Mathematical Model Of Heat Transfer Research Articles

Experimental and numerical study on the heat transfer performance inside integrated sublimator driven coldplate for aerospace applications

Integrated Sublimator Drive Coldplate (ISDC) is a novel sublimator, which couples the Sublimator Drive Coldplate (SDC) with a pump driven fluid loop so that the whole system loop can be cooled effectively. To study heat transfer characteristics of ISDC under different working modes, the detailed ISDC model, the mathematical models of heat and mass transfer and the ground heat transfer test system are established. In this study, the effects of state parameters of circulating cooling water (CCW) and heat flux on the heat transfer characteristics of ISDC under different working modes are studied experimentally and numerically. The results show that the heat flux is 7000 W/m2 with a surface temperature of only 286.4 K which justifies ISDC's heat-sinking capability. The heat dissipation effect of ISDC on avionics boxes is better than that of CCW in ISDC mode. The condition for CCW to cooperate with feed water sublimation for dissipating the avionics boxes is that CCW's inlet temperature is less than 298.15 K, when heat flux and CCW's mass flow are 6000 W/m2 and 40 kg/h, respectively. Numerical results through COMSOL Multiphysics software show good agreement with experimental results. Importantly, the studies provided an important reference for the rare experimental and numerical studies of sublimator.

Numerical simulation of processes in the latent-heat thermal energy storage tank

This paper has proposed a computer model for numerical calculations of heat flows in regular rhombic packed bed of capsules with phase change material. The mathematical model of heat transfer in a capsule is based on finding a zero-dimensional solution to the Stefan problem, considering the influence of convective flows arising in the liquid phase. To take into account the heat transfer due to the convective component in the liquid phase in the capsule, the effective thermal conductivity coefficient is calculated. An experimental dependence has been applied to describe the heat exchange conditions of the coolant and the capsule wall. The calculation is reduced to finding the temperature of the coolant t after passing one layer of packed bed. The resulting temperature is the input parameter for calculating the next layer. This operation is repeated until the calculation is made for all layers of packed bed. The numerical calculation has been performed in the mathematical software Scilab. According to the proposed model, the results of calculating the temperature of the coolant after passing the storage device correlate well with the experimental data for a thermal energy storage device with spherical capsules filled with paraffin.

Heat Transfer Analysis and Modeling of a Cylindrical Parabolic Solar Distiller

The parabolic cylindrical distiller is a new technique for desalinate salt water. It is dedicated to the use in the arid and desert climate. This prototype is composed by a pump, a reflective surface, a green house tube, and a condensation room. This simplicity has allowed it to be used by the small communities. In this work, the operation and the yield of this prototype are modeled as function of a three different solar power (1800 W/m2, 1600 W/m2and 1400 W/m2). A numerical code that has allowed understanding in which way the distiller work and its behavior under different weather conditions has been created. A comprehensive heat transfer mathematical model containing an energy balance for the different heat transfer happened between the several components of this distiller is implemented. This equation system will be solved by the numerical method (finite difference) and programmed by informatics tools (Fortran). With this code, it is possible to control the enters parameters of each distiller component. The results obtained show that the productivity of water distillate can attained until 20l/d. This quantity is linked to the solar power and the debit of water given by the pump. This quantity of desalted water 20l / h proves the effectiveness of this technique compared to current techniques such as solar greenhouse distiller, which does not exceed 5 l/h.

Analysing the Contact Conduction Influence on the Heat Transfer Intensity in the Rectangular Steel Bars Bundle.

Bundles of steel bars, besides metal foams, are an example of cellular solids. Such bundles constitute a charge during the heat treatment of bars. The paper presents a mathematical model of transient heat transfer in a bundle of rectangular steel bars based on the energy balance method. The key element of this model is the procedure of determining the effective thermal conductivity using the electrical analogy. Different mechanisms of heat transfer occurring within the analysed medium (conduction in steel and contact conduction) are assigned corresponding thermal resistances. The discussed procedure involves expressing these resistances with the use of arithmetic relationships describing their changes in the temperature function. Thermal contact resistance has been described with the use of the relationships determined experimentally. As a result of the performed calculations, the influence of contact conduction between the adjacent bars and bundle arrangement on its heating time was established. The results of the calculations show that the heating time of bundles can be lowered by 5–40% as a result of a decrease in the thermal contact resistance. This effect depends on the bar size and bundle arrangement. From the practical point of view, the analysed problem is connected with the optimization of the heat treatment processes of steel bars.

