One-dimensional Heat Transfer Research Articles

Development of a robust multi-phase heat transfer model and optimization of multi-layer core catcher for future Indian sodium cooled fast reactors

In the evolutionary design of Sodium Cooled Fast Reactors (SFR), core catcher has to handle debris generated from damage of whole core. This requirement combined with large core size demand that newer core catcher has to accommodate large volume of debris and consequently a thick debris bed having the risk of re-melting. To cater to this, a one-dimensional multi-phase heat transfer model for re-melting/re-solidification of core debris on a multi-layer core catcher is developed. Versatility of the model for various conditions is established. Then the model is applied to core catcher of future Indian SFR of 600 MWe capacity. Based on parametric studies, it is found that a 40 mm thick delay bed made of Thoria restricts the heat shield plate temperature within permissible limit. The corresponding minimum radius of debris spread is 3.25 m. This avoids core debris re-melting, provided melt-arrival time exceeds 1000 s.

Augmentation of gas turbine performance using integrated EAHE and Fogging Inlet Air Cooling System

In the present work, new hybrid cooling system is demonstrated and compared with other configurations of gas turbine inlet air-cooling systems. The cooling configurations include the earth-air heat exchanger, fogging and a new hybrid cooling system. Three models are developed, the first is for prediction of the cooling potential of the fogging system and the second is based on the transient one-dimensional heat transfer modeling which is used to describe the thermal behavior of the earth-air heat exchanger. The third model is a combination of earth-air heat exchanger and fogging cooling system as a new hybrid cooling system. New Damietta power plant located in the coastal region in Egypt (Latitude = 31.4 and Longitude = 31.7) is applied as a case study. A comparison between the effects of the three air cooling techniques on the gas turbine performance was performed. It is observed that the hybrid system is superior to the unitary systems as it is capable of boosting the average annual energy by 9.8% versus 8 and 6.6% for fogging and earth-air heat exchanger system; respectively. In addition, the hybrid system reduces the water consumption by 50% compared to the fogging system. Moreover, the hybrid cooling system is the most efficient method in the areas where the temperature is over 30°C and the relative humidity is less than 60%.

Direct methods for solving the Boltzmann equations: Comparisons with direct simulation Monte Carlo and possibilities

The possibilities of direct methods for solving the Boltzmann equation in comparison with direct simulation Monte Carlo are discussed. The general features of these different methods are considered, in particular, from the point of view of application of different variants of discretization in phase space. The advantages and disadvantages of both approaches are clarified. Comparative solutions of some simple problems are given. An important issue concerns anomalous heat transfer and validation of the effect by calculations based on these two methods. The solutions of the stationary one-dimensional heat transfer problem between two infinite plates with nonclassical nonequilibrium reflection from the surface are obtained; the anomalous heat transfer with a temperature gradient and a heat flux having the same sign is observed. One-dimensional and two-dimensional (in the square domain) problems with nonequilibrium “membranelike” boundary conditions are solved numerically; the anomalous heat transfer for all the considered cases is demonstrated.

Numerical studies of thermal comfort for semi-transparent building integrated photovoltaic (BIPV)-vacuum glazing system

Building integrated photovoltaic (BIPV)-vacuum system is promising for advanced window application due to its ability to reduce heat transfer, control over admitted solar heat and generates environmentally benign electricity. In this work, numerically thermal comfort for an unfurnished room comprising of BIPV-vacuum glazing was evaluated for the United Kingdom (UK) climate. Required parameters to determine thermal comfort, one-dimensional heat transfer model was developed and validated for BIPV-vacuum glazing and results were compared with BIPV-double-pane glazing system. PV cell temperature difference between these two different types of glazing was 24 °C. For the UK climate, BIPV-vacuum glazing offered 26% higher room temperature at clear sunny day compared to BIPV-double system. BIPV–vacuum glazing system provided soothing or comfortable thermal comfort during mid-day period for a clear sunny day at temperate climate. In a combined BIPV-vacuum glazing, it was also predicted that vacuum glass facing external ambient is suitable for the UK climate whilst vacuum glass facing internal room ambient is applicable for Indian climate.

