Radial Heat Transfer Research Articles

DEM simulation of heat transfer of binary-sized particles in a horizontal rotating drum

A numerical simulation was conducted by using discrete element method and granular heat conduction model to investigate the heat transfer mechanism inside a horizontal rotating drum. A particulate system containing binary-size spherical particles heating up through the wall was considered as the simulation domain. Radial segregation phenomenon and heat transfer of the particulate system were considered simultaneously. The effects of binary-mixture parameters such as volume ratio (the volume ratio of the small particles to all particles) and diameter ratio (the ratio of large to small diameter of particles) on the heat transfer were investigated. It was found that increasing the volume ratio of small particles causes faster heat up of the particulate bed. Conversely, higher diameter ratios led to lower heat transfer. The temperature difference between small and large particles was more obvious in the case of segregation, and the bed became more thermally non-uniform, particularly in the case of high diameter ratios. Moreover, the effects of important parameters such as rotation speed and filling level, on the heat transfer of the bed were also studied. The results showed that heat transfer rate is in direct relation with rotation speed, but it is inversely related to filling level in the binary-size bed.

Effective Thermal Conductivity of Stainless Steel Fiber Sintered Felt With Honeycombed Channels

Abstract A novel stainless steel fiber sintered felt (SSFSF) with honeycombed channels (SSFSFHC) is a promising support for catalytic combustion of the volatile organic compounds (VOCs). The SSFSFHC consists of stainless steel fiber, three-dimensionally reticulated porous structures, and interconnected honeycombed channels. The equivalent thermal conductivity (ETC) of the SSFSFHC is tested. It is found that the ETC of the SSFSFHC increases with the hot side temperature increasing but decreases with the porosity increasing and channel occupied area ratio increasing. The ETC of the SSFSFHC changes little with channel diameter increasing. The heat transfer model of the SSFSFHC is considered as parallel/series combinations of relevant thermal resistances. In order to estimate the ETC of the SSFSFHC, the correlation of the ETC of the SSFSF is derived. The expressions of the axial temperature under different porosities are deduced when eliminating the radial heat transfer between the channel section and the SSFSF section. The relationships of the transferred heats and the corresponding resistances along the radial direction are obtained by assuming that the radial heat transfer can be simplified as a serial of heat resistances located between the channels and the SSFSF.

Calculation Model of Effective Thermal Conductivity of a Spiral-wound Lithium Ion Battery

This paper proposed an analytical model which can calculate the effective thermal conductivity (ETC) of a spiral-wound Lithium-ion battery (Li-ion battery). It bases on a two-dimensional energy balance with both radial and spiral heat transfer, as well as internal thermal contact resistance (TCR) considered simultaneously and studies the influence of winding layers and winding tension on the ETC. Results show that the analytical data are in good agreement with the numerical results. With the winding layers decreased and the winding tension enhanced, the ETC of Li-ion battery increases gradually. The radial temperature in Li-ion battery is also investigated which demonstrates a relatively higher temperature when considering the internal TCR.

Current Tolerance Capability Calculation Model of Transmission Lines and its Application in Overload Protection

Traditional overload protection depends on pre-set values and cannot reflect the current tolerance capability of the line. If the current of a line exceeds the setting value of its overload protection, then it will be subsequently tripped off and cause power flow transferring, which may trigger the cascade tripping of power grid. So it is of significant importance for the overload protection to accurately evaluate the real-time safety status of transmission line and coordinate with power system control to eliminate the overload. In this article, starting from the mechanism analysis of conductor heat transfer, a thermal network model is established by focusing on radial and circumferential heat transfer paths. The temperature rise response of the network node is obtained through nonlinear iteration. The calculation model, which is verified by a test platform, is better than standard models. Then, the current tolerance capability calculation model of the whole line is constructed on the basis of the thermal network and applied to improve the overload protection. The proposed multi-parameter overload protection can effectively prevent unnecessary tripping to avoid the expansion of accidents. Finally, the validity of the proposed protection is verified by the New England 10-machine 39-bus test system.

