Numerical heat transfer analysis of encapsulated ice thermal energy storage system with variable heat transfer coefficient in downstream

During charging and discharging processes, the heat transfer behavior of the encapsulated ice thermal energy storage (TES) system changes during downstream case and this should be taken into account since the temperature of heat transfer fluid (HTF) and especially the heat transfer coefficient varies considerably around each capsule. This requires a careful study of the problem with variable heat transfer coefficient to contribute to the state-of-the-art. This has been the primary motivation behind the present study. Here, we first develop a new heat transfer coefficient correlation by simulating a series of 120 numerical experiments for different capsule diameters, mass flow rates and temperatures of HTF and second undertake a comprehensive numerical analysis using the temperature based fixed grid solution with control volume approach for studying the heat transfer behavior of an encapsulated ice TES system. Thirdly, we validate the present numerical model and the new correlation with some experimental data obtained from the literature, and hence a good agreement is obtained between the model results and experimental data. The results indicate that the heat transfer coefficient varies greatly during downstream and highly affects the heat transfer taking place during the process. So, the solutions with constant heat transfer coefficient appear to be unreliable for analysis and system optimization. The results also show that the solidification process is chiefly governed by the magnitude of Stefan number, capsule diameter and capsule row number.     

Numerical study of transient heat transfer in semitransparent porous medium

Transient solutions were obtained for heat transfer through a semitransparent porous medium placed in a flow passage and submitted to incident radiation. The one-dimensional physical model takes into account, conduction, convection and radiation simultaneously. The porous medium is assumed to be homogenous continuum, which absorbs, emits and scatters thermal radiation. A fully implicit time-marching algorithm was used to solve the nonlinear coupled energy equations for gas and porous medium numerically. The present study utilizes the differential–discrete–ordinate (DDO) method to account for the radiation contribution. The effects of the Reynolds number, optical depth, anisotropic scattering, conduction–radiation parameter and scattering albedo on temperatures and fluxes profiles are investigated.     

Numerical investigation on porous media heat transfer in a solar tower receiver

In order to investigate the steady heat transfer characteristics of a porous media solar tower receiver developed in China, this paper applies the steady heat and mass transfer models of the porous media to solar receivers, chooses the preferable volume convection heat transfer coefficient model, solves these equations by using the numerical method, and analyzes the typical influences of the porosity, average particle diameter, air inlet velocity, and thickness on the temperature distribution. The following conclusions have been drawn: in the same position or relative position along the downstream, the bigger the average particle diameter is, the higher the solid matrix dimensionless temperature is, the higher the air dimensionless temperature is. The bigger the porosity is, the lower the solid matrix dimensionless temperature is, the bigger the porosity is, the higher the air dimensionless temperature is. The bigger the thickness is, the lower the solid matrix dimensionless temperature is, the higher the air dimensionless temperature is. In a certain depth, the bigger the air inlet velocity is, the higher the solid matrix dimensionless temperature is. After a certain depth, the bigger the air inlet velocity is, the lower the solid matrix dimensionless temperature is, and the bigger the air inlet velocity is, the higher the air dimensionless temperature is. The paper can provide a reference for this type of receiver design and reconstruction.     

Numerical investigation of heat transfer coefficient in a low speed 1.5-stage turbine

The paper numerically investigated the heat transfer coefficients over the rotating blades in a 1.5-stage turbine. The hexahedral structured grids and k-ε turbulence model were applied in the simulation. A film hole with diameter of 0.004 m, angled 36°and 28° tangentially to the suction side and pressure side in streamwise respectively, was set in the middle span of the rotor blade. Simulations are done at three different rotating numbers of 0.0239, 0.0265 and 0.0280 with the blowing ratio varying from 0.5 to 2.0. The effects of mainstream Reynolds number and density ratio are also compared. Results show that increasing blowing ratio can increase the heat transfer coefficient ratio on the pressure side, but the rule is parabola on the suction side. Besides, increasing rotating number and Reynolds number is positive while increasing density ratio is negative to the heat transfer on both the pressure side and the suction side.     

