Thermal Resistance Approach Research Articles

A thermofluid temperature modeling, prediction of closed-loop cooling system of roll grinder based on circulation differential equations

Roll grinders are essential in high-precision roll manufacturing. However, lubricant temperature fluctuations decrease the precision of grinders. The complicated dynamic heat transfer within the closed-loop cooling systems of roll grinders poses significant challenges to accurately modeling their thermal states. This study proposed a novel model based on circulation differential equations for the thermofluid temperatures in roll grinders. Based on thermodynamic principles, differential equations of each component within the closed-loop cooling system were derived. To improve model accuracy, a thermal resistance approach was utilized, and the thermal interaction between lubricant and hydrodynamic bearings under different speeds and the heat convection between hydraulic hoses and air are considered. To validate the proposed model, a series of experiments across a range of spindle speeds were carried out. The results showed the model could achieve prediction accuracy less than 5.27%. Subsequently, the influence of system design parameters on cooling performance was analyzed. The proposed temperature model better comprehends the thermodynamic interaction within closed-loop cooling systems featuring hydrodynamic bearings. The limitations and potential application in other industrial areas were discussed.

Development of dynamic simulation model for 20 kWe micro heat pipe fission battery with dual power conversion system

Recent advancements in politics, technology, and economics have sparked interest in small-scale nuclear power generation. Heat-pipe micro-reactors, a type of small modular reactor (SMR), are ideal for remote and specialized applications like deep-sea and deep-space exploration. Traditionally, these reactors have used thermoelectric generators (TEGs) or Stirling engines for power conversion. However, TEGs suffer from low efficiency, and while Stirling engines have improved, they still have lower long-term stability compared to TEGs. Furthermore, comprehensive studies on system-level transients, dynamic behavior, and thermal responses are lacking. This study designs and models a dual power conversion system integrating TEGs and Free-Piston Stirling Generators (FPSGs) for micro heat pipe reactors to enhance efficiency, stability, and reliability. By integrating the two systems in parallel, the limitations of each technology are addressed, offering a robust solution for small, portable nuclear power generation. A dynamic simulation model incorporating the reactor core, heat pipes, and power conversion system enabled a comprehensive study of system transients and interactions. The core was modeled using thermal energy balance equations, and a thermal resistance approach was applied to the heat pipe. The TEG model included the Thomson and Seebeck effects, while neutronics feedback used a point kinetics model. The nonlinear analysis model was applied to simulate the FPSG. The system reached a stable operation after about 1000 s, generating 20kWe with 29.39% efficiency. It maintained stability without external control during transients within a specific range, demonstrating its feasibility. The TEG and FPSG exhibited independent yet complementary behaviors, ensuring reliable performance across scenarios.

The role of shadowed droplets in condensation heat transfer

Dropwise condensation (DWC) is a phenomenon of common occurrence and significant utility in nature and technology. In energy applications, sustenance of DWC and avoidance of transition to film formation is directly related to efficient heat removal, ensuring high performance of related devices and processes. The efficiency of heat transfer in DWC depends on the heat transfer rates of individual droplets and the droplet size distribution. While the former can be summarily captured in engineering analysis through thermal resistance modeling, the theoretical analysis of the droplet size distribution involves assumptions often oversimplifying the complexity of droplet interactions, especially in the important sub–10 μm regime. Here, a modeling framework based on the thermal resistance approach is coupled with a dynamic model of droplet interactions: Droplet growth, coalescence, jumping, and removal of condensate due to gravity are all present during the unfolding of the phenomenon to accurately predict the droplet size distribution. The motivation is condensation experiments on superhydrophobic surfaces, namely rough aluminum substrates with a hydrophobic coating. Through the “interaction” of computations with measurements, the experimental findings are explained and critical parameters for condensation heat transfer on superhydrophobic surfaces are illuminated. Although larger droplets can be easily observed in experiments, it is shown that large droplets do not significantly affect heat transfer after reaching such state of growth. Instead, it is the small (with radius < 10 μm) and what we term “shadowed” droplets, i.e., the droplets grown in the shadow of the vertical projection area of the larger droplets, that play an important role in the heat transfer process. Due to the growth of these droplets and their concomitant shadowed coalescence and ensuing re-nucleation, the shift in the droplet size distribution towards smaller sizes is significant-enough to render the heat transfer rate rather insensitive to the presence of large droplets. In this regime, the effect of contact angle hysteresis on heat transfer is not crucial. Through the comparison with measurements, the dominant role of the density of nucleation sites on heat transfer is revealed and an estimation of the density of sites (∼105 mm−2) as a function of subcooling is extracted. Finally, the distribution of sites is found critical for heat transfer; an ordered distribution of sites outperforms random and clustered distributions.