Modeling of heat transfer in a fuel pellet based on uranium dioxide and ceramics (beryllium oxide)

The results of heat transfer mathematical model calculations in the “UO2-BeO” pellet are presented. The fuel pellet consists of uranium dioxide (UO2) and beryllium oxide (BeO) ceramics. Modeling of heat transfer was carried out by a system of generalized heat conduction equations with variable thermophysical properties. The calculated data of the temperature field in the fuel pellet were obtained using the COMSOL Multiphysics software code. The results of temperature calculations were compared with the data of other authors. The agreement of the calculated data shows the mathematical model and the COMSOL Multiphysics code algorithms correctness. Various arrangements of beryllium oxide ceramics BeO in a fuel pellet are considered. The arrangement of the BeO ceramics in the centre of the fuel pellet showed a noticeable decrease in temperature in the energy release zone. Calculations have shown that the composite fuel “UO2-BeO” is the most effective for regulating the thermal regime of fuel elements.

Mathematical Modeling of Heat and Mass Transfer in Heat Pipes in a One-Dimensional Formulation when Cooling Active Phased Antenna Arrays

The work proposes test one-dimensional models of heat and mass transfer in heat pipes during cooling of active phased antenna arrays, which can be used in processing the test results of flat heat pipes in order to determine their performance characteristics and identify the parameters required for modeling in a more complex setting (for example, in flat and taking into account the presence of several localized sources of heat supply). To take into account the influence of the heat release power on the equilibrium temperature inside the heat pipe, the model has been added to take into account the dependence of the steam saturation temperature on the pressure, which is realized inside the steam pipeline when the heat pipe is heated. Numerous calculations carried out made it possible to refine the mathematical model. In particular, a significant effect on the temperature distribution along the heat pipe is shown, taking into account the dependence of the steam saturation temperature on the pressure in the parawire. It is shown that the introduction of standard functions for the characteristics of the coolant (water) in the liquid and vapor state, as well as taking into account the capillary pressure on temperature, makes it possible to refine the resulting solution.

How far can membrane characteristic parameters bestow at the vacuum membrane distillation (VMD) performance: Modeling and simulation

ABSTRACT A mathematical model of simultaneous heat and mass transfer was presented to describe for the first time the effects of the variation in the characteristic parameters of the membrane during the VMD process on the permeation flux. The modeling approach was derived by dividing the module axially into multi-cells and a set of nonlinear simultaneous equations representing the VMD process were numerically solved via FSOLVE code using MATLAB® software. The validation of the presented model was estimated by simulation with a wide range of 135 diverse published experimental results related to the influence of various operating conditions, module properties, and membrane characteristics on the water permeation flux through the membrane. A good agreement was obtained between the experimental data and the results of the developed model. The same change in the membrane characteristics during the MD operation reported experimentally in the literature was confirmed by the simulation results of the developed model.

Modeling of laser surface modification processes of tool steel to predict the temperature distribution and modification zone

Process of metal surface modification during laser treatment requires a long search and control of the treatment technological parameters, depending on the technical requirements imposed on it. The article proposes a method of mathematical modeling of heat transfer during laser processing of the high carbon steel 9HS (equivalent to DIN 150Cr14). The dimensions of the hardening area are calculated with high accuracy by the isotherm of the critical temperature Ac3. The influence of the main technological parameters (radiation power, laser spot diameter, processing speed) on the depth and width of the hardening zone is shown. The paper also presents the use of the build model for the selection of multitrack processing modes to harden high-carbon steel 9HS to the required depth without surface melting.