Study on thermal parameters of asphalt concrete for countermeasures against high surface temperature of pavement in tunnel

It is reported that the surface temperature of asphalt pavement in a road tunnel in an urban area in summer days gets hot especially when the tunnel is long and the traffic volume is heavy. Since the asphalt pavement absorbs a large amount of heat generated by vehicles and keeps it for a long time, a high-temperature environment in the tunnel also continues for a long time. This phenomenon brings uncomfortableness for users, especially for motor-bikers and maintenance workers. On this background, this study aims to estimate the thermal parameters of the various types of asphalt concrete and investigate their effects on a high-temperature pavement surface. Six types of asphalt concrete specimens were tested in a wind-tunnel where a hot temperature air inside was generated by a forced circulation boiler system. Thermal parameters: specific heat capacity, heat conductivity, heat diffusivity, and heat transfer coefficients were analysed using a one-dimensional partial differential heat transfer equation and a finite difference approximation method. Additionally, the effects of different basement boundary conditions and water spray on the surface temperature were investigated to find effective countermeasures to decrease the surface temperature of asphalt concrete in the tunnel.

An experimental-numerical method for transient infrared measurement of film cooling effectiveness and heat transfer coefficient in a single test

ABSTRACTAn experimental technique for assessing film cooling performance is proposed which can determine both film effectiveness and heat transfer coefficient distributions from a single infrared experiment. First, the film effectiveness is determined in the experiment’s steady-state phase on a series of film-cooled nozzle guide vane leading edge geometries made of a low thermal conductivity foam. Then, the effectiveness is used to calculate the distribution of the transient phase driving gas temperatures, which is applied to a finite element conduction model. Heat transfer coefficients are guessed and iteratively refined until the surface temperature histories predicted by the finite element model match those which were experimentally observed. Unlike conventional methods based on one-dimensional analytical heat transfer solutions, this approach does not require assumptions about the material thickness underlying the test surface or the uniformity with depth of its initial temperature distribution. This relieves certain experimental constraints and reduces uncertainty in results.

Optimization analysis of high temperature workwear based on one-dimensional multilayer flat wall heat transfer process

In order to design costumes that can satisfy high temperature working environment, this paper constructed a one-dimensional heat conduction model through Fourier law and finite difference method. As the actual situation is one-dimensional unsteady heat conduction, numerical analysis method and MATLAB programming are required to solve the problem. The accuracy of the model is confirmed by error analysis. Finally, the sensitivity of the model is estimated roughly. Correlation analysis is made on the measurement of heat release and the convergence rate of temperature field in the working process of high temperature working clothes, and the prospect of high temperature resistant clothing is predicted.

Optimization of fire-related properties in layered structures

In present paper, fire-related properties of materials with multilayered structure are obtained through reverse heat transfer analysis. For this purpose, one-dimensional heat transfer equation including pyrolysis is analyzed to simulate the fire phenomenon of multi-layered solid materials. The fire-related properties can be obtained by optimizing the objective function expressing the difference between the measured values and the results (surface temperature and mass loss rate under constant incident heat flux) obtained by analyzing the considered heat transfer equations. Repulsive particle swarm optimization is used as the optimization technique. The optimized properties of single-, two- and three-layered materials obtained with the assumed properties were compared to the assumed for various incident heat fluxes. Using a cone calorimeter, the surface temperature and mass loss rate were measured over time with three constant heat fluxes applied to three layers of sandwich type material. The fire-related properties of each layer of the sandwich type material were calculated using the measured results. The technique considered in this study can be applied for determining the fire characteristics of multilayered materials is suitable for engineering the necessary properties to predict fire propagation in solid material.

Modelling and numerical simulation of hygrothermal transfer through a building wall for locations subjected to outdoor conditions in Sub-Saharan Africa

In the building sector, the improvement of the heat and mass insulation of the walls can reduce the values of the global energy demand and the CO2 emission. A coupled one-dimensional heat and mass transfer model through a building wall was proposed in this study. The governing equations integrate the influences of Dufour and Soret effects and are numerically resolved using FORTRAN 90 and finite difference method in Crank-Nicolson scheme. Gauss-Seidel relaxation iteration method is used in order to generate the numerical solutions. The accuracy of the model was evaluated with experimental data on wooden wall and concrete wall from literature. A very satisfactory agreement is noted between the numerical predictions, experimental observations and physical phenomenon obtained. The model was further used to simulate the hygrothermal transfer through five tropical woods used as building walls in sub-Saharan African region after integration of outdoor conditions. These five woods have densities ranging from 430 to 800 kg/m3 and the conditions of the interior air were fixed to maintain a comfortable state for the occupants. Twelve towns located within latitudes 4.33°S to 12.37°N in Sub – Saharan Africa were used to discuss the results given by the model. At the end, influences of anatomical direction, tropical wood types, wall thickness, latitudes of the locations and solar radiation on evolutions of temperature and moisture content in the wall are studied. Our results showed that these parameters have significant effects on temperature and moisture content propagation within the wall. Using a wooden wall of 5 cm thickness, it is possible to reduce significantly the effect of the exterior heat.

