Mathematical Model Of Heat Transfer Research Articles

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.

Experimental and numerical study on temperature control performance of phase change material heat sink

With the increasing power consumption of electronic products, the rising temperature leads to the deterioration of working environment and the reduction of service life. In order to control the temperature rise of electronic products, in this paper, the heat sinks with phase change material (PCM) and honeycomb metal were designed. And their performance was compared with that of the original heat sink (without PCM and honeycomb metal) then studied under various working conditions. Paraffin (n-eicosane) and prepared low melting point alloy were filled into the heat sink with honeycomb metal. The temperature control performance of heat sink was tested experimentally under different heating power. A two-dimensional heat transfer mathematical model of honeycomb metal PCM heat sink was established and solved numerically. The numerical results were compared with experimental data to verify the mathematical model. The results demonstrate that PCM heat sinks effectively controls the temperature of electronic devices and the low melting point alloy makes heat sink better performance than paraffin. Honeycomb metal further decreases the temperature of the paraffin heat sink by up to 3.6 °C, and extends the effective working time of the alloy heat sink by 14 %. The performance of the low melting point honeycomb metal heat sink is superior to that of the paraffin honeycomb metal heat sink at high heating power, and is close to the latter at low heating power. The effective working time of PCM honeycomb metal heat sink is significantly extended when the PCM melting point is close to the limit temperature, especially at high heating power and for the PCM with low thermal conductivity. This study provides valuable reference for temperature control design of electronic products.

Mathematical modeling and experimental validation of heat transfer during upward subcooled flow boiling in a vertical annulus

Mathematical modeling and experimental validation of heat transfer during upward subcooled flow boiling in a vertical annulus

Identification of Mathematical Models of Heat Transfer of HTSC Coils. 2. Algorithm for Solving IHP and the Results of Experimental Data Processing

Identification of Mathematical Models of Heat Transfer of HTSC Coils. 2. Algorithm for Solving IHP and the Results of Experimental Data Processing

Multiscale Mathematical Model of Heat and Mass Transfer in a Thin Vapor Chamber

Multiscale Mathematical Model of Heat and Mass Transfer in a Thin Vapor Chamber

Study on Mushy Zone Coefficient in Solidification Heat Transfer Mathematical Model of Thin Slab with High Casting Speed

When the casting speed of the thin slab continuous caster is increased, the ratios of the solid and liquid phases in the solidification front of the molten steel in the mold change, which affects the thickness of the solidified shell. In order to accurately calculate the thickness of the solidified shell and determine the value range of the mushy zone coefficient suitable for the mathematical model of solidification heat transfer at high casting speed, this paper established the solidification heat transfer mathematical model in thin slab funnel mold, and the influence of different mushy zone coefficients on the accuracy of solidification heat transfer mathematical model was analyzed and compared with the actual solidified shell thickness. The results showed that, when the casting speed was increased to 4~6 m/min and the coefficient of the mush zone coefficient was 3 × 108~9 × 108 kg/(m3⋅s), the thickness of solidified shell calculated by the solidification heat transfer model was in good agreement with that measured in practice. The research in this paper provides an important reference for the establishment of the solidification heat transfer mathematical model at high casting speed in the future.

Modeling of the flow and heat exchange in pipes with turbulators of viscous heat carriers in the laminar region, as well as in the transition to turbulent flow

Objective. Mathematical modeling of heat transfer in pipes with turbulators for viscous heat carriers at Reynolds numbers characteristic of laminar and transient flow regimes is carried out by the calculation method. The solution of the heat exchange problem for semicircular cross-section flow turbulators based on multiblock computing technologies based on the solution of the Reynolds equations (closed for the transient mode using the Menter shear stress transfer model) and the energy equation (on multi-scale intersecting structured grids) by the factorized finite-volume method (FCOM) was considered.Method. The calculation was carried out on the basis of a theoretical method based on the solution of the Reynolds equations, closed for transient modes using the Menter shear stress transfer model, and the energy equation on multiscale intersecting structured grids (FCOM), by a factorized finite-volume method.Result. Both local and averaged characteristics of the flow and heat exchange in pipes with turbulators for a viscous coolant for laminar and transient flow modes of the coolant were obtained using the FCOM method in the work, which made it possible to determine for these modes the levels of heat exchange intensification that satisfactorily correlate with the existing experiment.Conclusion. The calculated relative hydraulic resistance for low turbulators increases quite slightly, and for medium-altitude turbulators reaches 2÷2.5 to the critical Reynolds number, and subsequently it increases up to 3 times; for high turbulators, the relative hydraulic resistance increases up to 4 times even before the transition flow regime is reached, after which it increases up to 4.5 times. The calculated relative isothermal intensified heat exchange under the laminar flow regime of a viscous coolant for relatively high turbulators increases almost 2 times; for relatively medium heights of turbulators — almost one and a half, and for low relative heights, the intensification of heat exchange is insignificant.