Mathematical Simulation of Heat Transfer in the Structures of a Passenger Carriage Under the Influence of Forest Fires

Forest fires have a negative impact on the functioning of the railway. The aim of the work is a mathematical modeling of heat transfer in the structures of a passenger carriage under the influence of radiation from a forest fire front. The originality of the study is explained by modeling heat transfer in structural materials of a passenger carriage under the influence of radiation from a forest fire front. Low and high intensity surface forest fires, crown forest fires are considered. Most of the previously published works are devoted to the analysis of the causes of forest fires, including the ones near the railway. The software implementation of the mathematical model is performed in the RAD Studio software in the high-level programming language Delphi. Mathematically, heat transfer in the materials of a passenger carriage is described by non-stationary differential heat conduction equations with corresponding initial and boundary conditions. In order to solve the partial differential equations, the finite-difference method and the locally one-dimensional method are used. Difference analogs of differential equations are solved by the marching method. The main findings of the study are: 1) physical and mathematical models of heat transfer in the structures of a passenger carriage under conditions of exposure to radiation from a forest fire; 2) the obtained temperature distributions in the inhomogeneous structure of the passenger carriage wall; 3) simulation has shown that a low-intensity surface forest fire causes a relatively safe forest fire impact scenario, while a high-intensity surface forest fire impact is a potentially dangerous scenario; 4) the scenario of the impact of a crown forest fire is unambiguously dangerous at any parameters; 5) the results obtained in this paper and the expected in future investigations will create a physical basis for the development of software for fire safety systems for rolling stock on the railway. The presented results are proposed to be used for forecasting, monitoring, and assessing forest fire dangers during the operation of the rolling stock of JSC Russian Railways.

Математическое моделирование влияния лесного пожара на ветвь хвойного дерева

It is necessary to develop quantitative methods to assess the formation of thermal burns in the morphological parts of coniferous trees. The purpose of the study can be formulated as follows: mathematical modeling of heat transfer in the layered structure of a coniferous tree branch under the influence of a forest fire front. The heat propagation in the “branch-needles-flame zone” system is described by a system of non-stationary differential equations of heat conduction with the corresponding initial and boundary conditions. As an object of research, a digital model of a branch of a coniferous tree for various species, namely, pine, larch and fir, was used. Temperature distributions are obtained for different variants of the branch structure and conditions of the impact of the forest fire front. Conclusions are made about the need for further modernization of the mathematical model. The developed model is the basis for creating software tools for specialized geographic information systems.

Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications 2020

In this Special Issue, all aspects of fluid flow and heat transfer in geothermal applications, including the ground heat exchanger, conduction, and convection in porous media, are considered. The emphasis here is on mathematical and computational aspects of fluid flow in conventional and unconventional reservoirs, geothermal engineering, fluid flow and heat transfer in drilling engineering, and enhanced oil recovery (hydraulic fracturing, steam-assisted gravity drainage (SAGD), CO2 injection, etc.) applications.

Theoretical and numerical investigation of heat transfer characteristics of an integrated cookstove under different atmospheric pressures based on theoretical models of solid flame and impingement heat transfer

At present, the problems of the efficient use of energy and heat transfer characteristics of the stoves on plateaus have attracted much attention. In this work, a three-dimensional numerical calculation and theoretical analysis model of impact flame heat transfer was established for the integrated cookstoves widely used in China and verified with the experimental thermal efficiency value. It was found that, with decreased atmospheric pressure, the combustion intensity in the furnace decreases, the flame combustion temperature significantly decreases, the heat transfer rate of the stove decreases, and the total thermal efficiency decreases by 7.5% under pressure of 0.05 MPa compared with normal pressure. By using jet impinged and solid flame models, a heat transfer mathematical model suitable for the inner wok and water jacket of the integrated stove was established. The heat transfer error between theoretical calculation and three-dimensional numerical calculation was no more than 6%. In addition, some methods are proposed to improve the thermal efficiency of integrated stoves under a high-altitude and low-pressure environment. This study not only theoretically reveals the change law of heat transfer characteristics of convective shock and flame radiation heat transfer under low pressure but also has constructive theoretical guiding significance for the improvement of thermal efficiency of highland stoves.

