Mathematical Model Of Heat Transfer Research Articles

The Numerical Study on Indoor Heat and Moisture Transfer Characteristics of an Ancient Palace Building in Beijing

The heritage of ancient buildings is an important part of the world’s history and culture, which has extremely rich historical–cultural value and artistic research value. Beijing has a large number of ancient palace buildings, and because of the age of their construction, many of them have problems with varying degrees of peeling and molding on the inner surfaces of the envelope. To solve the problems of damp interiors of palace buildings, a mathematical model of indoor heat and moisture transfer was established based on an ancient wooden palace building in Beijing. The model was validated by fitting the measured and simulated data. And the effects of outdoor relative humidity, soil moisture, wall moisture, and other factors on indoor heat and moisture transfer of ancient buildings were simulated and analyzed via the control variables method. The results showed that the measured and simulated data are within the error range, which verifies the accuracy of the model. And the simulation of indoor humidity matched the measured humidity. Thus, the simulation results were consistent with the actual situation. The variable trend of the relative humidity of the indoor environment with the outdoor humidity is inconsistent from plane to plane, i.e., it increases or remains constant with the increase in the outdoor humidity. Indoor ambient relative humidity increased with increasing wall moisture. And the indoor average temperature is 24.5 °C, and indoor relative humidity ranged between 87.4% and 92.4%. Soil moisture and wall moisture were the main factors affecting indoor relative humidity.

Investigation of heating time of a bundle of steel bars

The paper deals with the problem of determining the heating time of a bundle of flat steel bars. To describe a mathematical model of transient heat transfer the energy balance method was used. The most important element is to determine the effective thermal conductivity coefficient using the electrical analogy. The simulations of heating were performed for increasing temperature of furnace. The results show that using different sizes and bundle arrangement the heating time can be reduced by 5–15%. The analysed problem is important from the practical point of view because it allows for optimization of heat treatment processes of steel bars.

Exploring and enhancing the volumetric behaviour in solar receivers through specular reflectivity and simplified design

One of the remaining challenges of point focusing concentrating solar power systems is the realization of a true volumetric receiver, one whose entire volume is utilized for the absorption of irradiance. Commercial state-of-the-art receivers (e.g., HiTRec-II and SolAir-200) have not demonstrated the volumetric effect, because of low radiation penetration within the absorber. Then, literature state-of-the-art receivers were able to demonstrate a volumetric behaviour (toward achieving the volumetric effect) through axially varied macro-scale porosity (void fraction), but at the cost of design complexity and manufacturability. This study presents the conceptual design and computational assessment of an improved volumetric receiver by employing varied reflectivity on the irradiated surfaces, thereby enhancing radiation penetration. This approach maintains the simplicity, manufacturability, and commercial viability of structured receivers. Three reflectivity distributions were initially investigated using a 3D heat transfer mathematical model, verified with literature experimental data, which incorporated a source term ascertained through Monte-Carlo Ray Tracing (MCRT). The findings from these three design cases revealed that while diffuse reflectivity distributions could improve thermal efficiency, they were unable to enhance radiation penetration. Consequently, an improved volumetric solar receiver was realized by integrating specular reflectivity, leading to a more uniform source term distribution and achieving a thermal efficiency of 96%, as opposed to the 85% thermal efficiency of the commercial state-of-the-art HiTRec-II receiver. The discovery of the specular receiver as a true volumetric receiver facilitated an exploration of quantitative definitions of the volumetric effect. The exploration concluded that volumetric effect metrics would only target designs that maximizing thermal efficiency when the receiver is exhibits a truly volumetric nature, characterized by a uniform source term distribution.

Phase change heat transfer enhancement based on topology optimization of fin structure

In the latent heat storage (LHS) system, topology optimization was applied to the design of the fin structure, and the material variable density interpolation method was adopted. Given the effect of natural convection heat transfer on heat transfer characteristics, the buoyancy source term and resistance source term were introduced in the momentum conservation equation to establish a mathematical model of heat transfer and topology of the heat storage system. To obtain a reasonable topology, we analyzed the effects of optimization parameters such as penalty factor, filter radius, steepness factor and threshold value on the topology. Then, four typical topologies were selected for heat transfer and flow analysis. The results show that at 500 s, Case 1 is nearly half melted, while Case 4 is almost completely melted. It can be seen that more branch structures and radial extension in Case 4 provide a larger heat transfer area and a more reasonable heat transfer path, which improves the uniformity of the temperature field and significantly increases the heat transfer rate. This study can provide a theoretical basis for topology optimization in the structural distribution of fins in the LHS system.

