Basic Heat Transfer Equations Research Articles

Investigation into the heat transfer models for the hot crude oil transportation in a long‐buried pipeline

AbstractBased on reasonable simplifications of a two‐dimensional (2D) energy equation, a basic heat transfer equation in 1D form is obtained for the hot crude oil transportation in a long‐buried pipeline. To enclose the heat transfer equation, the overall heat transfer coefficient and the numerical simulation of temperature fields of pipe wall and soil are introduced, and they together with the basic heat transfer equation constitute 1D and cross‐dimensional heat transfer models of crude oil transportation, respectively. Some numerical procedures, including grid generation, partial differential equation discretization, and algebraic equation solution, are combined to solve the two heat transfer models. Based on the designed cases with different pipeline parameters, the relative deviation between the numerical results from the two heat transfer models does not exceed 1%, and the two heat transfer models agree well. Furthermore, the nonuniform natural soil temperature field is designed, and its influence on the oil temperature and the deviation of the 1D heat transfer model is investigated. Under the condition of the nonuniform natural soil temperature field, the atmospheric temperature as the ambient temperature in the 1D heat transfer model causes an apparent deviation, whereas the soil temperature at the buried depth of the pipeline in the natural soil temperature field as the ambient temperature does not. This study can provide a reference for the reasonable selection and use of the heat transfer models of the buried hot oil pipeline.

Field measurements and parametric studies for the thermal environment of underground tunnel entrance in cold climate zones

In frozen regions, especially metro tunnel portal sections, which are vulnerable to an externally low-temperature atmosphere, would lead to frozen damage affecting traffic safety. To clarify how the air temperature field at tunnel portal sections varies with periodically changing atmospheric temperature, a site test was conducted on Metro Line 1 in Hohhot in the Inner Mongolia Autonomous Region, and the basic heat transfer equation and principle of energy conservation were introduced to establish a basic theoretical model, which was compared with the results from other regions. By comparison with testing results in other regions, the theoretical model was essentially consistent with the variation rules of the tested temperature. Therefore, the research could theoretically direct the heat preservation and freeze prevention of key facilities and equipment in metro tunnel portal sections in frozen regions.

Simulation of thermal processes in asynchronous traction electric motor of a locomotive

This article analyzes the problem of increasing the reliability of AC traction electric machines installed on traction rolling stock. In the course of the study, a finite element model of thermal processes was built, and the thermal state of an asynchronous traction motor (ATED) of a diesel locomotive was studied in the Solid Works program. The basic method for studying thermal processes in ATED was the finite element method (FEM), as well as the basic equations of heat transfer and the theory of heating a multicomponent solid. The constructed finite element model of the ATED rotor of a diesel locomotive makes it possible to determine the dependence of the temperature values of the rotor elements on the current flowing through them. The obtained values of the temperature distribution of the ATED squirrel-cage rotor are recommended to be taken into account in the design, manufacture and testing of AC electric machines of diesel locomotives.

Integrated thermal dissipation micro structures for CDFP optical module

400 Gbit/s optical module will soon be commercially deployed on a large scale due to the need for high capacity information transmission. It has much higher power density than that of 100 Gbit/s and 40 Gbit/s and therefore the thermal management still remains an obstacle. Microscale and nanoscale thermal management technology emerges and blooms. Concentrating on the thermal design of CDFP optical module, we propose two integrated thermal dissipation micro structures (ITDMS). The first is graphene thermal pad (GTP)-based one, the second is Ω-typed (OMEGA). Based on basic heat transfer equations and by SOLIDWORKS Flow Simulation software, the ITDMS are numerically validated for effective heat dissipation of CDFP optical modules and hence have great prospects for solving the heat dissipation problem of high-speed broadband optical modules due to the thermal integration solutions.