Numerical Modelling of Heat Transfer in Fine Dispersive Slurry Flow

Slurry flows commonly appear in the transport of minerals from a mine to the processing site or from the deep ocean to the surface level. The process of heat transfer in solid–liquid flow is especially important for the long pipeline distance. The paper is focused on the numerical modelling and simulation of heat transfer in a fine dispersive slurry, which exhibits yield stress and damping of turbulence. The Bingham rheological model and the apparent viscosity concept were applied. The physical model was formulated and then the mathematical model, which constitutes conservative equations based on the time average approach for mass, momentum, and internal energy. The slurry flow in a pipeline is turbulent and fully developed hydrodynamically and thermally. The closure problem was solved by taking into account the Boussinesque hypothesis and a suitable turbulence model, which includes the influence of the yield shear stress on the wall damping function. The objective of the paper is to develop a new correlation of the Nusselt number for turbulent flow of fine dispersive slurry that exhibits yield stress and damping of turbulence. Simulations were performed for turbulent slurry flow, for solid volume concentrations 10%, 20%, 30%, and for water. The mathematical model for heat transfer of the carrier liquid flow has been validated. The study confirmed that the slurry velocity profiles are substantially different from those of the carrier liquid and have a significant effect on the heat transfer process. The highest rate of decrease in the Nusselt number is for low solid concentrations, while for C > 10% the decrease in the Nusselt number is gradual. A new correlation for the Nusselt number is proposed, which includes the Reynolds and Prandtl numbers, the dimensionless yield shear stress, and solid concentration. The new Nusselt number is in good agreement with the numerical predictions and the highest relative error was obtained for C = 10% and Nu = 44.3 and is equal to −12%. Results of the simulations are discussed. Conclusions and recommendations for further research are formulated.

Research on Multi-Physics Coupling Simulation for the Pulse Electrochemical Machining of Holes with Tube Electrodes.

Electrical parameters of the power supply are significant factors affecting the accuracy and stability of the electrochemical machining (ECM). However, the electric field, flow velocity and temperature in the machining area are difficult to measure directly under the influence of the power supply. Therefore, taking the film cooling hole as an example, the multi-physics coupling simulation analysis of the ECM is performed on the basis of Faraday’s law and fluid heat transfer mathematical model. The machining characteristics of the direct current and pulse ECM are compared through simulation. The results show that the pulse ECM improves the distribution of temperature and current density in the machining area. The period has little effect on the temperature, current density and side removal rate. The side removal rate increases with the increase of the duty ratio and lateral gap. Increasing of the duty ratio and decreasing of the lateral gap will increase the temperature and current density. Increasing the inlet pressure accelerates the frequency of renewal of heat and electrolysis products, which can reduce the single side gap. The experience of the ECM holes verifies the results of the simulation. The accuracy and stability of the ECM of holes are enhanced by optimizing the duty ratio, lateral gap and inlet pressure.

Numerical solution of nonlinear dual‐phase‐lag model for analyzing heat transfer in tissue during thermal therapy

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.

Cookies Internal Temperature Estimation Using IHCP Methodology

This work constitutes a continuation of previous work on determining the internal temperature of foods by applying inverse heat transfer problem solving techniques. In this research, a mathematical model of heat transfer applied to foods is developed whose central part heat transfer can be described in Cartesian coordinates. This model uses techniques established in the previous work. The technique is based on the adjustment of parameters involved in heat transfer, minimizing the sum of squared errors between the measured temperatures and those calculated by the mathematical model. This paper discusses how the precision of this method would be affected with respect to the measurement time of the surface temperature and the delay time of the measurement.

Wellbore Temperature and Pressure Field in Deep-water Drilling and the Applications in Prediction of Hydrate Formation Region

In the process of deep-water drilling, gas hydrate is easily formed in wellbores due to the low temperature and high pressure environment. In this study, a new, systematic, and accurate prediction method of temperature, pressure, and hydrate formation region in wellbores is developed. The mathematical models of wellbore pressure and transient heat transfer are established, the numerical solution method based on fully implicit finite difference method is developed, and the accuracy is verified by comparing with the field measured data. Combined with the hydrate phase equilibrium model, the hydrate formation region in wellbore is predicted, and the sensitivity effects of nine factors on wellbore temperature, pressure, and hydrate formation region are analyzed. Finally, the influence regularities and degree of each parameter are obtained. The increases of circulation time, geothermal gradient, displacement of drilling fluid, and injection temperature will inhibit the formation of hydrate in wellbores, and the influence degree increases in turn; the increases of wellhead backpressure and seawater depth will promote the formation of hydrate in wellbores, and the influence degree increases in turn. The changes of drilling fluid density, well depth, and hole deviation angle have little effect on the formation of hydrate in wellbores.

