Heat Transfer Law Research Articles

Investigation on the role of tri-nanoparticles for non-Fourier thermal enhancement by MHD non-Newtonian rheological fluid composed charged particles

Heat transfer enhancement in partially ionized Williamson fluid using tri-nanoparticles has not been studied yet. This article provides a comparative analysis of the enhancement of heat and mass transfer in Williamson fluids for mono, hybrid, and tri-nanoparticles. This is a theoretical study based on mathematical modelling using governing laws of heat transfer in a fluid medium (here fluid medium is Williamson fluid). The system of governing PDEs is transformed via a change of variables suggested under the similarity principle. Finite element method (FEM) is implemented to solve the dimensionless problems. Computer code is tested and convergent meshed free solutions are computed. Aluminium oxide, titanium oxide, and silicon oxide are taken as tri-nanoparticles whereas ethylene glycol is considered plasma and is subjected to the applied magnetic field of non-uniform intensity. An optimized improvement in thermal performance is noticed for the cause of tri-nanoparticles. The wall of heat transfer rate for mono, hybrid, and tri-nanofluids was computed and their numerical values are compared. It is noted that the wall heat transfer rate by tri-nanofluid is maximum in respect of wall heat transfer rates by mono and hybrid nanofluids. Wall shear stress exerted by tri-nanofluid is noted to have a minimum value in comparison with the wall shear stress exerted by mono and hybrid nanofluids. Hall and ion slip effects on the flow of tri-nanofluid are stronger than those on the flow of mono and hybrid nanofluids.

Minimum power consumption of multistage irreversible Carnot heat pumps with heat transfer law of q ∝ (ΔT) m

Abstract For the given initial finite high-temperature heat reservoir temperature, continuous Hamilton–Jacobi–Bellman equations are established to obtain optimal finite high-temperature heat reservoir temperature for minimum power consumption of multistage Carnot heat pumping system with generalized convective heat transfer law [q ∝ (ΔT) m ]. Analytical expression of optimal heat reservoir temperature with Newtonian heat transfer law (m = 1) is obtained based on generalized optimization results for minimum power consumption. For other heat transfer laws (m ≠ 1), numerical solutions for minimum power consumption are provided. Optimization results for multistage Carnot heat pumps are compared with maximum power output solutions of multistage irreversible Carnot heat engines.

Influence of Marangoni Effect on Heat and Mass Transfer during Evaporation of Sessile Microdroplets.

Evaporative cooling is an important method for controlling the temperature of micro devices, and heat and mass transfer from the microdroplets in the evaporation process directly affect the cooling performance. In order to study the droplet heat and mass transfer law in the droplet evaporation process, this paper builds a coupled thermal mass model of droplet evaporation and tests the accuracy of the numerical model through theoretical results. In order to study the influence of the Marangoni effect on the droplet evaporation process and the effects of different initial droplet radius and ambient temperature on the temperature and flow, fields within the droplet are compared. From this result, it can be seen that the droplet volume is 20 μL, and the maximum flow velocity in the droplet is 0.34 mm/s, without taking into account the Marangoni effect. When the Marangoni effect is taken into account, the maximum flow velocity increases by almost 100 times. The Marangoni effect can cause the convection in the droplet to change direction, and the formation of the Marangoni flow may affect the temperature distribution within the droplet, thereby increasing the evaporation efficiency by 2.5%. The evaporation process will increase the velocity of the air close to the surface of the liquid, but the increase in air velocity close to the liquid surface is not sufficient to reinforce evaporation. There is a non-linear relationship between increasing ambient temperature and increasing evaporation efficiency. For every 5 °C increase in ambient temperature, the maximum increase in the rate of evaporation is approximately 22.7%.

Optimization of stator ventilation structure of high‐speed railway traction motor based on the genetic algorithm

AbstractAiming at the problems of high power density and difficult heat dissipation of high‐speed train traction motors, this study takes a 600 kW asynchronous traction motor as a research object and optimises the motor cooling structure through the fluid‐structure coupled heat transfer analysis and genetic algorithm. Based on the principles of fluid dynamics and heat transfer, the motor's fluid flow and heat transfer laws are calculated and analysed, and the calculation accuracy is verified by the experimental data. Based on exploring the influence of the stator ventilation aperture and the number on motor fluid and temperature, aiming to reduce the maximum temperature of each motor component, a bivariate multi‐objective mathematical model of stator ventilation aperture and number is established, and the optimal solution is found with the help of the genetic algorithm. Finally, the optimisation effect is verified by comparing the motor temperature before and after optimisation.