Ameliorating the Methodology to Chill Rocket Fuels for Launch Vehicle

AbstractCurrent Launch vehicles of ISRO uses Earth storable propellant such as UH25/MMH and N2O4/MON3 as fuel and oxidizer respectively for their liquid engines. Chilling of these rocket fuels is necessary before loading them in Launch Vehicles to meet the liquid engine requirements so as to meet the desired net positive suction head for the turbo pumps of rocket engines (like VIKAS engines). Pressure fed engine is cooled using regenerative cooling technique. To compensate for the pressure drops in the piping when fuel flows, the chilled propellant makes it heavy in density and helps to maintain greater injection pressure. In ISRO spiral plate heat exchanger is used or chilling the propellants. The chilling activity requires around 10 to 12 hours to chill propellants from ambient to 10° C for given flow rate and effective reynolds number. Reducing this time will be very helpful in reducing the time required for overall system readiness for launch activities. Existing chilling process involves circulating propellant through one heat exchanger using a pump. The storage facility has two heat exchangers and two pumps and out of which only one heat exchanger and one pump is being used and the other act as standby. The paper aims to find possible alternate configurations using the idle heat exchanger and pump and also to study the effect of mass flow rate of propellant on chilling time. Study in this paper is done considering N2O4 propellant. A theoretical model is developed using basic heat transfer equations in MATLAB, it is evaluated by comparing the results with previous mission data. This is later applied on different configurations possible and chilling time for each configuration is calculated. The results obtained suggested that by operating two heat exchanger in parallel and one pump, time required for chilling of propellants can be reduced significantly.

Modelling of heat transfer for progressive freeze concentration process by spiral finned crystallizer

Abstract This study presents a novel design for a spiral finned crystallizer which is the primary element of progressive freeze concentration (PFC) system, which simplifies the setup of the conventional system. After the crystallizer has been designed, the research experiments have been conducted and evaluated through a thorough analysis of its performance by developing a mathematical model that can be used to predict the productivity of ice crystal at a range of coolant temperature. The model is developed based on the basic heat transfer equation, and by considering the solution's and the coolant's convective heat transfer coefficient (h) under the forced flow condition. The model's accuracy is verified by making comparison between the ice crystal mass' experimental value and the values predicted by the model. Consequently, the study found that the model helps in enhancing the PFC system.

Heat transfer regimes for a flow of water at supercritcal conditions in vertical channels

Heat transfer regimes observed in experiments with water at supercritical conditions flowing in vertical channels of various cross-sections (such as round pipes, annulus, or rod bundles) are analyzed. In accordance with the established practice, the normal and the deteriorated heat transfer regimes were singled out as the basic regimes specific for heat carriers with highly variable properties. At the same time, it has been established that most published experimental data on supercritical pressure water heat transfer along the length of test sections demonstrate combined (or transient) heat transfer regimes. The features can be presented as a superposition of characteristics of the above-mentioned basic regimes. The combined regimes are not stable in certain ranges of water flow conditions in which sudden transitions between the basic regimes can occur. A system of similarity criteria governing heat transfer rate in the vicinity of the critical point is examined. As applicable to cores of water-cooled reactors, due to a small hydraulic diameter of cooling channels, buoyancy forces acting in these channels are negligible as compared with the inertia effects caused by thermal acceleration of the flow and viscous force. This concept yields two integrated criteria whose use in the correction factors for the basic heat transfer equation, which we proposed previously for the normal regimes, adequately (with an error of 20–25%) describes the specific of the heat transfer coefficient in the normal, deteriorated, and combined regimes. A system of equations is proposed for design calculation of heat transfer in channels of nuclear reactors cooled with supercritical pressure water.

Numerical Modeling of Urban Air Temperature

This paper is devoted to provide an understanding of the urban warming phenomenon by analyzing the urban surface and air temperature variation profiles. The aim is to investigate the temporal variation of air temperature of different urban locations in Trivandrum city. Various methods adopted in the present study include theoretical analysis, field measurements and numerical simulation. Using the basic heat transfer equation, temporal variation of temperature was evaluated at each nodal point after discretizing the domain. Finite difference scheme was employed for the calculations and a numerical code was developed in Mat-lab for the evaluation of temperature.