Numerical analysis of natural convection heat transfer in a horizontal annulus partially filled with a fluid-saturated porous substrate

The current study centers around a numerical investigation of natural convection heat transfer within a two-dimensional, horizontal annulus that is partially filled with a fluid-saturated porous medium. In addition, the porous sleeve is considered to be press fitted to the inner surface of the outer cylinder. Both cylinders are maintained at constant and uniform temperatures with the inner cylinder being subjected to a relatively higher temperature than the outer one. Moreover, the Forchheimer and Brinkman effects are taken into consideration when simulating the fluid motion inside the porous sleeve. Furthermore, the local thermal equilibrium condition is assumed to be applicable for the current investigation. The working fluid is air while copper is used to represent the solid phase. The porosity is considered to be uniform and constant with ε = 0.9. The main objective of this study is to examine the effect of the porous sleeve on the buoyancy induced flow motion under steady-state condition. Such an effect is studied using the following dimensionless parameters: Pr = 0.05–50, Ra = 10²–10⁶ and Da = 10^?4–10^?6. Also, the study highlights the effect of the dimensionless porous sleeve thickness (b) and thermal conductivity ratio (k_s/k_f) in the range between 1.1–1.9 and 1–150, respectively.     

Numerical analysis of heat flow in contact heat transfer

A finite difference analysis of heat conduction problem in a cylinder terminating in a frustum of a cone is presented. The constriction can be either in vacuum or in a gaseous environment. A fine mesh of 2500 × 800 was used for the construction of the grid such that very small constrictions could be analysed sufficiently accurately. Small constrictions i.e., small contact areas separated by large voids filled with a gas are typical of most practical applications involving contact heat transfer. The result of the finite difference analysis shows that gap conductance is predominant for all the gases considered. Gap-to-solid conductance ratio increases as the cone angle decreases due to the decrease of gap thickness. It also indicates that increase of conductance ratio is less significant at higher constriction angles. Finally, predicted conductance parameters are compared with the experimental results for different interfacial gases and a very good agreement is obtained.     

Experimental analysis of flow and heat transfer in a miniature porous heat sink for high heat flux application

A novel miniature porous heat sink system was presented for dissipating high heat fluxes of electronic device, and its operational principle and characteristics were analyzed. The flow and heat transfer of miniature porous heat sink was experimentally investigated at high heat fluxes. It was observed that the heat load of up to 280 W (heat flux of 140 W/cm²) was removed by the heat sink with the coolant pressure drop of about 34 kPa across the heat sink system and the heater junction temperature of 62.9 °C at the coolant flow rate of 6.2 cm³/s. Nu number of heat sink increased with the increase of Re number, and maximum value of 323 for Nu was achieved at highest Re of 518. The overall heat transfer coefficient of heat sink increased with the increase of coolant flow rate and heat load, and the maximal heat transfer coefficient was 36.8 kW(m² °C)^?1 in the experiment. The minimum value of 0.16 °C/W for the whole thermal resistance of heat sink was achieved at flow rate of 6.2 cm³/s, and increasing coolant flow rate and heat fluxes could lead to the decrease in thermal resistance. The micro heat sink has good performance for electronics cooling at high heat fluxes, and it can improve the reliability and lifetime of electronic device.     

Numerical analysis of thermal response tests with a groundwater flow and heat transfer model

The Kelvin line-source equation, used to analyze thermal response tests, describes conductive heat transfer in a homogeneous medium with a constant temperature at infinite boundaries. The equation is based on assumptions that are valid for most ground-coupled heat pump environments with the exception of geological settings where there is significant groundwater flow, heterogeneous distribution of subsurface properties, a high geothermal gradient or significant atmospheric temperature variations. To address these specific cases, an alternative method to analyze thermal response tests was developed. The method consists in estimating parameters by reproducing the output temperature signal recorded during a test with a numerical groundwater flow and heat transfer model. The input temperature signal is specified at the entrance of the ground heat exchanger, where flow and heat transfer are computed in 2D planes representing piping and whose contributions are added to the 3D porous medium. Results obtained with this method are compared to those of the line-source model for a test performed under standard conditions. A second test conducted in waste rock at the South Dump of the Doyon Mine, where conditions deviate from the line-source assumptions, is analyzed with the numerical model. The numerical model improves the representation of the physical processes involved during a thermal response test compared to the line-source equation, without a significant increase in computational time.     

Laminar heat transfer in a porous channel simulated with a two-energy equation model

Laminar heat transfer in a porous channel is numerically simulated with a two-energy equation model for conduction and convection. Macroscopic equations for continuity, momentum and energy transport for the fluid and solid phases are presented. The numerical methodology employed is based on the control volume approach with a boundary-fitted non-orthogonal coordinate system. Fully developed forced convection in a porous channel bounded by parallel plates is considered. Solutions for Nusselt numbers along the channel are presented for laminar flows. Results simulate the effects Reynolds number Re, porosity, particle size and solid-to-fluid thermal conductivity ratio on Nusselt sumber, Nu, which is defined for both the solid and fluid phases. High Re, low porosities, low particle diameters and low thermal conductivity ratios promote thermal equilibrium between phases leading to higher values of Nu.     