Effect of passive commutation on heat transfer and flow characteristics of non-circular pipes

Based on the need for energy-saving and consumption reduction in industrial applications, the effect of an internal concave structure on a heat exchanger tube with a right-angle trapezoidal cross-section and changing the flow direction on the heat transfer and flow characteristics in the tube was investigated. CFD techniques were used to study the effect of the inner concave structure with 15mm and 30mm center spacing and 1.88mm and 3.75mm radius of curvature on the heat transfer and flow characteristics of air under turbulent flow conditions in the range of Re13349 to 57847, and the heat transfer law was explored in terms of the combined heat transfer performance PEC and the coefficient of variation of the convective heat transfer coefficient and verified to be consistent with the field The effect of the variation of the synergy angle was confirmed. The results show that the PEC of the pipe is enhanced with the increase of the inner concave radius and the decrease of the inner concave center spacing.

Study on Heat and Mass Transfer Performance during Heating, Pressurization and Expansion Stage in Explosion Puffing at Low Temperature and High-Pressure

China is a large agricultural country that is leading worldwide in the annual number of agricultural products and exports. However, the growth and harvest of fruits and vegetables are greatly affected by geographical conditions, climate and other factors, which will lead to their rotting in peak season and shortages in the off-season. Therefore, it is necessary to vigorously promote the development of drying technology. The explosion puffing technology at low temperature and high pressure is a kind of compound drying technology which can enable the puffed product to obtain the advantages of honeycomb, good rehydration, a short running time, etc. With the guidance of the theory of heat and mass transfer and relevant thermodynamics laws, this study has established high-pressure extruding technology in low-temperature heating; expanded the two-phase theoretical model, using mass conservation and the law of the conservation of energy to analyze the coupled heat and mass transfer process and influencing factors; and researched the influence of the operation temperature, pressure and time on the properties of dried fruit.

Optimal piston motion paths for a light-driven engine with generalized radiative law and maximum ecological function

Searching optimal piston motion path (OPMP) by using optimal control theory for various thermal cycles is an important task in finite time thermodynamics. Some optimization objectives have been used in this type of researches, including maximum work output (MWO) and minimum entropy generation (MEG). This paper introduces maximum ecological function (MEF) into OPMP problem for light-driven engine (LDE) with generalized radiative heat transfer law (HTL) [q∝Δ(Tn)]. The LDE is with working fluid of reacting system [A]⇌[B] and irreversibilities of piston friction and heat conduction. Numerical examples of OPMPs at MEF with Newtonian (n=1), linear phenomenological (n=−1) and radiative (n=4) HTLs are provided. The results are compared with those obtained by MWO and MEG objectives as well as different HTLs. Utilizing MEF as objective can effectively accomplish entropy generation reduction with a little decrease in work output. Time-parametrized piston velocity, working fluid temperature and piston position for MEF are situated between those for MEG and MWO. Moreover, OPMPs for MEF with different HTLs are also quite different. Although all of the values of ecological function are negative for three special HTLs, work output and ecological function decrease with the increase in n, and entropy generation increases when n increases.

Four-Objective Optimization of an Irreversible Stirling Heat Engine with Linear Phenomenological Heat-Transfer Law.

This paper combines the mechanical efficiency theory and finite time thermodynamic theory to perform optimization on an irreversible Stirling heat-engine cycle, in which heat transfer between working fluid and heat reservoir obeys linear phenomenological heat-transfer law. There are mechanical losses, as well as heat leakage, thermal resistance, and regeneration loss. We treated temperature ratio of working fluid and volume compression ratio as optimization variables, and used the NSGA-II algorithm to carry out multi-objective optimization on four optimization objectives, namely, dimensionless shaft power output , braking thermal efficiency , dimensionless efficient power and dimensionless power density . The optimal solutions of four-, three-, two-, and single-objective optimizations are reached by selecting the minimum deviation indexes with the three decision-making strategies, namely, TOPSIS, LINMAP, and Shannon Entropy. The optimization results show that the reached by TOPSIS and LINMAP strategies are both 0.1683 and better than the Shannon Entropy strategy for four-objective optimization, while the s reached for single-objective optimizations at maximum , , , and conditions are 0.1978, 0.8624, 0.3319, and 0.3032, which are all bigger than 0.1683. This indicates that multi-objective optimization results are better when choosing appropriate decision-making strategies.