Analysis of the Main Factors Controlling the Formation of Subaerial Taliks, Using a One-Dimensional Mathematical Model. A Case Study for the Shestakovka River Basin (Central Yakutia)

Received March 9, 2023; revised September 7, 2023; accepted October 2, 2023This study presents a mathematical model of heat transfer in a subaerial talik. The model is based on the concepts presented in classical works on permafrost, as well as on the results of geological and geophysical research carried out in the Shestakovka River basin (Central Yakutia). This model is based on the solution of the classical Stefan problem on the moving of the phase transition boundaries for a multilayer and multiphase medium. The solution was calculated on a unstructured mesh. When the phase boundaries move, thawed or frozen layers of soil are formed or wedged out. The layers include: snow cover, seasonally thawed soil, seasonally frozen and frozen sand deposits, as well as soil-vegetative layer. Published empirical relationships were used to calculate thermophysical coefficients, which are presented in this article. Simple variants of the model were considered to clarify the contribution of various factors to the process of formation and evolution of taliks. It has been established that the presence of snow cover and soil-vegetative layer have the most significant effect on the formation of taliks. Calculations show that taliks are formed in the first years of the modeled period, in the presence of snow and the absence of soil-vegetative layer. The soil-vegetative layer, depending on its composition and moisture content (ice content), can prevent the formation and development of taliks. The authors do not consider cases where shrubs contribute to snow accumulation. The humidity and iciness of the layer of sand sediments located in Central Yakutia have practically no effect on this process.

Mathematical Model of Heat and Mass Transfer of Coal in a Stack

A mathematical model of coal’s self-heating in the stack is presented, where the heat exchange and gas exchange processes are described by a system of two non-linear differential equations of the second order concerning temperature t of coal’s self-heating and volume fraction C of oxygen in the cavities of the stack with boundary and initial conditions. The differential equations took into account that self-heating of coal in the stack and initiation of self-ignition are observed in a relatively small layer adjacent to the surface of the stack and called the zone of oxygen influence. In this mathematical model authors have taken into account the influence on the process of coal’s self-heating of parameter Ф – specific heat release power, which in addition characterises the preservation of coal during storage. There were also used such physical parameters as thermal conductivity, diffusion coefficient, specific heat capacity of coal in the stack, bulk density, thermal effect of oxidation, stack cavity, temperature coefficient of exponential growth of heat release power when compiling the differential equations. For numerical implementation of this mathematical model, there were introduced dimensionless variables and criteria, which allowed to apply the grid method. Analysis of the final results allowed to obtain: changes in stack temperature profiles in time; changes in stack oxygen concentration profiles in time; influence on stack temperature profile of specific heat release power; influence on stack temperature profile of the parameter characterising exponential growth of heat release intensity with increasing temperature. It has been found that the greatest influence on the dynamics of self-heating of coal in the stack has the Lykov criterion, proportional to the diffusion coefficient, and the Nusselt criterion related to the effective thermal conductivity and the effective thermal diffusivity of coal. The results obtained suggest that self-heating in the stack is due, on the one hand, to intensive penetration of air oxygen and, on the other hand, to impaired heat dissipation. Self-heating and the transition of self-heating into ignition is associated with the occurrence of turbulent diffusion in the stack, arising from increased heat blowing, the effect of which can be enhanced when directed perpendicular to the surface of the stack.