Comparison of two numerical approaches to the domestic hot water circuit in a combi boiler appliance

This study mainly touches on natural gas fueled combi boiler appliances having space and water heating functions. The hot water demanded in any type of building for daily activities such as personal hygiene, cleaning, and bathing is referred to as domestic hot water (DHW). Since high efficiency targets have been already reached with respect to the space heating, most of the research and development activities are now focusing on the DHW heating function. Therefore, the subject of this study is concerned with only DHW heating function and the basic objective is making a comprehensive comparison between two mathematical models via different approaches for the same DHW circuit. In the first approach, basic heat transfer equations for DHW heating function are established by means of one-dimensional and time dependent differential equations. Later on, those transient energy equations were discretized by finite-difference method implicitly and solved simultaneously in Matlab®. The second model has been constructed with the help of commercial software, Flowmaster® which is one-dimensional thermo-fluid simulation tool. Then, the numerical results have been compared with the experimental data and the validity of the models has been discussed separately on the basis of the agreement between them. The advantages of both models have been evaluated as the distinctive contributions to the literature from DHW circuit modeling viewpoint. Among the intensive research and development activities of the combi boiler manufacturers to achieve high DHW comfort scores for high selling rates in the market, decreasing the time and money spent on the laboratory tests of the appliances is a challenging issue. Number of the laboratory tests is proposed to be decreased due to the preliminary results obtained from properly working numerical models for the performance analyses of completely new appliance concepts or design modifications on the regular appliances.

A NUMERICAL APPROACH FOR MODELLING THERMAL PROFILES AND EFFECTS OF PROCESS PARAMETERS ON IT IN SUBMERGED ARC WELDING OF AISI 1518 GRADE STEEL

A comprehensive methodology for the analysis of thermal analysis due to welding has been studied in this present investigation. A finite volume methodology (FVM) among term of the basic heat transfer equation was enforced to simulate the temperature profiles in submerged arc welding (SAW) of AISI 1518 grade steel. The supply of the arc is assumed to be a moving conicoidal heat supply with a Gaussian distribution. The obtained results from the simulation methodology are compared with experimental results and determined a good agreement with experimental results, with associate degree overall proportion of error calculable to be between 5.23%. The influence of welding current and speed of temperature analysis has been evaluated and located that each one those parameters are playing a necessary role in moving the temperature distribution of the assembly, i.e.when current inflated, the temperature conjointly inflated with constant speed yet like higher speed temperature is decreased for constant current . Finally, the influence of heat input on peak temperature variations in various welding parameters has been evaluated and shown that the higher heat input in higher temperature is obtained.

Electrical-Thermal-Structural Coupled Finite Element Model of High Temperature Superconductor for Resistive Type Fault Current Limiters

A multi-physics finite element model of high-temperature superconductors (HTS) will be presented in this article. The electrical-thermal model is mainly based on Maxwell’s equation and basic heat transfer equation to calculate the temperature propagation along the length of the superconducting tapes. According to the calculated temperature profile during quench, the surface thermal stress of the tape is obtained by a structural model. This model can be used to evaluate the degradation of tape performance due to the surface thermal stress, and the results can be used to minimize these effects in the SFCL system. The proposed model is used to investigate the uneven tape, the thickness of the copper layer and YBCO layer which is non-uniform. Methods of smoothing the degradation effect by adding auxiliary fixed points to the tape and changing the basic thickness of copper layer are discussed.

Light-induced instability generated by photo-thermal effect in switchable molecular crystals

The photo-thermal effect of thermo-chromic crystals generates a novel kind of light-induced instability. We investigate here a mean-field (zero-dimensional) approach of the problem using basic equations of heat transfer and spin-crossover phenomena. This mean-field approach compares to the well-known Stoner-Wolfarth mechanism for the magnetization reversal of nano-particles, it should be suited to switchable micro-crystals and leads to auto-catalytic oscillations which remain to be observed. The stabilization of the high-spin–low-spin interface by photo-thermal effect is noticed.

Overall thermal energy and exergy analysis of hybrid photovoltaic thermal array

In this paper, overall thermal energy and exergy analysis has been carried out for different configurations of hybrid photovoltaic thermal (PVT) array. The hybrid PVT array (10.08m×2.16m) is a series and parallel combinations of 36 numbers of PV modules. A one-dimensional transient model for hybrid PVT array has been developed using basic heat transfer equations. On the basis of this transient model, an attempt has been made to select an appropriate hybrid PVT array for different climatic conditions (Bangalore, Jodhpur, New Delhi, and Srinagar) of India. On the basis of high grade energy (i.e. overall exergy gain), case-III has been selected as the most appropriate configuration because overall exergy for case-III is 12.9% higher than case-II. The overall thermal energy and exergy gain for Bangalore is 4.54×104kWh and 2.07×104kWh respectively which is highest in comparison to the other cities.