Experimental research on the heat transfer characteristics of fluid flowing through rock with intersecting fractures

The research on the seepage and heat transfer characteristics of fluid flowing through fractured rock mass is of great significance to the utilization of geothermal resources. The behaviors and characteristics of heat transfer when fluid flowing through a single fracture channel, two intersecting fractures channels, and three intersecting fractures channels were investigated and compared. Firstly, the calculation formula of convective heat transfer coefficient of water flowing through multi channels was deduced. Then the relationship between the seepage characteristic parameters and the confining pressure during the loading and unloading process was analyzed and discussed. Finally, the heat transfer mechanism of water flowing through rock sample with multi fractures was studied. This work supplements the law and theory of heat transfer when fluid flowing through fracture networks, which is of practical significance to the underground space utilization and geothermal resource exploitation.

Effect of Vertical Pressure on Temperature Field Distribution of Bulk Paddy Grain Pile

Grain storage pressure is an important factor affecting grain pile temperature, and its influencing mechanism needs to be studied further. The distribution and variation of the temperature field of a bulk grain pile under different vertical pressures and a temperature difference of 25 °C are studied by a model test and numerical simulation. Initially, the temperature change and heat transfer law at different points in the bulk grain pile space are studied under different vertical pressures using a self-made test device. Thereafter, a multi-field coupling software platform COMSOL is used to simulate and study the distribution law of the temperature field in the bulk grain pile under different vertical pressures. The influence mechanism of vertical pressure on the temperature field of the grain pile is discussed based on the micro-airflow velocity field obtained by numerical simulation. The results show that the numerical simulation and experimental results are in good agreement. With the increase in vertical pressure, the heat transfer rate of the grain pile increases gradually, the convective heat transfer in the grain pile is hindered, and the temperature distribution gradually attains uniformity. When the vertical pressure increases from 50 kPa to 200 kPa, the temperature of the grain pile decreases by approximately 0.6–2.7 °C, and the rate of change of the temperature gradient reaches 7.4%. Under different vertical pressures, the proportion of the high-temperature area decreases linearly with the storage duration. The micro-airflow velocity field affects the temperature transfer in the bulk grain pile, resulting in the temperature at the top of the storage structure being higher than that at the bottom. The research methods and conclusions in this study can provide theoretical support and reference for the multi-field coupling research on bulk grain pile storage.

Weak solution to a Robin problem of anomalous diffusion equations: Uniqueness and stable algorithm for the TPC system

A Riemann‐Liouville fractional Robin boundary‐value problem is proposed to describe the fast heat transfer law both within isotropic materials and through the boundary of the materials in high temperature environment. The variational formulation of the fractional model is derived, and further, the energy estimation of the weak solution is deduced. Subsequently, the uniqueness theorem of weak solution is proved. A valid and stable finite difference scheme is developed for the fractional model. The numerical experiments are implemented to indicate that the fractional model is applicable to discover the thermal superdiffusion in the thermal protective clothing (TPC) system and numerical algorithms are effective to improve the intelligence of TPC design.

Heat-mass transfer coupling effects in water-ice phase transformation of water-bearing coal frozen with liquid nitrogen

• The equation of coal freezing and water-ice phase transformation under the action of cryogenic LN 2 is derived. • A new discretization method is proposed to solve the equation of coal temperature and water-ice phase transformation. • The water-ice phase transition law of LN 2 flowing through water-bearing coal is studied quantitatively. • The influence of ice water conversion process on temperature distribution in water-bearing coal at low temperature is analyzed. • The law of heat and mass transfer in the process of LN 2 flowing through water-bearing coal is revealed. Liquid nitrogen (LN 2 ) fracturing, as a waterless and environmentally friendly fracturing technology, has a broad application prospect in coalbed methane (CBM) exploitation. Currently, there is a lack of sufficient understanding of the heat mass transfer mechanism of LN 2 fractured coal mass. In this paper, the heat-flow coupling problem of LN 2 frozen coal mass was systematically studied by means of numerical simulation. A fluid-solid coupled multiphase module was mathematically modeled on LN 2 flow, coupling between LN 2 and coal mass temperature, and the variation law of coal temperature and water-ice phase with time and geometric position during LN 2 flow was obtained under the coal seam freeze-thaw simulation analysis program by FORTRAN language. The results showed that the most obvious heat mass transfer occurred in the coal mass area close to the LN 2 inlet and the fluid-solid interface. Along the direction of coal burial depth, the changes of temperature and water-ice phase are broadly divided into rapid change zone, slow change zone and stable zone, and along the horizontal direction of LN 2 flow, the temperature and unfrozen water volume first peaked, then decreased and gradually stabilized, while the ice content was diametrically opposed, which indicating that the change of temperature and water-ice phase have significant anisotropic characteristics, and the hydrothermal coupling effect out to be one of the most important factors affecting the effect of LN 2 fracturing coal. The main findings of this study are the keys to the research of LN 2 fracturing physical mechanisms in CBM reservoirs.