Stirling engine regenerators: How to attain over 95% regenerator effectiveness with sub-regenerators and thermal mass ratios

A combined theoretical and experimental approach is used to determine how to achieve a desired value for the Stirling engine regenerator effectiveness. A discrete one-dimensional heat transfer model is developed to determine which parameters influence the effectiveness of Stirling engine regenerators and quantify how they influence it. The regenerator thermal mass ratio and number of sub-regenerators were found to be the two parameters that influence the regenerator effectiveness, and the use of multiple sub-regenerators is shown to produce a linear temperature distribution within a regenerator, which enables the effectiveness to be increased above 50%. It is shown that increasing the regenerator thermal mass ratio and number of sub-regenerators results in an increase in regenerator effectiveness and a corresponding increase in the Stirling engine efficiency. A minimum of 19 sub-regenerators are required to attain a regenerator effectiveness of 95%. Experiments validated the heat transfer model, and demonstrated that stacking sub-regenerators, such as wire meshes, provides sufficient thermal resistance to generate a temperature distribution throughout the regenerator. This is the first study to determine how Stirling engine designers can attain a desired value for the regenerator effectiveness and/or a desired value for the Stirling engine efficiency by selecting appropriate values of regenerator thermal mass ratio and number of sub-regenerators.

Modeling of heat and mass transfer in the process of drying of colloid capillary - porous materials

The process of drying is an energy-consuming process, therefore, in order to optimize these energy costs during drying and to choose the rational structural and regime parameters of the equipment intended for this process, it is necessary to carry out a calculation analysis of heat and mass transfer on the basis of adequate mathematical models. The study of various mechanisms of diffusion in capillary - porous materials has become the basis for the creation of a mathematical model of heat - mass transfer and for the formulation of a corresponding system of nonlinear differential equations. Using mathematical model of heat-mass transfer A.V. Lykova constructed an appropriate numerical algorithm for modeling this process, numerical studies of the convection drying process of colloidal capillary - porous materials (KKPM) have been performed. The boundary conditions on the contact surface of the material in the drying chamber with the heat carrier flow are formulated. Based on the numerical solution of the system of one-dimensional heat and mass transfer equations in the material, depending on the time of its specific moisture content and temperature, as well as other characteristics of the convection drying process, the dependence was obtained. The estimated results are compared with the results of experimental studies. From the results of the comparison, it follows that the calculated model on the basis of the proposed system of equations satisfactorily describes the process of mass transfer in colloidal capillary - porous materials and can be used to approximate the characteristics of the drying process of colloidal capillary - porous materials, in particular the time required for drying the material. Numerical modeling of heat and mass transfer processes in colloid capillary and porous materials helps to solve an important scientific and technical problem, which is connected with the creation of software and hardware complexes, automated systems of scientific researches of energy-saving heat-technological processes of drying of materials with the provision of necessary quality indicators. Having analyzed the literature data concerning the existing developed mathematical modeling of colloidal capillary-porous materials, it has been established that this direction has a limited amount of information and therefore requires in-depth study and is an actual direction of research.

An energy efficient hydraulic system to cool manure and reduce ammonia emissions from livestock buildings

Abstract A sustainable hydraulic system is proposed to cool the slurry manure and mitigate the ammonia emissions of livestock buildings, a major source of environmental pollution. In this paper, analytical and numerical methods are used to evaluate the energy efficiency and the mitigation capability of the hydraulic cooling system. Results show that annual primary energy use of only 6.08 kWh per animal can reduce 5.87 kg of ammonia per animal per year. The system is most efficient for manure with less than 12% total solids content. Results also show that the liquid region above the cooling pipes features one-dimensional transient heat transfer formed by unique flow patterns. A simplified analytical model is derived to predict the surface temperature of liquid manure. The analytical solution shows that the manure surface temperature can be reduced by 7.4 and 12 °C after 2 and 5 h, respectively. The temperature reduction results in up to 37.3% decrease in ammonia emissions with only 0.8% of the total energy use in livestock buildings.