Математическое моделирование переноса тепла в биологических жидкостях при лазерной термотерапии кист

The paper proposes a mathematical model of heat transfer by a jet of hot liquid that occurs during laser thermotherapy of cysts. This model is semiempirical, since the hot jet is set using sources obtained from the analysis of experimental data. Based on this model, a series of computational experiments were carried out for different laser powers.

Study on the influence of borehole heat exchanger structure and soil thermal property on soil heat storage characteristics of the HST-BHE system

To effectively solve the problem of soil thermal imbalance in cold regions, a new soil heat storage system that absorbs heat from ambient air through heat source tower (HST) and injects the heat into soil through borehole heat exchanger (BHE) in the non-heating season has been proposed in author’s previous research. However, the influence of structure parameters of the BHE and soil thermal properties on soil heat storage characteristics is not deeply studied. In this paper, heat and mass transfer mathematical model of the integrated system of HST and BHE (named as HST-BHE system) was built based on the developed models of BHE and HST firstly. Then, the influence of BHE structural parameters and soil thermal properties on soil heat storage characteristics was studied. The results show that the soil heat storage capacity of the HST-BHE system and temperature difference between the inlet and outlet of BHE increase with the increases of borehole length, buried pipe spacing or soil thermal conductivity, and decrease with the increases of borehole radius under specific conditions. While the borehole wall temperature of the BHE increases with the increase of buried pipe spacing and decreases with the increase of borehole depth, borehole radius or soil thermal conductivity. Unusually, increasing the water flow velocity in BHE will decrease the temperature difference but increase the soil heat storage capacity. These soil heat storage characteristics are controlled by the heat transfer thermal resistances between water and soil in the BHE as well as water and air in the HST, and all of the impact parameters should be optimized in actual engineering applications when considering the economy of the HST-BHE system.

Prevent of clogging via a mathematical model of heat transfer in submerged entry nozzle

Clogging of the steel in the submerged entry nozzle (SEN) is mainly due to the agglomeration and/or interaction of the steel with the SEN refractory material. However, the continuous casting steel also leads to clogging - the freezing of the steel in the SEN at the beginning of the casting. The freezing of the steel in the SEN results mainly in the change in the geometry, the low casting temperature of steel, the insufficient preheating of the SEN and the low initial casting speed. To eliminate the problems of steel freezing at the beginning of continuous casting, the authors solved them using a mathematical model of heat transfer in the SEN. Using the mathematical model, it is possible to simulate the layout of temperatures in the SEN and the temperature of the steel at the interface of steel - the inner surface of the SEN. To determine the temperature layout in the SEN after installation on the tundish, a method of measuring the decreased average temperatures of the SEN by free convection after heating was used. Based on the analysis of the current state using simulations in a mathematical model, it is possible to define conditions for preventing the freezing of steel in the SEN when the wall thickness or isolation thickness is changing.

Mathematical Modeling of Heat Transfer in a Plate During Plasma Spraying of Thermal Protection on It

Mathematical Modeling of Heat Transfer in a Plate During Plasma Spraying of Thermal Protection on It

Mathematical Modelling of Heat and Mass Transfer during Jackfruit Drying Considering Shrinkage

Shrinkage is an obvious phenomenon that occurs when drying plant-based food materials, and it has a crucial influence on heat–mass transfer mechanisms, energy consumption in drying, and dried product quality. The present study aims to develop a theoretical shrinkage model considering the drying kinetics and shrinkage velocity approach during the convective drying of jackfruit. Since there is no theoretical model in the literature that considers the transfer process along with shrinkage phenomena for jackfruit drying, this work focuses on presenting the drying and shrinkage kinetics behaviour through the development of a mathematical model. Two distinct models were developed, each considering the presence or absence of shrinkage phenomena. Model validation was carried out by comparing the predicted results with experimental data from drying tests conducted at 60 °C, and model accuracy was evaluated through statistical error analysis. In the shrinkage-induced model, the shrinkage exhibited a linear relationship with drying time, as the moisture content decreased from 5.25 to 0.47 kg/kg on a dry basis when the temperature increased to 54 °C. Notably, the shrinkage-induced model demonstrated superior performance, displaying low mean absolute error (MAE) values—0.27 kg/kg on a dry basis for moisture content, 2.07 °C for temperature variation, and 0.04 for shrinkage, when compared to the model without shrinkage. Furthermore, the mean relative error (MRE) values for the shrinkage-induced model were 45.71% and 33.33% lower than those of the model without shrinkage for average moisture content and temperature, respectively. The findings of this study provide valuable insights for the food drying industry, offering new knowledge about drying kinetics and shrinkage characteristics that can contribute to the development of energy-efficient drying systems.