Heat Engine Cycle Configurations for Maximum Work Output with Generalized Models of Reservoir Thermal Capacity and Heat Resistance

Abstract A class of two finite-heat-reservoir endoreversible heat engine with the generalized models of both the reservoir thermal capacities and heat resistances is investigated. The optimality condition for cycle maximum work output is derived by applying optimal control theory, and impacts of both thermal capacity characteristics of heat reservoirs and heat transfer laws on the optimal configurations are discussed. The results obtained in some previous researches are special cases of those obtained herein, which can provide some guidelines for optimal design of actual heat engines.

Modeling Study of a Microbial Spray-Drying Process Based on Real-Time Sampling

The process of microbial spray-drying has inherent defects such as short time, complexity, and non-visualization of particle trajectory. However, there has been a lack of effective methods for real-time sampling, rehydration, and non-destructive storage of dried particles, as well as mathematical modeling of the drying process of yeast particles based on sampling and measurement data. Therefore, firstly, a real-time sampling system was developed which completed real-time sampling, rehydration, and non-destructive storage of spray-dried particles, and realized the real reproduction of the changes of yeast particles in the process of spray drying. The laws that the motion trajectory of microbial particles during spray drying are divided into the first cycle region and the reflux cycle region were concluded, and the partition mechanism was explored. Then, based on the sampling data and the law of heat and mass transfer, a mathematical model of porous media was established to predict the variation of moisture content and rehydration survival rate of dried microbial particles with drying time. Finally, the mathematical model was tested by a microbial spray drying experiment, and the maximum errors between the predicted value and the test value of moisture content and rehydration survival rate were Xmax1=0.027(d.b) and Qvmax1=1.06%, respectively, both were less than 5% which proved the correctness of the mathematical model of porous media and laid a foundation for the study of the damage mechanism of microbial spray drying.

Three-dimensional numerical simulation of heat transfer and flow of waxy crude oil in inclined pipe

The purpose of this study is to obtain the heat transfer and flow law of waxy crude oil in the inclined pipeline and to provide theoretical guidance for the safe operation of the pipeline. In this paper, three-dimensional numerical simulation of pipes with inclination angles of 0°, 25 °and 45 °is carried out by using CFD software. The temperature and velocity fields of waxy crude oil and the cooling gelation law of crude oil are basically the same in different cases. Affected by the initial temperature field of shutdown, the average temperature of horizontal pipeline decreases gradually along the flow direction of pipeline. The inclined pipe is mainly affected by the natural convection caused by gravity, and the temperature decreases gradually along the downward direction of the inclination of the pipe. The inclination angle of the pipe increases to 45°, the temperature difference between the highest and lowest points of the pipe increases to 5.012 °C, and the liquid volume fraction increases by 1.6%. Among them, the low-lying pipe section is more likely to cause pipeline blockage.

Artificial neural network analysis of the Nusselt number and friction factor of hydrocarbon fuel under supercritical pressure

This paper presents the Nusselt number and friction factor model for hydrocarbon fuel under supercritical pressure in horizontal circular tubes using an artificial neural network (ANN) analysis on the basis of the back propagation algorithm. The derivation of the proposed model relies on a large number of experimental data obtained from the tests performed with the platform of supercritical flow and heat transfer. Different topology structures, training algorithms and transfer functions are employed in model optimization. The performance of the optimal ANN model is evaluated with the mean relative error, the determination coefficient, the number of iterations and the convergence time. It is demonstrated that the model has high prediction accuracy when the tansig transfer function, the Levenberg-Marquardt training algorithm and the three-layer topology of 4-9-1 are selected. In addition, the accuracy of the ANN model is observed to be the highest compared with other classic empirical correlations. Mean relative error values of 4.4% and 3.4% have been achieved for modeling of the Nusselt number and friction factor respectively over the whole experimental data set. The ANN model established in this paper is shown to have an excellent performance in learning ability and generalization for characterizing the flow and heat transfer law of hydrocarbon fuel, which can provide an alternative approach for the future study of supercritical fluid characteristics and the associated engineering applications.