APPROACH TO DETERMINING BOUNDARY CONDITIONS ON THE EXTERNAL SURFACE OF THE HEIGHT CASE OF THE ADMINISTRATIVE BUILDING

Problem statement. The influence of the external climate on the thermal regime of the enclosures of premises and buildings is complex. The calculated values and combinations of parameters are determined, as a rule, taking into account the security factor of the calculated conditions. The main indicators of the cold season are the outdoor temperature and wind speed. As you know, an increase in wind speed with a constant outside air temperature causes an increase in pressure on the windward facade of the building, as a result of which the heat loss of the room, associated with heating of the incoming air, increases. Wind speed and direction have a stronger influence on the distribution of air flows in the ventilation system and on the infiltration costs than the outside temperature. A change in the outside air temperature from −15 to −30 °С leads to the same increase in air exchange in the apartment as an increase in wind speed from 3 to 6 m/s. The purpose of the article is to determine the heat transfer coefficients on the outside of an office building. Results. The basic principles of calculating heat transfer coefficients are presented. The zoning of the premises of the Institute is proposed, taking into account their thermal regime and boundary conditions on external surfaces. Scientific novelty and practical significance. The original values of the heat transfer coefficients, which are considered on the example of the climatic conditions of the city of Kharkov for the IP Mash complex of the NAS of Ukraine. On the basis of the presented methodology for determining the heat transfer coefficients, it is planned to present this building as a single energy system with three main energetically interconnected subsystems: the energy effect of the external climate on the building envelope; energy that is contained in the building envelope, that is, in the external building envelope; energy, which is contained within the volume of the building, that is, in the internal air, internal equipment, internal structures, etc. Then the mathematical model of the building as a unified energy system will consist of three submodels: the mathematical model of the influence of the external climate on the building envelope; mathematical model of heat transfer through the building envelope; mathematical model of radiant and convective heat transfer in the premises of the building.

Efficient Solver for a Simplified Model of the Multi-Physics Heat Transfer Problem in Radio Frequency Ablation of Hepatic Tumors

Mathematical modeling and computer simulation of heat transfer in the liver play a key role in prediction of radio frequency ablation outcome. While multi-physics modeling should be used for accurate simulation of heat transfer in a highly perfused organ like the liver, the computational cost of such a problem could have a negative impact on the simulation time. This article extends a highly parallel finite element-based method to simulate the multi-physics heat transfer problem in the liver efficiently. A message passing interface (MPI)-based strong coupling method is developed and tested on cluster nodes. The scalability of this work is assessed by performing simulations on up to 1024 cores.

Experimental and numerical study on performance enhancement of photovoltaic panel by controlling temperature with phase change material

In order to enhance the electricity generation performance of photovoltaic (PV) panel, experimental and numerical studies were carried out to control the temperature by using phase change material (PCM). The PV combined with PCM (PV-PCM) device and PV-PCM with foam copper were designed, and their temperature, voltage, and output power were measured and compared with those of PV panel. The mathematical model of heat transfer for PV-PCM was established and verified by experiment. And the influences of PV-PCM tilt angle, PCM properties and thickness, and ambient temperature on the temperature control effect were studied numerically. The results illuminate that the PV panel's temperature decreases significantly with the using of PCM, which correspondingly enlarges its open circuit voltage and output power. And the PCM with foam copper has a better effect. The temperature control effect of the PV-PCM system is better with the increase of the tilt angle, the PCM thermal conductivity and thickness, and the decrease of PCM phase change temperature. But there are limited conditions for them. The higher the ambient temperature, the worse the temperature control effect. The present study has important reference value for PV performance enhancement.