Computational fluid-dynamics-based simulation of heat transfer through vacuum glass

The heat transfer process of vacuum glass is very complicated. In particular, the heat transfer process of functional vacuum glass, which includes the coupling of heat conduction, convection, and radiation, does not have an exact mathematical solution. The most important parameter representing the thermal properties of vacuum glass, the heat transfer coefficient, is difficult to measure online because it increases over time, thereby decreasing the thermal-insulation performance. Thus, measuring it quickly and accurately for a vacuum glass in use is difficult. This study was conducted to develop an efficient method to simulate heat transfer through vacuum glass. To this end, based on advanced numerical-simulation technology, a computational fluid dynamics software was used to analyse the heat transfer process, and the simulation results applied to guide and analyse the non-steady-state test method. It was found that when a circular heating plate is used to heat the side of the vacuum glass, the ratio of the radius of the heating plate to the thickness of the vacuum glass should exceed three. This approach guarantees that the centre of the heating plate undergoes one-dimensional heat transfer, and the temperature measurement at the centre of the non-heated surface is of practical significance.

Simplified heat transfer model for parabolic trough solar collectors using supercritical CO2

The main Concentrated Solar Power (CSP) plants type installed worldwide corresponds to parabolic trough (PT) technology transforming solar energy into thermal energy on the receiver tubes. The use of alternative Heat Transfer Fluids (HTF) in order to increase the solar-to-electric efficiency by means of either higher HTF temperatures or the use of supercritical cycles have opened a new line of research. In this framework, super-critical carbon dioxide (sCO2) seems to be a good candidate to replace current HTFs in PTs. This work implements a one-dimensional heat transfer model for a PT solar collector considering different HTFs such as synthetic oil, sub-critical carbon dioxide, and sCO2. The numerical results of the outlet fluid temperature are compared to experimental data and numerical results published in the literature, obtaining maximum temperature deviations of 0.9%, 2.9% and 2.7% respectively. Finally, a sensitivity analysis was conducted to evaluate the influence of the solar irradiation, mass flow rate and HTF inlet temperature on the thermal performance of a PT working with sCO2 showing that the solar irradiation produces the greatest variations.

Development of pot-cover effect apparatus with freezing-thawing cycles

‘Pot-cover effect’ refers to the phenomenon of moisture accumulation beneath the pavement under condensation or desublimation because the vapor transfer in the soil is blocked by the pavement. To study this phenomenon in the laboratory, we have developed the pot-cover effect apparatus with freezing-thawing cycles (PEAFC), which consists of three parts, namely, the vapor transfer system, the temperature control system, and the temperature and water content monitoring system. The major functions of this apparatus include: simulation of both vapor transfer and freezing-thawing cycling in the soil, real-time monitoring of the temperature and the water content in soil samples, and one-dimensional heat and moisture transfer in the samples. The FDR (frequency domain reflectometry) sensors of the apparatus are calibrated and a calibration formula is proposed to eliminate the water content measurement errors induced by temperature changes. Constant temperature difference tests and a freezing-thawing cycling test are conducted with the apparatus. Results indicate that the apparatus can control the water replenishment in the soil samples, monitor the vapor transfer in the samples in real time, and simulate the vapor transfer process under the condition of the freezing-thawing cycling in the soil. These tests verify the effectiveness and reliability of the apparatus, which indicates that the development purpose is achieved.

On the basic concepts of the direct simulation Monte Carlo method

In this paper, the basic ideas underlying the Direct Simulation Monte Carlo (DSMC) method are examined and a novel nonhomogeneous N-particle kinetic equation describing the randomized mathematical model of DSMC is derived. It is shown that different collision-partner selection schemes, including No-Time-Counter (NTC) and Bernoulli-trials schemes, are approximations of the general transition operator of the randomized model. The popular collision-partner selection schemes, represented by the standard NTC and Bernoulli-trials approximations of the general transition operator, represented by Simplified Bernoulli-trials and Generalized Bernoulli-trials schemes, are tested on the one-dimensional rarefied gas heat transfer problem against conditions of two approximation limits: first, leading to the Boltzmann equation and, second, leading to the novel N-particle kinetic one.

A numerical solution for nonlinear heat transfer of fin problems using the Haar wavelet quasilinearization method

Abstract The aim of this paper is to study the new application of Haar wavelet quasilinearization method (HWQM) to solve one-dimensional nonlinear heat transfer of fin problems. Three different types of nonlinear problems are numerically treated and the HWQM solutions are compared with those of the other method. The effects of temperature distribution of a straight fin with temperature-dependent thermal conductivity in the presence of various parameters related to nonlinear boundary value problems are analyzed and discussed. Numerical results of HWQM gives excellent numerical results in terms of competitiveness and accuracy compared to other numerical methods. This method was proven to be stable, convergent and, easily coded.