Optimizing the energy and exergy of building integrated photovoltaic thermal (BIPVT) systems under cold climatic conditions

Building integrated photovoltaic thermal (BIPVT) system has the potential to become a major source of renewable energy in the urban environment. In this paper, the system has been used as the roof top of a building to generate higher electrical energy per unit area and to produce necessary thermal energy required for space heating. One-dimensional transient model has been developed using basic heat transfer equations. On the basis of this model, an analysis has been carried in order to select an appropriate BIPVT system suitable for the cold climatic conditions of India. The PV performances, net energy gain and exergy of the building are determined. The results show that for a constant mass flow rate of air the system connected in series gives a better performance whereas for a constant velocity of air flow the system connected in parallel gives a better performance. The BIPVT system, fitted on the rooftop in an effective area of 65 m 2, is capable of annually producing the net electrical and thermal exergies of 16,209 kW h and 1531 kW h, respectively, at an overall thermal efficiency of 53.7%.

Optimum Arrangement of Tube Coil in Radiation Type of Tubular Furnace

Tube coil arrangement dominantly influences the thermal-hydraulics characteristics of furnace and its economy. The presented method is based on standard long-used design methods (Lobo-Evans method, Belokon method). It is shown how these standard global design methods can be (for common-operating conditions) suitably generalized and simplified. It allows (for the purpose of optimum design of coil arrangement) to arrange the basic heat transfer equation for radiant chamber. In connection with investment cost relations for individual furnace subsystems (tube coil, burners, lining, etc.) and operating cost relations (fuel consumption, fluid pumping cost), the final objective function of total cost can be obtained. This objective function then allows finding the optimum coil arrangement from minimum total cost point of view. Moreover, the obtained results allow one to formulate some general recommendations suitable for furnace designers. The developed method can be used for the individual solution of a radiation-type of tubular furnaces and also for the first (preliminary) design stage usually connected with a proposal for the customer when only basic process and furnace design data are known. The developed method can be also used for the effective solution of the integration of radiation furnaces into processes. The application of the developed method is demonstrated through a case study—the optimum arrangement of coil in a gas plant regeneration furnace.

The Conceptual Design of a Radiant Chamber and Preliminary Optimization of a Process Tubular Furnace

The design procedure of a process tubular furnace (or fired heater) can generally be divided into three design stages: the preliminary design of furnace, a detailed thermal and hydraulic simulation of the furnace, and final design solution, and the mechanical solution of the furnace (stress analysis, drawings preparation, etc.). The first design stage (the preliminary design of the furnace and cost prediction) is usually connected with a proposal for the customer when only the basic process and furnace design data are usually known. In this design stage, it is appropriate for the furnace designer to not have much detail for a reliable design method. The procedure for the preliminary design of a radiant chamber is usually a main part of such a design method because the radiant chamber represents a basic and dominant part of the modern process tubular furnace. The conceptual (or preliminary) design of the radiant chamber makes up the main part of this process. The presented method is based on standard, time-tested design methods (e.g., the Lobo-Evans method and Belokon's method). It is shown how these standard global design methods can be (for common operating conditions) suitable, generalized, and simplified. It allows for the purpose of the conceptual radiant chamber design the arrangement of the basic heat transfer equation for the radiant chamber. The derived form of the heat transfer equation then allows one to obtain basic process and geometrical radiant chamber characteristics of the given furnace type (cylindrical, box, etc.) iteratively. A developed radiant chamber calculation connected with standard procedures for the design of the furnace convection parts and stack (together with cost predictions) is used, and the method for a quick preliminary evaluation of the influence of the main design and process furnace parameters (dimensions of radiant chamber and convection parts, average heat flux to radiant tubes, absorbed heat in radiant chamber and convection part of furnace, stack size, and fuel consumption) for the total costs was developed. It allows the optimization of the furnace from an investment, operating, or total cost point-of-view in the preliminary design stage of the furnace. The developed method can also be used for the effective solution of the furnace integration into the process. The application of the developed method is demonstrated through a case study—the optimum design of a furnace for a crude atmospheric distillation unit.

Cold but comfortable? Application of comfort criteria to cold environments.

