Mathematical Model Of Heat Transfer Research Articles

Enhanced water permeability and antifouling properties of cross-linked graphene oxide composite membranes with tunable d-spacings

Low flux and membrane fouling are major challenges in membrane distillation (MD) for treating concentrated wastewater. This study compared the performance of GO composite membranes with different interlayer distances, by covalently bonding the terminal amine groups of ethylenediamine (EDA) and 1,12-diaminododecane (DADD) with the carboxyl groups present on the GO sheets. The results indicated that the GO-DADD/PTFE membrane, with longer carbon chain cross-linking, achieved the highest flux and antifouling properties. At 70 °C, the pure water flux reached 68.5 kg/m2·h, and the fluxes for treating NaCl, HA containing NaCl, and BSA containing NaCl were 29.8 %, 37.1 %, and 38.5 % higher than the uncrosslinked GO/PTFE, and 95.7 %, 121.2 %, and 146.9 % higher than the PTFE membrane, respectively. Through mathematical models for mass and heat transfer, the study identified the key to this enhancement as the increased d-spacing within the GO layer due to cross-linking, which weakened the Kelvin effect and enhanced the vapor partial pressure on the hot side. The unique surface structure and electrostatic interactions induced by long-chain cross-linking further boosted the antifouling effect. These modifications not only overcome the typical trade-off between retention rates and flux but also offer a scalable and efficient solution for advanced membrane distillation applications.

Applying a heat transfer mathematical model for the cryopreservation of rainbow trout (Oncorhynchus mykiss) sperm: How straw location over liquid nitrogen level affects freezing rate and fertilization yield

Cryopreservation of rainbow trout semen under field conditions was analyzed. Straw location over liquid nitrogen level is a crucial variable that affects freezing rate and fertilization yield due to changes in nitrogen vapor external temperature. The objectives were: to analyze cryopreservation protocols by experimentally measuring the cooling rates and fertilization yield of 0.5 ml plastic straws located in nitrogen vapor at different heights corresponding to different external temperatures; to numerically simulate the freezing process, by solving the heat transfer partial differential equations with the corresponding thermo-physical properties of the biological system and the plastic straw; to evaluate and analyze the surface heat transfer coefficient (h) during the freezing process of the straws; to introduce a new variable, the characteristic freezing time (tc), that enables comparison between protocols; this variable was defined as the elapsed period between the initial freezing temperature and a final reference temperature of −40 °C (temperature in which more than 80 % of the water is in a frozen state). The mathematical model predicted the temperature distribution inside the straw, showing a low effect of straw plastic materials (polyethylene-terephthalate glycol, polyvinyl-chloride, and polypropylene) on freezing rates. The average h value obtained from numerical simulations was 25.5 W/m2 K, close to that obtained from the analytical Nusselt correlation for natural convection. An improvement on fertilization trials was observed when the average external nitrogen temperature was −129.6 °C (temperature range: −94 to −171 °C) with an average tc of 56.8 s (ranging between 47 and 72 s). These results corresponded to a height above the level of liquid nitrogen of 2 cm. Comparison with literature reported data showed satisfactory results. Applying mathematical models in the cryobiology field achieved results that are relevant for cryopreservation activities.

Thermal decomposition and combustion of interior design materials

Research findings on the patterns of thermal decomposition and combustion are reported for widely used interior design materials. The experiments were conducted using a hardware and software system including a thermogravimetric analyzer (to record the characteristics of thermal decomposition), a gas analyzer (with H2, CH4, H2S, SO2, CO and CO2 sensors) and a high-speed camera (to record the characteristics of ignition and combustion). The temperature of the oxidizing medium ranged from 500 to 900°C to investigate the conditions of thermal decomposition initiation and sustained combustion. It was established that the highest concentrations of toxic emissions were typical of the combustion of polypropylene at a maximum temperature of the oxidizing medium (900°C). Wood showed the shortest ignition delay time and the longest duration of combustion. The experimental data were used for a physical problem statement and mathematical model of heat and mass transfer to explore the thermal decomposition and combustion of interior design materials in different rooms. A comparison of the experimental findings with the mathematical modeling results validates the developed model. The growth rates of carbon monoxide and carbon dioxide concentrations were determined for construction (wooden) and interior design (polymer) materials. The maximum concentrations of CO and CO2, and the minimum times taken to reach their threshold values corresponded to wood and polyvinyl chloride panels. This research provides a deeper insight into the thermal decomposition of a wide range of fuels and the formation of gaseous pyrolysis products of these fuels. The results obtained can be used to evaluate the toxicity of construction and interior design materials during compartment fires as well as to estimate the safe egress time and risks involved in the process. They can also serve as a database for the development and testing of mathematical models describing fire outbreaks and propagation in confined spaces.