Design of Finite Difference Method and Neural Network Approach for Casson Nanofluid Flow: A Computational Study

To boost productivity, commercial strategies, and social advancement, neural network techniques are gaining popularity among engineering and technical research groups. This work proposes a numerical scheme to solve linear and non-linear ordinary differential equations (ODEs). The scheme’s primary benefit included its third-order accuracy in two stages, whereas most examples in the literature do not provide third-order accuracy in two stages. The scheme was explicit and correct to the third order. The stability region and consistency analysis of the scheme for linear ODE are provided in this paper. Moreover, a mathematical model of heat and mass transfer for the non-Newtonian Casson nanofluid flow is given under the effects of the induced magnetic field, which was explored quantitatively using the method of Levenberg–Marquardt back propagation artificial neural networks. The governing equations were reduced to ODEs using suitable similarity transformations and later solved by the proposed scheme with a third-order accuracy. Additionally, a neural network approach for input and output/predicted values is given. In addition, inputs for velocity, temperature, and concentration profiles were mapped to the outputs using a neural network. The results are displayed in different types of graphs. Absolute error, regression studies, mean square error, and error histogram analyses are presented to validate the suggested neural networks’ performance. The neural network technique is currently used on three of these four targets. Two hundred points were utilized, with 140 samples used for training, 30 samples used for validation, and 30 samples used for testing. These findings demonstrate the efficacy of artificial neural networks in forecasting and optimizing complex systems.

Research on heat and mass transfer characteristics of water-sprayed single-screw vapor compressor

Temperature increase in the working cavity caused by steam superheating is an important issue that affects the compressor performance in single-screw vapor compressor (SSVC). Therefore, working cavity water spraying is often accustomed to realize the cooling of pressurization process. There is a bidirectional phase change process in the SSVC water jet pressurization process, which makes the pressurization and heat transfer mechanism very complicated. To clarify the internal working mechanism, an evaporation-condensation bidirectional heat and mass transfer (HMT) mathematical model of water-vapor two-phase medium is established for the SSVC with multicolumn envelope meshing profile. The simulation results are compared and verified by the experimental data. The exhaust pressure error is within 5%. Based on the validated model, the HMT characteristics are nalysed and the influence of water-sprayed parameters are discussed. Results show that compressor performance can be significantly improved by water spraying, and the volumetric and adiabatic indication efficiency can be increased by 0.98% and 3.83%. After the vapor reaches saturation, with the continuous increase of the water spraying rate, the adiabatic indication efficiency will drop significantly. Conditions such as water-spraying temperature, pressure, suction superheat and back pressure all have an impact on compressor performance.

Study on heat transfer model of solid rocket motor combustor under high-temperature two-phase flow scour state

To address the issues with the multi-phase flow and heat transfer characteristics of the gas inside solid rocket motor combustor, this paper first establishes a mathematical model form that can express the heat transfer characteristics between gas and wall, and obtains the mathematical model of heat transfer by means of experiment and numerical simulation. The results show that heat transfer in the wall surface has obvious hysteresis during the actual working process of solid rocket motor, and that temperature in the wall surface will gradually reach the peak value after the motor works. The heat transfer trend between the numerical simulation results and the experimental data is relatively consistent, and the errors of heat transfer calculation in the stable working section of the motor can be controlled by 15%. It shows that the calculation model with the Sommerfeld number as the criterion selected in this paper can better reflect the heat transfer characteristics between the alumina droplet and the wall in combustor. The maximum error between the fitted value and calculated value is 9.43%, which indicates that the numerical model of heat transfer established under the state of two-phase gas and wall scouring has certain reliability.

Mathematical modeling of complex heat transfer in the context of the endovenous laser ablation

An initial-boundary value problem for quasi-linear model of complex heat exchange (where the conductive and radiative contributions are simultaneously taken into account), describing the mechanism of endovenous laser ablation, is studied. The existence and uniqueness of a solution is proved. An iterative procedure to find a solution is constructed and its convergence is established. The efficiency of the iterative procedure is illustrated by conducted numerical simulations.