Numerical heat transfer analysis of the packed bed latent heat storage system based on an effective packed bed model

Due to the complexity of the fluid flow and heat transfer in packed bed latent thermal energy storage (LTES) systems, many hypotheses were introduced into the previous packed bed models, which consequently influenced the accuracy and authenticity of the numerical calculation. An effective packed bed model was therefore developed, which could investigate the flow field as the fluid flows through the voids of the phase change material (PCM), and at the same time could account for the thermal gradients inside the PCM spheres. The proposed packed bed model was validated experimentally and found to accurately describe the thermo-fluidic phenomena during heat storage and retrieval. The proposed model was then used to do a parametric study on the influence of the arrangement of the PCM spheres and encapsulation of PCM on the heat transfer performance of LTES bed, which was difficult to perform with the previous packed bed models. The results indicated that random packing is more favorable for heat storage and retrieval as compared to special packing; both the material and the thickness of the encapsulation have the apparent effects on the heat transfer performance of the LTES bed.     

换热器结垢工况下换热系数变化的分析研究

介绍了换热器污垢热阻的数学模型,包括污垢沉积模型和剥蚀模型。分析了换热器结垢工况下的换热系数的变化,重点研究了时间、流体雷诺数Re和流体—污垢界面温度Ts对换熟系数K的影响,以及在结垢诱导期内换热系数K的变化。得到了冷却水流速与污垢热阻之间的关系式,界面温度Ts与污垢热阻和换热系数之间关系的示意图,并得出了诱导期内的换热系数K大于结垢过程的其他四个阶段的结论。最后,阐述了分析结果对工程的实际指导意义。     

Numerical investigation of heat transfer enhancement on a porous vortex-generator applied to a block-heated channel

The numerical simulation is used to obtain the unsteady laminar flow and convective heat transfer in the block-heated channel with the porous vortex-generator. The general Darcy–Brinkman–Forchheimer model is adopted for the porous vortex-generator. The parameters studies including porosity, Darcy number, width-to-height ratio of porous vortex-generator and Reynolds number have been explored on heat transfer enhancement and vortex-induced vibration in detail. The results indicate that heat transfer enhancement and vortex-induced vibration increase with increasing Reynolds number and width-to-height ratio. However, the porosity has slight influence on heat transfer enhancement and vortex-induced vibration. When Darcy number is 10^?3 or 10^?4, installing a porous vortex-generator with B/h = 1.0 improves overall heat transfer the best along heated blocks, and has a strong reduction of vortex-induced vibration.     

Experimental study and analysis on heat transfer coefficient of radial heat pipe

The experimental study was performed on five eccentric radial heat pipes with two outer-tube diameters.The test range can be given as follows,working fluid filling ratio Ω=44%～83%,heat flux q=10000W/m2～32000W/m2,and working temperature tv=50 ℃～120 ℃.The correlations between radial heat pipe heat transfer performance and filling ratio,heat flux,working temperature were studied in the experiment.Based on linear regression of experimental data,the relationship between heat pipe equivalent heat resistance R and working temperature tv,heat flux q and filling ratio Ω was obtained.     

Numerical technique for modeling conjugate heat transfer in an electronic device heat sink

A fast running computational algorithm based on the volume averaging technique (VAT) is developed to simulate conjugate heat transfer process in an electronic device heat sink. The goal is to improve computational capability in the area of heat exchangers and to help eliminate some of empiricism that leads to overly constrained designs with resulting economic penalties.VAT is tested and applied to the transport equations of airflow through an aluminum (Al) chip heat sink. The equations are discretized using the finite volume method (FVM). Such computational algorithm is fast running, but still able to present a detailed picture of temperature fields in the airflow as well as in the solid structure of the heat sink. The calculated whole-section drag coefficient, Nusselt number and thermal effectiveness are compared with experimental data to verify the computational model and validate numerical code. The comparison also shows a good agreement between FVM results and experimental data.The constructed computational algorithm enables prediction of cooling capabilities for the selected geometry. It also offers possibilities for geometry improvements and optimization, to achieve higher thermal effectiveness.     