Contribution to the use of palm kernel oil methyl esters as liquid bio-insulators in distribution transformers: Experimentation and simulation of heat transfer

This work examines the potential use of palm kernel oil methyl esters (PKOME) as liquid bio-insulators in distribution transformers. A mathematical model of heat transfer inside a transformer is developed and solved using COMSOL Multiphysics software. The results of the model are validated by experimental data, showing a temperature variation of 31–81.8 °C in the measurements and 31–82.5 °C in the simulation. This validation confirms the accuracy of the model in predicting the temperature distribution inside the PKOME-filled transformer, paving the way for their use in distribution transformers.

Mathematical modeling of heat transfer in tissues with skin tumor during thermotherapy.

The study of thermal therapy to tumors and the response of living cells to this therapy used to treat tumor is very important due to the complexity of heat transfer in biological tissues. In the past few years, there has been a growing interest among clinicians, mathematicians, and engineers regarding the use of computational and mathematical methods to simulate biological systems. Numerous medical proceedings also employ mathematical modeling and engineering techniques as a means to guarantee their safety and evaluate the associated risks effectively. This manuscript provides an analytical solution used for the first time to study the mechanism of biological thermal response during heat therapy on spheroidal skin tumor. The proposed method used a generalized thermoelasticity model with one relaxation time. The influence of relaxation times on the responses of diseased and healthy tissues is studied and interpreted graphically. Also, the impact of different laser irradiance on the thermal profile of the malignant tumor cells over a period of 2 minutes is interpreted graphically. To investigate the transfer of heat within biological tissues during the thermal therapy, the Laplace transform and inverse Laplace transform methods were applied. A comparison of the present generalized thermoelasticity model and different models based on Pennes bioheat transfer PBT shows that our proposed model yields more realistic and accurate predictions. The current model can be used to explain various therapeutic methods.

Study on heat transfer law of moving temperature variable gas in thermoacoustic plate stack

Taking gas and the heat transfer process between gas and plate as the research object, the mathematical model of heat transfer in one working cycle by moving variable temperature air mass under the action of sound field is established, which provides a new idea for understanding thermoacoustic effect. The influence factors in the model are analyzed and it is found that the amplitude of the air mass has a significant influence on the heat transfer, and the heat transfer of the air mass in one working cycle is proportional to the square of the amplitude. In a certain working environment, the thermoacoustic refrigerator has a critical operating frequency, and only when the operating frequency is greater than the critical frequency can refrigeration be realized. The critical operating frequency is independent of the amplitude and increases with the increase of the stack temperature gradient. With the pressure belly point as the reference position, the greater the distance from the reference position, the greater the critical operating frequency. On this basis, the idea of short plate overlapping is put forward and the formation mechanism of temperature difference between two ends of plate overlapping is explained.