The flow and heat transfer characteristics of compressed air in high-pressure air injection wells

High-pressure air injection (HPAI) is a significant enhanced oil recovery (EOR) technology of light oils especially in deep, thin, low-permeability reservoirs. The flow and heat transfer behaviors of compressed air in wellbore is essential to maximize performance of air in EOR. Due to strong compressibility of air and high injection pressure, wellbore temperature and pressure are greatly affected by friction and gas compression. However, the available models of wellbore flow and heat transfer are only accurate for thermal fluid, such as saturated steam and superheated steam, injected at relatively low pressure and high temperature. In this paper, a novel model is proposed to characterize wellbore pressure and temperature distribution for HPAI wells with consideration of dynamic behaviors of injected air. Flow and heat transfer in depth direction are coupled with air properties by iterative technique, and heat transfer in radial direction is treated as steady state in wellbore and transient state in formation. The mathematical model is solved by employing finite difference method and it is validated by field data. Then, integrated analyses of flowing pressure, heat transfer mechanism, and interaction between pressure and temperature are conducted. Results indicate that (1) as well depth increases, temperature difference between formation and air tends to become constant, and the radial heat transfer tends to reach an equilibrium state. The higher the flow rate is, the deeper the equilibrium depth is. (2) Air temperature is dominated by heat transmission from formation at low flow rates and dominated by frictional heat and gas compression effect at high flow rates. Fictional heat begins to affect air temperature at an injection rate beyond the critical value, while gas compression effect can increase air temperature in the whole calculated injection rate range. (3) Interaction between wellbore temperature and pressure is mainly achieved by altering air density. The effect of injection pressure on air temperature can be negligible, while the influence of injection temperature shows strong dependency on injection rate.

Investigation of heat transfer from a totally blocked fuel subassembly of fast breeder reactor with 7 and 19 pin bundles

Abstract Liquid metal cooled fast breeder reactor is emerging as an important future power source. It uses sodium as the primary coolant, due to its favourable neutronic properties, high boiling point and large heat transfer coefficient. It is essential to continuously monitor adequacy of fuel pin/fuel subassembly cooling, so that sodium does not reach its boiling point. Sodium boiling within the fuel subassembly leads to large coolant flow reduction (as the density ratio of sodium liquid to sodium vapour is very high), under-cooling of fuel pins and hence damage to fuel subassembly. Development of partial flow blockage in the fuel pin bundle is possible due to the compact nature of fuel pin arrangement within the fuel subassembly, with small hydraulic diameter (typically, ∼3 mm), despite the elaborate design provisions and coolant chemistry control. In the safety analysis, a total flow blockage is usually considered as an upper bound of all the partial blockages. The present work investigates the power level at which liquid sodium reaches its boiling point for different sizes of fuel subassembly. A porous body model has been developed based on local pressure-drop correlations for the axial/cross flow through fuel pin bundles. The model considers the total flow blockage situation in the fuel subassembly wherein the fuel pins and sodium (within the blocked subassembly) are considered as heat generating orthotropic porous medium. The proposed porous body model has been compared with a Computational Fluid Dynamics (CFD) model describing the same blockage condition. The commercial CFD code ANSYS FLUENT 15.0 has been used for the computational purpose. It has been found that the trapped liquid sodium coolant inside the blocked subassembly reaches its boiling point (1153 K at atmospheric pressure) at lower power input per pin in a 19 pin bundle model than that in a 7 pin bundle. This is traced mainly due to the fact that as the number of pins in the subassembly increases, the surface area of the hexcan wall (which is the ultimate heat sink) increases leading to enhanced heat dissipation in large size subassemblies. However, as the number of pins increases, the internal resistance for radial heat transfer increases, leading to increased sodium temperature inside the subassembly. These two competing effects determine the peak sodium temperature in the subassembly. Since the later effect is dominant, the permissible heat generation per pin decreases as the number of fuel pins in the bundle increases.