Protection Design and Effectiveness Verification of High-temperature Fire for Civil Aviation Emergency Locator Transmitter

Considering the coupling between the heat of emergency locator transmitter and the external high-temperature fire environment, a thermal protection system for external insulation and internal heat absorption is proposed. The external insulation layer consists of flexible nanofiber heat insulation film and quartz ceramics to withstand the thermal impact of the external environment. The internal heat absorption layer is composed of microcapsulated paraffin, which is used to absorb the heat transmitted through the insulation layer and the heat generated by emergency locator transmitter. Using the enthalpy method to establish a transient heat transfer mathematical model of thermal protection system, and the protection performance of the system in high-temperature fire is analyzed. The calculation results show that the system can withstand a high-temperature fire for at least 15 minutes, during which the temperature of emergency locator transmitter is controlled below 60℃. After the fire is over, under the coupling of the waste heat of the incoming system and the heat of emergency locator transmitter, the temperature of emergency locator transmitter continues to rise to a maximum of 107℃. Then, as the influence of the waste heat of the incoming system weakens, the temperature of emergency locator transmitter gradually decreases. Finally, the accuracy of the simulation model and the effectiveness of the thermal protection system are verified through destructive experiments.

Trefftz functions methods in analysis of the effect of enhanced heated surface on FC-72 flow boiling in minichannels

This paper focuses on time-dependent flow boiling heat transfer. The main element of the research stand was the test section with 11 rectangular minichannels of 1 mm depth. The FC-72 was heated by a thin foil during upward flow. The temperature of the outer surface of the foil was measured by infrared thermography. Two types of foil surface were tested: smooth and enhanced with recesses produced using emery paper. The main objective was to verify whether the enhanced surface helps to obtain a better heat transfer efficiency compared to the smooth surface. The 2D mathematical model of heat transfer was proposed, while methods with Trefftz functions were applied to solve the time-dependent problem of heat transfer. The Robin condition was used to determine heat transfer coefficients at the interface between the foil and the fluid. Experimental data on temperature and pressure and their validation were presented and discussed. Results based on the heat transfer coefficients were provided. They covered the calculation procedure, the determination of the mean relative error and results validation with using the 1D approach. The heat transfer coefficients as a consequence of application of the Trefftz method and the hybrid Picard-Trefftz method in the calculation procedure with comparison analysis of the results were shown. Furthermore, comparisons aimed at obtaining the results characteristic for smooth and enhanced surfaces were also conducted. In the experiment with an enhanced heated surface, the values of the heat transfer coefficient appeared to be higher. Boiling curves were illustrated and discussed.

Membrane-based packed-sheet liquid desiccant dehumidification system

Humidity control plays a vital role in both buildings and greenhouses. The thermally-driven liquid desiccant dehumidification systems are getting an increasing traction because of their high moisture removal capacity and the possibility of their integration with waste-heat or renewable energy sources. In this work, a novel design concept for liquid desiccant dehumidification systems is proposed to overcome the practical challenges of the conventional systems, such as solution carryover, crystallization, and corrosion. The presented system utilizes a compact “packed-sheet” sorption bed that houses spherical membrane-based micro-absorbers with LiBr as a liquid desiccant. A bench-scale system is designed and tested under the typical dehumidification working conditions. The experimental results showed that the proposed design has up to two-fold higher moisture removal rate per volume (MRR = 75 g/s-m3) than a conventional LiBr liquid desiccant dehumidification system (MRR = 35 g/s-m3). In addition, a one-dimensional coupled heat and mass transfer mathematical model is developed to simulate the transient behavior of the proposed system. An optimization study, using the validated model, suggested that the performance of proposed design can be maximized to realize moisture removal rates of up to 135 g/s-m3 (270% higher than the conventional liquid desiccant systems) with a coefficient of performance of 0.25.

Experimental and numerical study on thermal performance of phase-change-material cool roofs in summer

Cool roofs can reduce building energy consumption and improve indoor and outdoor thermal environments. A phase change material cool roof (PCMC roof) was proposed in order to reduce roof heat gain in the indoor thermal environment in summer. Indoor thermal and energy environmental parameters in three full-size rooms (ordinary room, PCM room, and PCMC room) were tested from July to September 2022. The heat transfer characteristics and energy saving effect of roofs were investigated by combining experimental analysis with numerical analysis. Compared with the ordinary roof, the PCMC roof decreased external and internal roof surface real-time temperatures up to 30.0 °C and 6.4 °C respectively, and reduced the roof inner surface heat flux of 33.3%-66.7%. Compared with the relevant roof studies, the energy saving and cooling effects are more significant. Then, based on the mathematical model of roof heat transfer, the correlation analysis between seven different elements was carried out to evaluate the energy-saving effect of PCMC roof. This study investigates the PCMC roof from the aspects of roof heat transfer characteristics, influence on indoor thermal environment, energy saving evaluation, etc., which provides a more complete and valuable reference for advancing building roofs.