Перспективные конструкторские решения для сушки жидких пищевых систем

An assessment of promising alternative design solutions for drying liquid food systems is given. Drying technology and techniques for removing moisture from liquid materials in a dispersed state have found widespread use in the food industry. The almost instantaneous drying of the sprayed particles in the coolant flow causes the formation of a developed phase interaction surface and acceleration of heat and mass transfer procedures, as well as the exclusion of overheating of the material due to intensive volumetric evaporation of moisture. A number of dryer designs have been developed to eliminate disadvantages (such as the large size of the dryers and their relatively high energy consumption and complexity of structural elements) or to reduce their impact on the course of the dehydration operation. The design specifics of devices for dewatering in the atomized state are due to the methods of supplying thermal energy, technological conditions and limitations, parameters of the dried product and the final powder substance, as well as its specific yield, peculiarities of the spraying operation, etc. The justification of the method of spray drying of liquid food material and the constructive use of the apparatus should be based on the study of a set of parameters and characteristics of the dehydration object, as well as on the construction and solution of a mathematical model of heat and mass transfer and exchange processes at the boundary of the phase section, as well as their mechanism in the development of a rational method of moisture removal to ensure the quality of finished products and energy- and resource saving. The proposed plant designs are recommended for organizing the drying process of liquid products, in particular for drying broths in fish production technologies.

Formation of subaerial taliks in Larsemann hills, princess Elizabeth land, East Antarctica

This study presents a mathematical model of heat and mass transfer for modelling the formation and evolution of taliks in the upper subsurface of the Larsemann Hills in East Antarctica. Four simulation scenarios were considered. The first one showed that thawed areas cannot form under snowfields. The second and third scenarios demonstrated the taliks did not form if the snow melted immediately after set the positive air temperatures and covered the surface 20 days before the set of negative air temperatures or immediately after that. According to the last scenario, talik forms when snow cover persists even with positive air temperature, and snow falls before the air temperature becomes negative. Modelling demonstrates that taliks in the Larsemann Hills exist, but they are mostly in an unstable state.

Design and Optimization of a Mixed-Flow Drying Chamber for Tiger Nuts Based on CFD-DEM Heat and Mass Transfer Model

In order to solve the problem of inconsistent moisture content in particles during the drying process of tiger nuts (Cyperus esculentus) due to uneven air flow and temperature distribution in the drying chamber, an open-hole corner box was designed based on the principle of negative pressure micro-perforated air supply. Using computational fluid dynamics (CFD) and discrete element method (DEM) simulation, coupled with the basic theory of interphase heat and mass transfer, a mathematical model for interphase heat and moisture coupling transfer was established. The effects of different aperture rates of corner boxes in the drying chamber, spatial location arrangement, and other related variables on the airfield distribution, temperature field distribution, tiger nut temperature, and moisture content changes were investigated. The results show that the average air velocity below the air inlet gradually increases as the opening ratio increases. When the opening rate is 0.33%, the wind field uniformity is better, and the inhomogeneity of the drying chamber wind field is improved. As the lateral distance increases, the consistency of the moisture content distribution increases and then decreases, and the flow rate of the tiger nuts gradually increases when the grain is discharged. The rate of decrease in water content decreases gradually with the increase in longitudinal distance. When the wind speed reaches 4 m/s, the drying chamber wind field is more uniform, and the water vapor diffusion efficiency at the outlet is basically the same. Therefore, the appropriate corner box has a horizontal distance of 320 mm and a longitudinal distance of 420 mm, providing a basis for the design of tiger nut drying equipment.

Molecular-Level Kinetic Model for Light Hydrocarbon Steam Cracking Based on the SU-BEM Framework.

In this work, a molecular-level kinetic model of ethane/propane steam cracking was developed by using a hybrid structural unit-bond electron matrix framework. The molecular-level simulation was conducted, creating a detailed feedstock composition, formulating the reaction rules, and automating the generation and visualization of reaction networks. Ordinary differential equations were automatically generated based on the Arrhenius equation, while the kinetic parameters were reduced via linear free energy relations (LFERs). Furthermore, proper mathematical models for mass transfer, heat transfer, and momentum transfer within the cracking furnace were integrated into the molecular-level kinetic model, enabling the simultaneous calculation of the transfer process and chemical kinetics in steam cracking. The model was validated by its precise prediction of product yields, outlet pressure, and outlet temperature, which were collected from an industrial gas-cracking furnace.