Parametric effect investigation on surface heat transfer performances during cryogen spray cooling

Cryogen spray cooling (CSC) has been a widely used auxiliary tool in laser dermatology such as port wine stain to prevent unspecific thermal injury due to laser energy absorption by the melanin in the epidermis. The present paper presents an experimental research on the effect of ambient temperature, relative humidity, and initial substrate temperature on heat transfer performances during R134a spray cooling. Results demonstrated that the cooling capability of R134a spray cooling can be obtained with small ambient temperature (Ta = 10 °C) and relative humidity (RH = 25%). Further investigation of cooling mechanism was conducted by studying the temporal and radial heat transfer distributions with different spray distances and nozzles. The heat transfer distribution presented large non-uniformity along radial locations. Two uniform cooling sub-regions of 0 ≤ r < 2 mm and 6 mm ≤ r < 10 mm were found under the spray distance of 30 mm and nozzle with an inner diameter of 1.0 mm. The heat transfer barrier was produced due to indirect contact between cold droplets and the substrate surface caused by bubbles and heat transfer is weakened by the low thermal conductivity of these bubbles.

Review of the Accuracy of Single Core Equivalent Thermal Model for Offshore Wind Farm Cables

Cables intended to interconnect offshore wind farms with the mainland are currently treated as separate lead-type cables by IEC 60287. A single core equivalent thermal model (SCETM) is implied, that is, a thermal model accounting for 1-D (radial) heat transfer only. While this approach is expected to be reasonable when smaller cables are rated, the 1-D representation is less valid in larger cable sizes. This paper uses 2-D finite-element models to reveal certain weak points of the representation of the thermal resistances in the existing SCETM. For constant losses, the IEC SCETM seems to underestimate the temperature by up to 8 °C. Suitable replacement formulae are proposed that could improve the accuracy of the SCETM. Finally, the issue of nonsolid fillers is considered and modelling guidelines are given.

Numerical study of flow and heat transfer of supercritical water in rifled tubes heated by one side

Deep understanding of flow and heat transfer of supercritical fluids in rifled tubes with non-uniform heating is of great importance for the safety of modern supercritical steam power equipment. In this paper, the heat transfer of supercritical water flowing in a vertical one-side heated rifled tube was numerically investigated. The differences of flow and heat transfer between the circumferentially non-uniform heated rifled tube (NRT) and uniform heated rifled tube (URT) were investigated. The distributions of temperature field, thermophysical properties, axial velocity and turbulent kinetic energy were analyzed. The mechanism of heat transfer improvement of NRT was comprehensively revealed. Results showed that the maximum inner wall temperature in NRT (Tiw,N,max) was 10 K lower than that in URT for the simulation conditions. Both radial and circumferential heat transfers were improved in NRT due to the swirling flow. Under high q/G (ratio of heat flux to mass flux) conditions, the buoyancy effect was weakened in NRT comparing to that in URT. Flow turbulence in boundary layer of y+ > 30 was intensified in NRT, which was crucial for supercritical fluid heat transfer. The positions of Tiw,N,max were not always at the midpoint of the heated side. And a prediction method for Tiw,N,max was proposed.

A novel method based on thermal conductivity for material identification in scrap industry: An experimental validation

Fast, accurate and reliable identification and sorting of materials is still a challenge in recycling sector. Scrap metals are often classified through density and colour, which cause notable financial burdens to the companies in most cases. Within the scope of this research, a novel method based on thermal conductivity is presented for material identification in scrap industry. The unit consists of a constant heat flux source and a cooling system, in which axial heat conduction is enabled and radial heat transfer is eliminated. For the steady-state conditions, temperature gradient across the sample metals is measured along with the constant heat flux value, and the thermal conductivity of the samples is determined via the Fourier’s heat conduction law. Copper, brass and stainless steel samples are considered in this research to verify the accuracy of the results. For a reliable and scientific approach, three independent sets of experiments are conducted, and the results are evaluated in terms of accuracy and consistency. Experimental thermal conductivity values of the said samples are compared with the reported data in literature and a good accordance is achieved. Error in measurements is calculated to be 1.37, 3.31 and 4.46% for copper, brass and stainless steel sample, respectively which is acceptable. The tests are repeated with highly sensitive probes for aluminium sample, and the measurement error is calculated to be 0.56%.