Effect of mechanical stirring on the tubular heating process of crude oil

Research on thermal behaviors under the synergy of mechanical stirring and tubular heating can reveal the effect mechanism of mechanical stirring, and determine the optimal stirring parameters. In this paper, the physical and mathematical models of heat transfer in crude oil storage tank under the synergy of tubular heating and mechanical stirring are established, the sliding grid technique is used to model the stirring impeller, which are further numerical calculated by the FVM. Our outcomes demonstrate that through the enhancement of convection, mechanical stirring significantly changes the thermal behaviors and enhances the heat exchange. Precisely, for a 1,000 m3 crude oil storage tank, the stirring of 350 rpm can increase the average velocity by 329%, the heating rate by 89%, and rise the average crude oil temperature from 42.311 °C to 42.586 °C during 2 h of heating. However, the higher crude oil temperature will cause a 1,613 W increase in heat loss power. The heating efficiency has also increased by 10%. Furthermore, mechanical stirring can promote a more uniform temperature distribution. Thus, the volume ratio in the low-temperature region decreases by 10% and that in the high-temperature region increases by 26%. The temperature variance decreases from 4.517 °C2 to 0.275 °C2. However, the velocity and temperature fields are almost the same under different stirring rates. With increasing stirring rate from 100 rpm to 700 rpm, the average heating rate can only increase by 0.026 °C/h, and temperature variance decreases from 0.596 °C2 to 0.086 °C2. With increasing stirring rate, the efficiency of the heating tube does not change significantly. The optimal stirring rate is determined as 350 rpm based on the fitting curve of temperature variance stabilization time and the comprehensive effect.

An Implicit Finite Difference Scheme and Neural Network Approach for Non-Newtonian Nanofluid Flow Using Induced Magnetic Field

The aim of this contribution is to propose a numerical scheme for solving linear and nonlinear boundary value problems. The scheme is implicit and it is constructed on three grid points. The stability of the proposed implicit scheme is provided. In addition to this, a mathematical model for heat and mass transfer using induced magnetic field (IMF) is modified. Furthermore, this model is transformed into boundary value problems by employing similarity transformations. The dimensionless model of boundary value problems is solved using the proposed numerical scheme. The scheme is applied with a combination of a shooting approach and an iterative method. From the obtained results, it can be seen that velocity profile declines with enhancing Weissenberg number. The results are also compared with those given in past research. In addition to this, a neural network approach is applied that is based on the input and outputs of the considered model with specified values of parameters.

Design Selection Method of Exhaust Air Heat Recovery Type Indirect Evaporative Cooler

In order to promote the engineering application of indirect evaporative cooling (IEC) in the field of building air conditioning, as well as reduce air conditioning energy consumption and carbon emissions, this paper proposes a fresh air unit using indirect evaporative cooling to achieve heat recovery from exhaust air, which gives the recommended values of air and spray water operation parameters. The indirect evaporative cooler heat and mass transfer mathematical model and numerical solution procedure were made. In summer outdoor design conditions, the fresh air outlet state parameters, cooling capacity, fresh air cooling load, wet bulb efficiency and enthalpy efficiency were numerically solved for thirty typical cities from five climate zones of China. In addition, also based on the model results for the cities in China, two representative operating conditions points of medium and high humidity were selected. Eight models of fresh air unit coolers in the air volume range of 1000–10,000 m3/h commonly used in engineering were simulated to obtain the optimal heat transfer area and size selection of ERIEC heat exchangers for fresh air units, and economic analysis was performed. The results show that the wet bulb efficiency ranges from 0.67–0.98, and increases as the outdoor design wet bulb temperature decreases; the enthalpy efficiency ranges from 0.76–1.29, and increases as the outdoor design wet bulb temperature increases; and the fresh air load that the exhaust air heat recovery type indirect evaporative cooler can bear ranges from 55–100%, which could largely decrease the cold load of the matched surface cooler. As demonstrated, the energy-saving effect is remarkable.