Development of Fushchich’s Mathematical Model of Heat Transfer

Development of Fushchich’s Mathematical Model of Heat Transfer

Numerical analysis of mathematical model for heat and mass transfer through Bioconvective Maxwell nanofluid flow subject to Darcy-Forcheimer and Lorentz forces

The objective of this study to evaluate heat and mass transport rate of Maxwell nanofluid flow through a stretched medium in the existence of Darcy-Forcheimmer and Lorentz forces. In addition to above by involving motile microorganisms the heat and mass transport done through the process of bioconvection. Thermal radiation, activation energy, Brownian motion, and thermophoresis effects on the flow rate through this are also investigated. The governing model of the flow problem consist of momentum, thermal, concentration, and micro-organisms density equations, these equations are in the form of non-linear partial differential equations. To transform these non-linear partial differential equations (PDE‘s) to dimensionless non-linear ordinary differential equations (ODE‘s), we introduced couple of similarity variables. For numerical treatment of governing non-linear ODE‘s, MATLAB built in ‘bvp4c‘ solver along with shooting technique utilized. In graphical outcomes, the impact of various physical variables over the momentum, temporal, concentration, and micro-organism descriptions are elaborated briefly. The impact of deborah number on the velocity profile, by increasing the count of Deborah number the velocity profile become decrease. The effect of Lewis number over the concentration depiction, the rise in profile caused by maximizing the values of parameter. The rate of flow of mass and heat transport become increase while the values of thermophoretic parameter increases. Microorganism‘s profile decreases on increasing the Peclet number. In tabular analysis, the impacts of physical variables on the local skin friction, Nusselt number, Sherwood number, and microorganism density number are evaluated. All the physical quantities numerics computed by fixing the values of parameters as 0.2<λ<0.6, 0.3<Nb<0.5,2.0<Pr<4.0, 5.0<Le<5.3, 3.0<Lb<5.0, 0.4<Pe<0.8, 0.2<Nt<0.4, 0.2<Rb<0.4. The computed results are fine as compared to previous published results.

Research on Wellbore Stability in Deepwater Hydrate-Bearing Formations during Drilling

Marine gas hydrate formations are characterized by considerable water depth, shallow subsea burial, loose strata, and low formation temperatures. Drilling in such formations is highly susceptible to hydrate dissociation, leading to gas invasion, wellbore instability, reservoir subsidence, and sand production, posing significant safety challenges. While previous studies have extensively explored multiphase flow dynamics between the formation and the wellbore during conventional oil and gas drilling, a clear understanding of wellbore stability under the unique conditions of gas hydrate formation drilling remains elusive. Considering the effect of gas hydrate decomposition on formation and reservoir frame deformation, a multi-field coupled mathematical model of seepage, heat transfer, phase transformation, and deformation of near-wellbore gas hydrate formation during drilling is established in this paper. Based on the well logging data of gas hydrate formation at SH2 station in the Shenhu Sea area, the finite element method is used to simulate the drilling conditions of 0.1 MPa differential pressure underbalance drilling with a borehole opening for 36 h. The study results demonstrate a significant tendency for wellbore instability during the drilling process in natural gas hydrate formations, largely due to the decomposition of hydrates. Failure along the minimum principal stress direction in the wellbore wall begins to manifest at around 24.55 h. This is accompanied by an increased displacement velocity of the wellbore wall towards the well axis in the maximum principal stress direction. By 28.07 h, plastic failure is observed around the entire circumference of the well, leading to wellbore collapse at 34.57 h. Throughout this process, the hydrate decomposition extends approximately 0.55 m, predominantly driven by temperature propagation. When hydrate decomposition is taken into account, the maximum equivalent plastic strain in the wellbore wall is found to increase by a factor of 2.1 compared to scenarios where it is not considered. These findings provide crucial insights for enhancing the safety of drilling operations in hydrate-bearing formations.