Two-dimensional thermal analysis of radial heat transfer of monoliths in small-scale steam methane reforming

Monolithic catalysts have received increasing attention for application in the small-scale steam methane reforming process. The radial heat transfer behaviors of monolith reformers were analyzed by two-dimensional computational fluid dynamic (CFD) modeling. A parameter study was conducted by a large number of simulations focusing on the thermal conductivity of the monolith substrate, washcoat layer, wall gap, radiation heat transfer and the geometric parameters (cell density, porosity and diameter of monolith). The effective radial thermal conductivity of the monolith structure, kr,eff, showed good agreement with predictions made by the pseudo-continuous symmetric model. This influence of the radiation heat transfer is low for highly conductive monoliths. A simplified model has been developed to evaluate the importance of radiation for monolithic reformers under different conditions. A wall gap as thin as 0.05 mm significantly decreased kr,eff, while the radiation heat transfer showed limited improvement. A pseudo-homogenous two-dimensional model combined with the symmetric model has been developed for a quick evaluation of geometric parameters for a monolith reformers. Monolithic reformers based on highly conductive substrates e.g., Ni and SiC showed great potential for small-scale hydrogen production.

A novel hybrid approach for in-situ determining the thermal properties of subsurface layers around borehole heat exchanger

Performance of shallow geothermal systems such as borehole thermal energy storage (BTES) and ground source heat pump (GSHP) mainly depends on the thermal properties of the subsurface and proper design of borehole heat exchangers (BHE). This paper introduces a novel hybrid approach for measuring the effectiveness of BHEs and surrounding subsurface thermal properties, which combines traditional thermal response test (TRT) with the borehole temperature relaxation method (BTR), based on two dimensional radial conductive heat transfer. The new method allows for: (1) evaluation of how convective heat loss at groundwater layers influence estimation of subsurface thermal properties; (2) examination of non-uniform heat transfer through a BHE to stratified subsurface layers; and, (3) calculation of depth-dependency of thermal properties of unsaturated subsurface layers. The hybrid approach was tested using a 50 m U-type BHE, the results of which indicated that convective heat transfer at the groundwater level altered the real value of effective thermal conductivity from 0.45 to 1.56 W/m K. The non-uniformity of heat transfer along the BHE was confirmed by calculations that showed subsurface thermal conductivities were depth dependent, varying between 0.34 and 0.61 W/m K.

Parametrized analysis of a carbon dioxide transcritical Rankine cycle driven by solar energy

Several authors have reported in the literature the benefits of transcritical carbon dioxide regenerative Rankine power cycles using low - and medium - temperature sources. However, their technical potential when driven by solar-thermal collectors has not been fully addressed yet. The methodology presented herein is based on two parametric analyses: the first approach attempts to determine the heat transfer area of the regenerator and its respective cost, and the second approach studies the radial heat transfer in each solar collector, at different operation pressures, aiming to determine the heat losses, the pressure drop and the overall performance of the collectors with the use of supercritical Carbon Dioxide. Therefore, through this analysis, the total area required by each component is determined. Then, the solar field configuration is optimized to maximize the exergy efficiency. In that sense, by considering the differences of the specific costs for each area, a multi-objective optimization methodology is applied to the cycle, which determines the best configuration and operation pressure for the cycle based on exergy destruction minimization and the minimum thermoeconomic cost. These results allow determining an optimum size design for the regenerator and solar field configuration, which takes full advantage of the available energy at the lowest possible cost.