Thermo-poro-elastic analytical model of the heat extraction performance of EGS inlaid with multi-linked fractures

The existing analytical model of the heat extraction performance of EGS ignored the influences of both thermo-poro-elastic effect and multi-linked fractures. Therefore, a thermo-poro-elastic analytical model was proposed to simulate heat extraction performance of EGS inlaid with multi-linked fractures. First, the mathematical models of fluid flow, heat transfer, and fracture aperture variation were established based on the conservation of energy and mass. Second, the partial differential equations were converted to ordinary differential equations by Laplace transformation, and the analytical solutions of water and rock temperatures were obtained. Then, the proposed model was verified with the published single-fracture model, which has been demonstrated to be efficient. Finally, the influencing factors, including geothermal reservoir parameters, production parameters, thermo-poro-elastic effect, and fracture morphology, were systematically analyzed and discussed. The results indicated that both the thermo-poro-elastic effect and multi-linked fractures have significant influence on the heat extraction performance of the EGS. The thermo-poro-elasticity effect tends to cause the fracture aperture to increase. The heat extraction performance of the EGS inlaid with multi-linked fractures is much better than that of single fracture EGS. Compared to the uncoupled situation, the production temperature is lowered and the output energy is increased by the thermo-poro-elastic effect at a constant flow rate in the fracture due to the increase in injection rate caused by the increase in fracture aperture. With the increasing of initial fracture aperture, the production temperature gradually decreases, while the output energy first increases and then decreases, so that the optimal initial fracture aperture is 2 mm. The results can provide important guidance for the design and production of an EGS inlaid with multi-linked fractures.

Mathematical model-based performance assessment of a centrifugal humidifier under varying operating conditions

Evaporative cooling phenomenon yields a cooling and humidification process widely used in AC applications to maintain thermal comfort in the space. Present work deals with the design & construction of a dynamic humidifier that operates on the centrifugal action principle. Celdek pad is positioned inside a frame that holds the water effectively and later dispersed in the air. Heat & mass transfer mathematical model is constructed and parameters such as evaporation rate, cooling efficiency, cooling effect, coefficient of performance, specific humidity at the exit and exit temperatures are determined and validated with empirical values. Maximum Humidification efficiency of 82%, cooling effect of 3061 W and rate of evaporation of 0.82 g/s have been noticed from the experiments. Both Experimental and theoretical results agree with a maximum deviation of 8%. Also, it is found that packing in dynamic action gave maximum humidification performance compared to the stationary type except for coefficient of performance. Motor shaft speed of 150–160 rpm and the air velocity of 6.5 to 7 m/s yielded optimum results.

Mathematical Model for Heat and Mass Transfer of Concrete Heat Treatment Using Solar Power

In this article, a physical and mathematical model of the unsteady process of heat and mass transfer in a flat reinforced concrete structure during its heat treatment by solar energy is proposed and considered. Monolithic concreting in the conditions of a construction site is currently widespread in the construction industry. The subject of the article is to consider the issues of heat treatment of concrete and acceleration of its hardening processes using solar energy. Analytical expressions have been obtained that simulate the process at any stage of it, which makes it possible to actively intervene and adjust the external parameters of the environment to create rational and comfortable conditions for concrete strength growth.

Адаптация математической модели процесса кондуктивного замораживания к икре сазана как источнику лецитина и ее решение

In modern conditions the food industry of the Russian Federation needs high quality natural emulsifiers, for example, lecithins. It should be noted that the carp caviar, in particular, the sazan caviar contains a large amount of lecithin. Analysis of the positive and negative aspects of different approaches to the freezing process and its structural design leads to the conclusion that it is reasonable to use (both from the point of view of technology, power consuming and economy) a conductive energy removal from the product that is in contact with the working surface of the cooling unit made in the form of a drum with a refrigerant supplied inside it. Given that it is difficult to empirically determine the temperature over the volume of the frozen object, it is advisable to simulate the processes of internal transfer of thermal energy and its exchange at the interfaces between the sample and the external environment, as well as the cooling surface of the drum. The aim of the study was a mathematical model solution about internal heat transfer during sazan caviar freezing under heterogeneous boundary conditions. The object of the study is a thin layer of the sazan caviar. Putting into practice the mathematical model of heat transfer, which describes freezing a 5 mm thick caviar product by the contact method by means of the finite difference method was realized by using the Mathcad Professional software product. In the process of solving the mathematical model of freezing, it was revealed that at the end of the freezing procedure, the average volumetric temperature of the caviar reaches its rational value of –7.5°C, after which the caviar product can be transported to the storage places. Rational operating parameters 
 of the caviar product freezing process are: ambient air temperature up to 20°C; initial product temperature –10 ± 1°C; drum surface temperature up to –18°C; thickness of the frozen layer – 5 ± 0.5 mm; freezing time = 10 minutes.