Comparison of Heat Transfer Characteristics of the Hollow-Shaft Oil Cooling System for High-Speed Permanent Magnet Synchronous Machines

The rotor cooling poses a significant challenge for high-speed permanent magnet synchronous machines. This article presents a recirculating hollow-shaft oil cooling structure. Through the computational fluid dynamics (CFD) method, its convective heat transfer characteristics are studied in depth. Besides, the recirculating hollow-shaft cooling (RHSC) is compared with the direct-through hollow-shaft cooling (DHSC). Based on the CFD analysis, it is found that the convective heat transfer coefficient (CHTC) of the RHSC is higher than that of the DHSC, which can be as high as 58%. Furthermore, the advantage of the RHSC is most prominent at low rotational speed and small flow rate due to its relatively large oil friction loss at a high rotational speed. Moreover, the explanation for the fluctuation of the CHTC before the critical rotational speed, as well as the law of its variation with rotational speed and flow rate, are revealed in this study. The correctness of the simulation analysis is verified by experiments implemented on a rotor setup. In order to summarize the convective heat transfer law of the RHSC better, a dimensionless empirical equation is fitted finally.

Dissipation in spin chains using quantized nonequilibrium thermodynamics

We investigate the open dynamics of a chain of interacting spins using the quantized version of the general equation for the nonequilibrium reversible-irreversible coupling equation from classical out-of-equilibrium thermodynamics. We focus on both equilibrium and nonequilibrium scenarios for chains of different sizes. Whereas in the equilibrium case we demonstrate thermal equilibration to the correct many-body Gibbs density matrix, in the nonequilibrium dynamics we show a ballistic-to-diffusive transition in the steady-state energy current and a scaling that is consistent with Fourier's law of heat transfer.

Effect of windage heating on a micro high-speed rotor-stator cavity

The main objective of this work is to investigate the effect of windage heating on the micro high-speed rotor-stator cavity. The influences of centrifugal force and spacing on the windage heating are analyzed with and without the change of gap ratio respectively. The results demonstrate that there is no difference in the flow structure between micro and large-scale rotor-stator cavities at the same rotational Reynolds number and gap ratio. However, the windage heating induced by the larger centrifugal force and smaller spacing brings the different heat transfer laws for the micro rotor-stator cavity. The larger centrifugal force weakens the local heat transfer near the rotor periphery. Such influence can be strengthened at higher rotational Reynolds numbers and lower rotor excess temperatures. Besides, the smaller spacing further enhances the windage heating and reduces the average heat transfer especially under the condition of lower gap ratio. The findings of this work contribute to the design of rotor-stator cavity utilized in the micro rotating machinery.

An Indirect Method for Determining the Local Heat Transfer Coefficient of Gas Flows in Pipelines.

An indirect method and procedure for determining the local heat transfer coefficient in experimental studies on the intensity of heat transfer at a gas–surface interface is described. The article provides an overview of modern approaches and technical devices for determining the heat flux or friction stresses on surfaces in the study of thermophysical processes. The proposed method uses a constant-temperature hot-wire anemometer and a sensor with a thread sensitive element fixed on the surface of a fluoroplastic substrate. A substrate with the sensor’s sensitive element was mounted flush with the wall of the investigated pipeline. This method is based on the Kutateladze–Leontiev approach (the laws of friction and heat transfer) and the hydrodynamic analogy of heat transfer (the Reynolds analogy): this is an assumption about the unity of momentum and heat transfer in a turbulent flow, which establishes a quantitative relationship between friction stresses on the heat exchange surface and heat transfer through this surface. The article presents a method for determining the speed of the developed measuring system. An example of a successful application of the proposed method in relation to the study of thermomechanical processes in the gas exchange systems of reciprocating internal combustion engines is described.