Experimental investigation of the thermal hydraulics of a spent fuel pool under loss of active heat removal conditions

In case of a temporal undefined failure of the active cooling system of a spent fuel pool (SFP), the water inside the pool heats up depending on the decay heat of the stored spent fuel. In the worst case, this leads to a boil-off scenario with a water level decrease and, after appropriate time, to a progressive uncovery of the fuel assemblies (FA). The cooling of the uncovered structures is limited by the steam production in the lower still wetted part of the FA, radiative heat transfer, radial heat conduction and convection inside the FA and interaction with ambient air depending on the storage conditions. As a result, the removal of decay heat can be endangered and, by reaching certain cladding temperatures, the integrity of the cladding tubes can be compromised. The detailed heat and mass transfer mechanisms of the boil-off scenario are not yet sufficiently investigated – especially experimentally. Therefore, reliable conclusions about the development of the cladding temperatures cannot be made.Against this background, the SINABEL project was launched in 2013 at TU Dresden for an improved understanding of the heat transport processes inside a SFP under accident conditions. Studies are performed both experimentally on the test facility ALADIN and theoretically by using computational fluid dynamics (CFD) calculations and integral codes for severe accidents. The test facility simulates a generic boiling water reactor (BWR) FA on almost original scale with regard to the boundary and ambient conditions within a SFP. Through an appropriate unique net of instrumentation, the distribution and development of radial and axial cladding temperatures and the development of the water level can be investigated in detail.Experiments were carried out for various decay heats respectively rod powers and changing storage distances. The thermal hydraulics of the heat-up and the boil-off phase with the occurrence of subcooled boiling in the beginning followed by geysering-like instabilities are described in the present paper. The higher the heat load, the faster the heat-up and, as boiling temperature is reached, the lowering of the water level. The maximum limit of the water level and the influence by the radial heat conduction, convection and radiative heat transfer is shown and explained.The experimental data and thermohydraulic findings provide the basis for the phenomenological understanding of this accident scenario and are used for the validation and improvement of numerical simulations.

Self-Similar Solution of Radial Stagnation Point Flow and Heat Transfer of a Viscous, Compressible Fluid Impinging on a Rotating Cylinder

In this study, the radial stagnation point flow of strain rate $$\bar{k}$$ impinging on a cylinder rotating at constant angular velocity ω and its heat transfer are investigated. Reduction in the Navier–Stokes equations and energy equation to primary nonlinear ordinary differential equation systems is obtained by use of appropriate transformations when the angular velocity and wall temperature or wall heat flux all are constant. The impinging free stream is steady and normal to the surface from all sides, and the range of Reynolds number variation ( $$Re = \bar{k}a^{2} /2\upsilon$$ ) is 0.1–1000 in which a and υ are cylinder radius and kinematic viscosity, respectively. Flow results are presented for selected values of compressibility factor and different values of Prandtl numbers along with shear stress and Nusselt number. For all values of Reynolds numbers and surface temperature or surface heat flux, as compressibility factor increases the radial velocity field, the heat transfer coefficient and the wall shear stress increase, whereas the angular velocity field decreases. The rotating movement of the cylinder does not have any effect on the radial component of the velocity, but its increase increases the angular component of the fluid velocity field and the surface shear stress.

Coil model for magnesium alloy strips and its heat transfer analysis

The analysis of the heat transfer in the magnesium coil in the radial direction by laboratory tests using a deformation simulator Bähr BTA 800 was proposed. Based on the obtained results, the equivalent thermal conductivity as the radial heat transfer was determined as a function of thickness, temperature and pressure, which was further integrated into the developed coil model. The validation of the model was carried out by the comparison of the calculated and measured temperatures during coil cooling. The results showed a good agreement between predicted and experimental data.

The influence of swirling flows on pulverized coal gasifiers using the comprehensive gasification model

The burner swirl intensity plays an important role in membrane wall safety and the gasification performance of pulverized coal, swirl gasifiers. The comprehensive gasification model (CGM), having two reaction regions and one radial heat transfer region, was used to simulate the influence of the swirl number (SN) on gasification performance, multiphase flow, reactions in the space, and reactions regarding the membrane wall. The results show that an SN of 0.66 is a critical point to divide low-swirl and high-swirl flows for the single-swirl-burner gasifiers of this study. Gasifier performance increases sharply with increased SN for low-swirl burners, whereas SN has little influence on gasifier performance (and multiphase flow) for high-swirl cases.In this paper, we examine the relationship between burner swirl and flow fields, temperature distributions in the space and on membrane wall, slag thickness, and the molten slag velocity distribution on the membrane wall. The influence of SN on these parameters is more remarkable at the top of the reattachment point than below it. The slag layer formed on the membrane wall isolates high-temperature gas effectively, except around the reattachment point. To guarantee gasifier performance and membrane wall safety, the burner SN should be between 0.66 and 0.9 for the single-swirl-burner gasifiers of this study.