A diffuse-interface model of anisotropic interface thermal conductivity and its application in thermal homogenization of composites

In this work, we present a diffuse-interface model of anisotropic interface thermal conductivity considering the interface thermal resistance and conductance. It allows to perform simulations with interface thermal imperfections while circumventing the technical and numerical difficulties of reconstructing complex sharp-interface microstructure. The model is implemented in a finite element method. Numerical results show good agreement with the theoretical benchmarks for both thermal conduction simulation and thermal homogenization. To further demonstrate the feasibility of the model, complex microstructures from digitized characterizations and phase-field simulations are homogenized, taking Si-Hf-N as the material system. Normalized interface thermal resistance ranging from 1 to 108 show prominent influence to the homogenized thermal conductivity, which converges when the thermal resistance approaches zero or infinity. Increasing thermal resistance is also unveiled to enhance the thermal anisotropy of the microstructure with highly-oriented inclusions.

Thermal rectification of solid-liquid phase change thermal diode under the effect of supercooling

Solid-liquid phase change thermal diode (SL-PCTD) is potential for thermal rectification, however the unsustainable thermal rectification ratio of the SL-PCTD hampers its practical application, demanding a reasonably compatible design. Herein, a SL-PCTD composed of calcium chloride hexahydrate (CaCl2·6H2O) and paraffin wax is investigated, where the supercooling effect of CaCl2·6H2O plays a significant role in thermal rectification. In the forward direction, natural convection sustains in the SL-PCTD below the melting temperature (30 °C) due to the supercooling, leading a robust heat transfer within a temperature bias range of 10–40 °C. In the reverse direction, heat flux should be inhibited for effective thermal rectification, thus supercooling is dislodged via manual supercooling release (MSR) within a large temperature range of 30–7 °C. As a consequence, thermal rectification ratio of 2.95 is achieved, which is competitively sustainable at large temperature bias compared to the SL-PCTD without supercooling effect. Furthermore, a theoretical model base on thermal resistance approach is proposed to analyze the supercooling effect on thermal rectification comprehensively, and the theoretical and experimental results find a great agreement. According to the theoretical analysis, the SL-PCTD with supercooling works at a large thermal rectification ratio of around 2.8 within a wide temperature bias range of 33–87 °C, indicating the significant role of supercooling in thermal rectification.

Optimised performance of a thermally resistive PV glazing technology: An experimental validation

Thermally resistive PV glazing (TRPVG), which is a recently developed technology for low/zero carbon buildings, is in the centre of interest worldwide as a consequence of multifunctional benefits of this novel product such as remarkably better thermal insulation performance compared to conventional PV and other fenestration technologies in market, clean energy generation, self-cleaning, sound insulation, UV and IR absorption, etc. In this study, thermal insulation performance of TRPVG is numerically optimised through a well-known CFD software ANSYS FLUENT. Optimisation is based on determining the optimum inert gas (argon) thickness (τ) behind the amorphous silicon (a-Si) PV module which yields to minimum overall heat transfer coefficient (U-value) for the entire structure. For a typical case (τ=16 mm), CFD results are compared with the experimental data derived from the standardised co-heating tests, and a good accordance is achieved. CFD results are also compared with the findings of thermal resistance approach, which assumes heat conduction takes place in the inert gas medium only. The results reveal that natural convection effects become notable for the values of τ over 10 mm. In other words, τ stands as a parameter that needs to be optimised for its values greater than 10 mm. For the typical TRPVG sample with τ=16 mm, the overall U-value from the CFD research is determined to be 1.19 W/m2K, which is in good agreement with the experimental data. The optimised value of τ for the TRPVG structure introduced is determined to be 20 mm, which guarantees the minimum total heat transfer rate (Q) across the glazing and maximum temperature difference between internal and external glazing surfaces.