Investigations of Flow Boiling in Mini-Channels: Heat Transfer Calculations with Temperature Uncertainty Analyses

The article aims to explore boiling heat transfer in mini-channels with a rectangular cross-section using various fluids (HFE-649, HFE-7000, HFE-7100, and HFE-7200). Temperature measurements were conducted using infrared thermography for the heated wall and K-type thermocouples for the working fluid. The 2D mathematical model for heat transfer in the test section was proposed. Local heat transfer coefficients between the heated wall and the working fluid were determined from the Robin condition. The problem was solved by means of the finite element method (FEM) with Trefftz functions. The values of the heat transfer coefficient that were obtained were compared with the results calculated from Newton’s law of cooling. The average relative differences between the obtained results did not exceed 4%. The study included uncertainty analyses for temperature measurements with K- and T-type thermocouples. Expanded uncertainties were calculated using the uncertainty propagation and Monte Carlo methods. Precisely determining the uncertainties in contact temperature measurements is crucial to ensure accurate temperature data for subsequent heat transfer calculations. The results of the heat transfer investigations were compared in terms of fluid temperature, heat transfer coefficients, and boiling curves. HFE-7200 consistently exhibited the highest fluid temperature and temperature differences at boiling incipience, while HFE-7000 demonstrated the highest heat transfer coefficients. HFE-649 showed the lowest heat transfer coefficients. The boiling curves exhibited a typical shape, with a notable occurrence of ‘nucleation hysteresis phenomena’. Upon the analysis of two-phase flow patterns, bubbly and bubbly-slug structures were observed.

Numerical Simulation of Heat Transfer Behavior in Hot Spot Zone of Converter Molten Bath

The multiphase fluid flow and heat transfer behavior in the steelmaking converter are essential for efficient and stable smelting. Herein, a mathematical model of heat transfer for the hot spot zone of the converter is established. The temperature distribution of the molten bath is clarified, and the effects of operating parameters and the exothermic rate of hot spot zone on the heat transfer behavior of the molten bath are investigated. The results show that the temperature gradient between the hot spot zone and the liquid steel as well as the circulation of liquid steel will lead to the nonuniform distribution of temperature. Both the direction of flow field and the mixing characteristics of molten bath influence the heating rate of molten bath, whereas the direction of the flow field plays a dominant role. In addition, the oxygen lance height has a significant influence on the heat transfer behavior; as the lance height increases from 1.35 to 1.65 m, the heating rate increases by 68.32%. The increase of exothermic rate will remarkably increase the temperature gradient and the heating rate increases by 65.84% and 114.28% when the exothermic rate increases by 1.5 and 2 times, respectively.

HEAT TRANSFER IN A FORM-STABLE DIRECT-CONTACT LATENT THERMAL ENERGY STORAGE UNIT

This study investigated various aspects of thermal storage concept, including material characterization and analysis of form-stable, unencapsulated phase-change materials (PCM) that underwent solid-solid phase transition and was in direct contact with the working fluid. The study focused on temperature range between 100-140&amp;deg;C (212-284&amp;deg;F). Mathematical heat transfer models were developed to examine the operating characteristics of the thermal energy storage unit, identify key parameters influencing storage, and conducted parametric studies. Both single-phase and phase-change working fluids were considered in the models. Experiments were conducted using a packed bed of PCM pellets and a single-phase working fluid (tri-ethylene glycol) to evaluate and demonstrate the heat storage concept during charging and discharging. The experimental results aligned well with the heat transfer models, validating their accuracy. Parametric studies explored a wide range of parameters not feasible in laboratory experiments, shedding light on charging, discharging, and thermal storage characteristics. These models facilitated the development and implementation of optimization algorithms for packed bed latent heat storage units. The findings indicated that form-stable latent heat units utilizing commercially available polymers undergoing solid-solid phase transition can serve as long-term stable thermal storage candidates for use with several single-phase working fluids as well as two-phase steam.

Heat transfer characteristics of oil-water two-phase in pipeline transportation during shutdown

Gathering and transportation pipelines often appear shutdown condition due to damage, leakage, and other reasons. The reasonable maintenance time should be controlled by closely combined with the change law of the oil-water temperature in the pipeline. This paper established a multi-field coupling 3-D heat transfer mathematical model of the oil-water pipeline environment based on the two-phase shutdown pipeline as the research object. According to the changing law of the oil-water temperature field and flow field under a typical pipe diameter, the evolution behavior of the gelation layer in the pipe and the transformation process of heat transfer mode were analyzed, and the heat transfer characteristics between oil-water phase and its interface in the pipe were defined. With the liquid phase ratio of the oil phase changing the rule, reasonable maintenance time suggestions were given for gathering and transporting pipelines with different water content.