Modeling Effective Thermal Conductivity of Thermal Radiation for Nuclear Packed Pebble Beds

In nuclear packed pebble beds, it is a fundamental task to model effective thermal conductivity (ETC) of thermal radiation. Based on the effective heat transfer cells of structured packing, a short-range radiation model (SRM) and a subcell radiation model (SCM) are applied to obtain analytical results of ETC. It is shown that the SRM of present effective heat transfer cells are in good agreement with the numerical simulations of random packing and it is only slightly higher than empirical correlations when temperature exceeds 1200 °C. In order to develop a generic theoretical approach of modeling ETC, the subcell radiation model is presented and in good agreement with Kunii–Smith correlation, especially at very high temperature ranges (over 1500 °C). Based on SCM, one-dimensional (1D) radial heat transfer model is applied in the analysis of the HTTU experiments. The results of ETC and radial temperature distribution are in good agreement with the experimental data.

Modeling of unmixed combustion based packed bed reactor system for heat transfer applications

Unmixed Combustion (UMC), a novel variant of combustion, occurs when air and fuel alternately pass over an Oxygen Storage and Release Material (OSRM), usually metal/metal oxides, that undergoes oxidation and reduction reactions. The energy released during these reactions can potentially be utilized for various heat transfer applications. In this regard, a dynamic 2-D pseudo-homogeneous model has been developed for an UMC based annular packed bed reactor incorporating the phenomena of heat transfer across a surface to a representative coolant, i.e. air. A CFD software COMSOL Multiphysics™ was used for model implementation and simulation. Cu/CuO on alumina was chosen as a representative OSRM, while zero air and methane (diluted with nitrogen) were used as reactive gases in the simulations. For prescribed operating conditions, the model predicts temperature profiles in the bed and total heat transfer. Model results for one cycle comprising of oxidation and reduction at 1.25 kg of OSRM loading and an operating temperature range of 823.15–973.15 K, were compared with those obtained from experimental data. Good agreement to within ±2% for radial heat transfer to coolant and ±9% for bed temperature profiles was found. The effect of varying reactive gas and coolant flowrate on the radial heat transfer was also simulated. This sensitivity analysis helped identify the limits of operating variables for optimal performance and confirm theoretical viability of operation. The results validate the use of a pseudo-homogeneous model in predicting the behaviour of dynamically operated UMC systems under the operating conditions in which the present study was carried out.

Temperature field analysis on the highly-deviated wellbore in backwashing condition

Based on the measured borehole trajectory, a prediction model of temperature field of highly-deviated wells in backwashing condition is established. To verify the model, a test instrument to measure the temperature variations in the wellbore is developed and used to measure the temperature of two typical highly-deviated wells in backwashing condition. The comparative analysis shows that the wellbore temperature predicted by the model is close to that measured in field with the relative error less than 8%. The model was further used to analyze the influence of liquid-injection speed and injection time on the temperature distributions of oil pipe, annulus space and radial direction under the backwashing operation with original-temperature and hot washing liquid. It is found that for the backwashing operation with original-temperature washing liquid, the temperature at the lower part of the shaft is most affected by the displacement rate and backwashing time, whereas the curve section and the lower part of the shaft are most affected by the displacement rate and backwashing time in hot washing operation. Along the depth of the borehole, there is a constant temperature section which is almost unaffected by displacement rate and backwashing time. The radial heat transfer analysis shows that the heat exchange range is not large and near the wellbore.