Numerical study of local heat transfer coefficient and fin efficiency of wavy fin-and-tube heat exchangers

Three-dimensional numerical simulations were performed for laminar flow of wavy fin-and-tube heat exchangers by using body-fitted coordinates (BFC) method with fin efficiency effect accounted. The prediction results of average Nusselt number, friction factor and fin efficiency were compared with the related experimental correlations [R.C. Xin, H.Z. Li, H.J. Kang, W. Li, W.Q. Tao, An experimental investigation on heat transfer and pressure drop characteristics of triangular wavy fin-and-tube heat exchanger surfaces, J. Xi'an Jiaotong Univ. 28 (2) (1994) 77–83] and Schmidt approximation [T.E. Schmidt, Heat transfer calculations for extended surfaces, Refrigerating Engineering (April 1949) 351–357]. For Reynolds numbers based on the tube outside diameter ranging from 500 to 4000, the mean deviation is 3.3% for Nusselt number, 1.9% for friction factor and 3.6% for fin efficiency. The distributions of local Nusselt number and fin efficiency on fin surface were studied at wavy angle equal to 0° (plain plate fin), 10° and 20° respectively. The local Nusselt number decreases along the air flow direction, but fin efficiency increases in general. The wavy angle can greatly affect the distributions of local Nusselt number and fin efficiency, and make the distributions present fluctuation along the flow direction. The result also shows that the fin efficiency at the inlet region of wavy fin is larger than that of plain plate fin at the same region. With the increase of Reynolds number, the effects of wavy angle on the distributions of local Nusselt number and fin efficiency are more and more significant.     

Analytical model of heat transfer in porous insulation around cold pipes

A thermal insulation system is analysed that consists of a cold tube insulated with a porous material faced with a vapour retarding foil.Water vapour will diffuse through the vapour retarding foil and condense on the cold tube. To avoid build-up of water in the insulation a hydrophilic wicking cloth is wrapped around the cold tube and extended through a slit in the tubular insulation and a slot in the facing to the ambient so that condensed water can evaporate into the air. Some of the moisture in that part of the wicking cloth situated in the slit in the tubular insulation will diffuse backwards to the cold pipe and contribute to the heat uptake of the cold tube. This part is calculated for the stationary case and compared with the sensible heat transfer through the tubular shaped insulation material, using measured dry λ values and measured fictitious moist λ values.     

Numerical development of a heat transfer and pressure drop porosity model for a heat exchanger for aero engine applications

Heat exchangers are used in various applications. In a typical CFD approach, where it is necessary to model the flow in a device with a heat exchanger, a first step can be the construction of a very detailed mesh modeling each flow passage inside the device. However, this approach can lead to very fine grids with high demands of CPU power and memory requirements. In order to overcome this problem, the presence of the heat exchanger can be modeled as a porous medium having the same thermal and flow behaviour as the original device. In this work, a generalized porous medium model was developed for a heat exchanger designed to be used as a heat recuperator for an aero engine. For the porosity model a modified anisotropic formulation of the Darcy–Forchheimer pressure drop law was introduced together with a heat transfer model in the form of a Nusselt–Reynolds–Prandtl numbers correlation. For the derivation of the pressure drop and heat transfer coefficients various data from experimental measurements were used. In order to assess the performance of the proposed model, CFD computations were performed. For all the examined cases, the CFD results were in close agreement with the experimental data and thus, the developed porosity model could sufficiently, describe the macroscopic behaviour of the heat exchanger.     

管内填充多孔介质强化换热的数值研究

管内填充多孔介质强化换热的基本原理是构造热边界层,增大壁面附近流体的温度梯度,并且流动阻力增幅不大。本文运用数值模拟的方法,模拟填充多孔介质管内的流场和温度场,探讨填充比例φ、渗透率Da以及空隙率ε对管内对流换热的影响规律。研究表明,提高填充比例φ和减小渗透率Da都能明显提高换热效果,但也增加了管内流动阻力。空隙率ε对强化换热作用不大,但高空隙率可以明显降低管内流动阻力,在实际中应选用空隙率较大的多孔介质。     

Numerical analysis of laminar heat transfer in a channel with diamond-shaped baffles

Laminar periodic flow and heat transfer in a two dimensional horizontal channel with isothermal walls and with staggered diamond-shaped baffles is investigated numerically. The computations are based on the finite volume method, and the SIMPLE algorithm has been implemented. The fluid flow and heat transfer characteristics are presented for Reynolds numbers based on the hydraulic diameter of the channel ranging from 100 to 600. Effects of different baffle tip angles on heat transfer and pressure loss in the channel are studied and the results of the diamond baffle are also compared with those of the flat baffle. It is observed that apart from the rise of Reynolds number, the reduction of the baffle angle leads to an increase in the Nusselt number and friction factor. The computational results reveal that optimum thermal performance is at the baffle angle of 5° for baffle height and spacing of 0.5 and 1 times of the channel height, respectively. The thermal performance of the 5°–10°diamond baffle is found to be higher than that of the flat baffle for all Reynolds numbers used.