Numerical parametric analysis of the decomposition and propagation of combustion products in a confined environment in the early stages of a fire

Numerical research findings are presented on the patterns of spread of thermal decomposition products of wood-based materials in confined spaces isolated from the external environment. Based on the experimental data, a physical problem statement was formulated and a mathematical model of heat and mass transfer was developed for rooms with the most typical sources of fire hazard. The experimental and numerical research findings were obtained for the conditions corresponding to compartments isolated from the external environment (e.g., rooms at dedicated facilities, like ships, small and medium-sized rooms) and to underventilated rooms. The performed experiments and calculations revealed satisfactory agreement in the findings and demonstrated the validity of the proposed model of heat and mass transfer. Wood was used as the main material in fires. A comparative analysis was also carried out for paper of different quality. The modeling was performed for the most frequent causes of fires: careless handling of fire, unsafe operation of heating equipment and electrical short circuits. The rates of growth of thermal decomposition product concentrations were determined for different distances from the material. The impact of a number of factors on the characteristics under study was determined. These are the fire and room sizes, fire cause, supply and exhaust ventilation. The data were extrapolated to the conditions corresponding to business, warehouse and residential premises.

Numerical Analysis of the Boiling Heat Transfer Coefficient in the Flow in Mini-Channels

Abstract This paper deals with boiling heat transfer in the flow of water through an asymmetrically heated horizontal rectangular mini-channel. The mini-channel was made by gluing three transparent glass plates and a copper block. Through the glass window, the variable along the length of the mini-channel two-phase flow structures were recorded to determine local values of the void fraction. Four resistance heaters were attached to the copper block, powered by direct current, generating the heat initiating the flow boiling inside the channel. During the experiment, the following were measured: water volumetric flow rate, inlet pressure with pressure drop, inlet and outlet water temperature, copper block temperatures at three points inside its body, voltage and current supplied to the heaters. Stationary and laminar fluid flow with low Reynolds numbers were assumed in the mathematical model of heat transfer in selected elements of the measuring module. The temperature distributions in the copper block and flowing water were described by the appropriate energy equations: the Laplace equation for the copper block and the Fourier–Kirchhoff equation with parabolic fluid velocity for the flowing water. These equations were supplemented with a set of boundary conditions based on measurement data; moreover, data from experimental studies were the basis for numerical calculations and their verification. Two-dimensional temperature distributions of the copper block and water were calculated with the Trefftz method (TM). The main objective of this study was to determine the heat transfer coefficient on the contact surface of the copper block and water, which was calculated from the Robin boundary condition. The results of the calculations were compared with the results of numerical simulations performed using the Simcenter STAR-CCM+ software, obtaining consistent values. Computational fluid dynamics (CFD) simulations were verified based on experimental data including void fraction and temperature measurements of the copper block and flowing water.

Developing and solving the mathematical model of transient heat and mass transfer in the freeze-drying of Cordyceps militaris

This study developed a mathematical model of the transient mass and heat transfer of Cordyceps militaris during lyophilization. This mathematical model was solved using a program coded in MATLAB to simulate the relationship between product temperature and sublimation rate over time. The parameters of the drying mode were set in the simulation as follows: heating plate temperature from 273.2 to 303.2 K, the absolute pressure of the drying chamber is from 30 Pa to 60 Pa. The fruiting body of cordyceps analyzed in the study is considered a cylindrical shape with a radius of 1.5 mm and length of 60 mm, which was arranged in 1 layer on a tray with dimensions of 200x300x20 mm. Research shows that the sublimation rate increases when the heating plate temperature increases. Besides, the decrease in sublimation chamber pressure will lead to rapid increases in drying speed. This result can also be used to build software to set the technological mode for the cordyceps drying process by sublimation.