Fanger defined two physiological criteria that are basic requirements for people's perception of thermal neutrality and, eventually, thermal comfort. Mean skin temperature and evaporative heat loss are defined as functions of metabolic rate. The equations are derived from experiments in light clothing at or close to normal indoor climate. Relations between skin temperature and sweating on the one hand and thermal sensation and comfort on the other are well recognized; the precise description of the relationships vary and may differ from normal indoor environments to more extreme thermal stress. In moderately cold environments (around +10 degrees C) ISO/DIS 7730 and ISO/DIS 11079 prescribe significantly different responses. Evaluation of the rationale behind the comfort criteria and the basic heat transfer equations in the two models reveals some clear differences. By modification of the sweating criteria and some of the heat transfer equations, predictions become much more similar. It is concluded that the basic comfort criteria may apply also to moderately cold and cold environments, but must consider the complex heat transfer through multilayer clothing in a more adequate way. The suggested, modified comfort criteria incorporated either in the PMV-index or in the IREQ-index, provide more realistic and reliable prediction of heat balance and conditions for comfort in cool and cold environments.

Combustion and heat transfer characteristics in boilers with asymmetrical reversed flow flame tube

An experimental study of the combustion characteristics in an industrial three-pass asymmetrical reversed flow flame tube boiler is presented, based on measurements of mean gas temperature, gas velocity, species concentration (CO, CO 2, O 2, SO 2 and NO x ) and soot fraction. The experiments, which were carried out at different firing rates and furnace lengths, included analysis of the influence of simultaneous use of three stabilization techniques on the combustion process inside the furnace. The three stabilization techniques used, are namely asymmetrical jet stabilization, vane type swirler stabilization and reversed flow stabilization by using reversed flow combustion chamber. Also experimental and predictive studies of heat transfer characteristics in the three-pass asymmetrical reversed flow flame tube boiler have been carried out. The experimental investigation is achieved by measuring the boiler heat transfer and its portion in the third pass pipes. The optimal furnace length and pitch of swirl generator, used in the third pass pipes, have been determined. The prediction study presents models to estimate the first–second and third pass heat transfer rates depending on the basic heat transfer equations and some of the experimental results. The predictions were compared with experimental data and found to be in a good agreement. Analysis of the results is aimed at improving the understanding of combustion and heat transfer processes in this type of flame tube boilers.

Blood flow cooling and ultrasonic lesion formation.

This article examines lesion formation using focused ultrasound and demonstrates how blood flow may affect lesion dimensions using a theoretical model. The effects of blood flow on temperature distributions during ultrasonic lesioning are examined for both regional cooling by the microvasculature and localized cooling due to thermally significant vessels. Regional cooling was critically assessed using two models: the Pennes bioheat transfer equation and the scalar effective thermal conductivity equation. Localized cooling was modeled by adding an advective term in the heat diffusion equation in regions enclosed by thermally significant vessels. A finite difference approach was used to solve the basic equations of heat transfer in perfused tissues in cylindrical coordinates. The extent of the lesioned tissue was determined by the accumulated thermal dose at each location. The size of the lesion was then calculated from the boundaries of the thermal isodose curves generated by the simulations. The results were compared to published in vivo lesion data in rat liver. It was shown that even for short ultrasound exposure times (approximately 8 s), blood flow may play an important role in the thermal dose distribution.

Large blood vessel cooling in heated tissues: a numerical study

Large blood vessels can produce steep temperature gradients in heated tissues leading to inadequate tissue temperatures during hyperthermia. This paper utilizes a finite difference scheme to solve the basic equations of heat transfer and fluid flow to model blood vessel cooling. Unlike previous formulations, heat transfer coefficients were not used to calculate heat transfer to large blood vessels. Instead, the conservation form of the finite difference equations implicitly modelled this process. Temperature profiles of heated tissues near thermally significant vessels were calculated. Microvascular heat transfer was modelled either as an effective conductivity or a heat sink. An increase in perfusion in both microvascular models results in a reduction of the cooling effects of large vessels. For equivalent perfusion values, the effective conductivity model predicted more effective heating of the blood and adjacent tissue. Furthermore, it was found that optimal vessel heating strategies depend on the microvascular heat transfer model adopted; localized deposition of heat near vessels could produce higher temperature profiles when microvascular heat transfer was modelled according to the bioheat transfer equation (BHTE) but not the effective thermal conductivity equation (ETCE). Reduction of the blood flow through thermally significant vessels was found to be the most effective way of reducing localized cooling.