution for thermal stresses is derived using a homotopy perturbation method (HPM)-based closed-form solution of steady-state nonlinear heat transfer equation, coupled with classical elasticity theory. The effect of thermal parameters on the temperature field and the thermal stress fields are discussed. The various thermal parameters, such as a parameter describing the temperature-dependent thermal conductivity, coefficient of thermal expansion, coefficient of radiative parameter, and the variable radiative parameter, are inversely estimated for a given stress field. For inverse modeling, a population-based sine cosine algorithm (SCA) was employed to estimate the thermal parameters. The inverse modeling is verified by using the estimated thermal parameters in the closed-form solution of stress field. The reconstructed stress fields obtained from the inversely estimated parameters are then compared with the reference stress field. Results show a very good agreement between the reference stress field and the inversely estimated stress fields.

Stability of Stationary Solutions of the Radiative Heat Transfer Equations

A model of complex heat transfer, including the $${{P}_{1}}$$ -approximation for the radiative transfer equation, is considered. The asymptotic stability of the steady states without requiring the smallness of the initial perturbations is proven.