Effect of the Solid Particle Diameter on Frictional Loss and Heat Exchange in a Turbulent Slurry Flow: Experiments and Predictions in a Vertical Pipe

The study deals with experiments and predictions on turbulent flow and heat exchange in a fully developed slurry flow in a vertical upward pipe. Four slurries were considered: two with glass spheres particles with diameters of 0.125 mm and 0.240 mm, respectively, and two with sand spheres particles with diameters of 0.470 mm and 0.780 mm, respectively. The volume concentration of the particles was changed in the range of 10% to 40%. This study has indirectly demonstrated the existence of turbulence suppression to a degree dependent on the diameter of the solid particles. A mathematical model for heat transfer between slurry and pipe was developed using the two-equation turbulence model and a specially designed wall function, including particle diameter and solid concentration. The model assumed a constant wall temperature and heat flux. The study’s objective was to determine the influence of the diameter of the solid particles on the heat exchange. The Nusselt number was found to change sinusoidal, reaching a maximum for a slurry with d = 0.125 mm, and a minimum for d = 0.470 mm. The higher the solid concentration, the lower the Nusselt number. The novelty and value of this study lies in the deeper characterisation and understanding of the influence of the diameter of solid particles on heat exchange.

Identification of Mathematical Models of Heat Transfer of HTSC Coils. 1. Technical Tools and Experimental Technique

Identification of Mathematical Models of Heat Transfer of HTSC Coils. 1. Technical Tools and Experimental Technique

A Novel Molecular PCM Wall with Inorganic Composite: Dynamic Thermal Analysis and Optimization in Charge-Discharge Cycles.

The combination of electric heating and thermal energy storage (TES) with phase change material (PCM) can achieve load shifting for air conditioning energy saving in building sectors. Their non-flammability, relatively good mechanical properties, and low cost make inorganic PCMs attractive in construction engineering. However, PCMs often show poor thermal conductivity, low heat transfer efficiency, leakage risk, etc., in applications. Moreover, the practical thermal performance of PCM-TES sometimes fails to meet demand variations during charge and discharge cycles. Therefore, in this study, a novel integrated electric PCM wall panel module is proposed with quick dynamic thermal response in space heating suitable for both retrofitting of existing buildings and new construction. Sodium-urea PCM composites are chosen as PCM wall components for energy storage. Based on the enthalpy-porosity method, a mathematical heat transfer model is established, and numerical simulation studies on the charge-discharge characteristics of the module are conducted using ANSYS software. Preliminary results show that the melting temperature decreases from 50 °C to approximately 30 °C with a 30% urea mixing ratio, approaching the desired indoor thermal comfort zone for space heating. With declining PCM layer thickness, the melting time drops, and released heat capacity rises during the charge process. For a 20 mm thick PCM layer, 150 W/m2 can maintain the average surface temperature within a comfort range for 12.1 h, about half the time of a 24 h charge-discharge cycling periodicity. Furthermore, placing the heating film in the unit center is preferable for improving overall heat efficiency and shortening the time to reach the thermal comfort temperature range. This work can provide guidance for practical thermal design optimization of building envelopes integrated with PCM for thermal insulation and energy storage.

A two-stage multi-step numerical scheme for mixed convective Williamson nanofluid flow over flat and oscillatory sheets

The novelty of this contribution is to propose an implicit numerical scheme for solving time-dependent boundary layer problems. The scheme is multi-step and consists of two stages. It is third-order accurate in time and constructed on three-time levels. For spatial discretization, a fourth-order compact scheme is adopted. The stability of the proposed scheme is analyzed for scalar linear partial differential equation (PDE) that shows its conditional stability. The convergence of the scheme is also provided for a system of time-dependent parabolic equations. Moreover, a mathematical model for heat and mass transfer of mixed convective Williamson nanofluid flow over flat and oscillatory sheets is modified with the characteristic of the Darcy–Forchheimer model. The results show that the temperature profile rises by developing thermophoresis and Brownian motion parameter values. Also, the proposed scheme is compared with an existing Crank–Nicolson method. It is found that the proposed scheme converges faster than the existing one for solving scalar linear PDE as well as the system of linear and nonlinear parabolic equations, which are dimensionless forms of governing equations of a flow phenomenon. The findings provided in this study can serve as a helpful guide for future investigations into fluid flow in closed-off industrial settings.