Using transient temperature–depth profiles to assess vertical groundwater flow across semi-confining layers in the Chianan coastal plain aquifer systeme, southern Taiwan

The quantification of vertical groundwater fluxes across semi-confining layers is fundamental to evaluate groundwater recharge and discharge rates to and from aquifer systems. Methods to estimate vertical groundwater fluxes from temperature–depth profiles have been available since the 1960s. While some methodologies assume steady-state conditions, changes in land-surface temperatures as well as hydrogeological conditions can lead to transient heat flow conditions. Indeed, many studies have indicated that transient temperatures in deeper confined aquifers are widespread. A study is presented that uses transient-temperature–depth curves obtained from groundwater observation wells in the Chianan coastal plain in southern Taiwan. In this area, sedimentary aquifer systems consist of a stack of alternating sand and mud layers, over several hundred meters in thickness. Groundwater has been abstracted from these aquifers for decades, resulting in large hydraulic gradients between the shallow and deeper aquifers. Hence, vertical groundwater flow is likely enhanced across finer-grained, semi-confining units. A set of temperature–depth profiles is available from this area. Constrained by these profiles, numerical models of one-dimensional transient heat transfer were used to infer vertical fluxes of 3.3 × 10−8 to 3.9 × 10−8 m/s using thermal data from 2013 to 2016. An analytical solution was also employed that assumes steady-state conditions. Calculated fluxes using the latter approach were lower, at approximately 1.1 × 10−8 to 1.6 × 10−8 m/s. The study suggests that vertical fluxes derived from using Bredehoeft and Papadopulos’s analytical solutions result in underestimates of actual vertical seepage rates across aquitards.

A numerical methodology for comprehensive assessment of the dynamic thermal performance of horizontal ground heat exchangers

Heat transfer takes place simultaneously with moisture transfer in unsaturated soil and the transport processes interact with a ground heat exchanger (GHX) installed for a ground source heat pump. This paper presents a numerical methodology to produce spatiotemporally varying soil properties and assess their interactions with a horizontal GHX and the impacts on its dynamic performance. First, moisture and temperature profiles are generated from the numerical solution of coupled one-dimensional heat and moisture transfer equations and using soil properties that vary with time and depth. Next, governing equations for a three-dimensional mathematical model are solved numerically for a system of atmosphere, soil and horizontally coupled GHX. The model is then used to assess the thermal performance of the GHX under different atmospheric conditions at five installation depths in five soil types. Results demonstrate the importance of coupling moisture transfer with heat transfer in a mathematical model for dynamic thermal simulation of heat exchangers in shallow ground. The atmospheric conditions have been shown to have significant impacts on the dynamic performance which cannot be predicted using a model for heat transfer only. The heat transfer rate of a horizontal GHX varies with time and the depth of installation and the total amount of heat transfer for an operating season increases with installation depth. Heat transfer in moist sandy soil is found to be higher than that in loamy sand soil and much higher than that in loam, clay loam or clay soil.

Experimental and theoretical study of a water-vapor chamber thermal diode

Similar to an electrical diode, a thermal diode/switch is a device which allows heat to flow to a preferential direction. While a number of different types of thermal diodes/switches exist, a phase-change thermal diode/switch yields a greater diodicity performance compared to other types. However, most phase-change thermal diodes/switches have complex designs, complicated fabrication processes, and sophisticated working principles. Moreover, some materials used in thermal diodes/switches are rare, expensive and toxic. Thus, in this study, a simple water-vapor chamber thermal diode using latent heat of vaporization is designed, assembled and investigated, both experimentally and theoretically. The effects of the temperature difference between the hot side and the cold side and the water-air volume ratio on the effective thermal conductivity and diodicity of the water-vapor chamber thermal diode are also investigated. Mathematical models are also developed, not only for predicting one-dimensional phase change heat transfer performance in a rigid enclosure, but also for verifying the results from the experiment. This is the first study in which the water-vapor chamber thermal diode is studied both experimentally and theoretically. The experimental results show that an increase in temperature at the hot side of the thermal diode significantly enhances the performance of the thermal diode. The effective thermal conductivity at the hot side temperature of 70 °C shows a 50% improvement when compared with that at the hot side temperature of 40 °C in the forward direction. Additionally, with the water-air volume ratio of 0.5, the maximum diodicity of 1.43 is reported. Moreover, it is also found that the water-vapor volume ratio affects heat transfer performance and diodicity of the water-vapor chamber thermal diode. The results of these findings can further advance knowledge on phase-change heat transfer and can be applied to several applications, including heat transfer enhancement, waste heat power systems, thermal management and solar thermoelectric power generation.