Conductive heat flow pattern of the central-northern Apennines, Italy

We analyzed thermal data from deep oil exploration and geothermal boreholes in the 1000-7000 m depth range to unravel thermal regime beneath the central-northern Apennines chain and the surrounding sedimentary basins. We particularly selected deepest bottom hole temperatures, all recorded within the permeable carbonate Paleogene-Mesozoic formations, which represent the most widespread tectono-stratigraphic unit of the study area. The available temperatures were corrected for the drilling disturbanceand the thermal conductivity was estimated from detailed litho-stratigraphic information and by taking into account the pressure and temperature effect. The thermal resistance approach, including also the radiogenic heat production, was used to infer the terrestrial heat flow and to highlight possible advective perturbation due to groundwater circulation. Only two boreholes close to recharge areas argue for deep groundwater flow in the permeable carbonate unit, whereas most of the obtained heat-flow data may reflect the deep, undisturbed, conductive thermal regime.

Estimation of effective thermal conductivity of packed beds incorporating effects of primary and secondary parameters

This paper presents a detailed description and experimental validation of a modified collocated unit cell model for the estimation of effective thermal conductivity of packed beds. The effect of primary and secondary parameters influencing the effective thermal conductivity viz. conductivity ratio (α) and concentration (ν) of the spherical particles (fraction of total volume occupied by the particles) of the packed bed, inter-particle gap, thermal contact conductance between the surfaces in contact, temperature, pressure and Knudsen number respectively are investigated in detail. Analytical expressions for effective thermal conductivity are derived for spatially periodic 2D square cylinder and in-line touching geometries based on the unit cell based thermal resistance approach. Using the developed model, the effective thermal conductivity of various packed materials in the conductivity ratio (ks/kf) range between 1–1000 and concentration (ν) 0 to 1 are predicted for varied temperature and pressure regimes. Predictions obtained from the developed model are compared against existing models available in literature in the pressure range 10−2 to 103 kPa at constant temperature. Furthermore, effective thermal conductivities of packed beds comprising of glass and ceramic beads are predicted using the developed model and compared with measured values obtained using the standard square guarded hot plate (SGHP) apparatus in the temperature range of 323–673 K. Both values are found to agree within ±12.24% and ±14.54% for glass and ceramic beads respectively.

Thermal resistance approach to analyse temperature distribution in thick hollow FGM sphere: under dirichlet boundary condition

A thick hollow FGM sphere with radially varying material property is considered under thermal loading. Thermal conductivity is assumed to vary radially following two different power functions separately and results for both have been analysed. Temperature distribution is obtained using Thermal Resistance Approach (TRA) where spatially varying thermal conductivity is assumed to be a discontinuous piece-wise function of radial distance rather than the continuous power functions. Whole body is considered to be constructed of layers having different material property but each layer is assumed to be homogeneous. Then temperature values are obtained considering each layer’s thermal resistance and the total thermal resistance network. Results were compared with other established studies and results obtained by FEM.

A Thermal Resistance Model for Problems Involving Chemical Reactions and Phase Transition

This paper formulates a modified thermal resistance model (MTRM) for dealing with heat transfer situations involving heat sources from chemical reactions or phase transition. The modified thermal resistance model describes the various heat transfer mechanisms by three common thermal resistors, radiation, convection, and conduction (in media with no internal mass diffusion), adding a new coupled thermal resistor that stands for conduction and enthalpy flow in the gas phase. Similarly to the classical thermal resistance approach, the present model is valid for one-dimensional, quasi-steady heat transfer problems, but it can also handle problems with an internal chemical heat generation source. The new thermal resistance approach can be a useful modular tool for solving relatively easily and quickly complex problems involving chemical reactions and phase transition, such as combustion problems.

Bulk water freezing dynamics on superhydrophobic surfaces

In this study, we elucidate the mechanisms governing the heat-transfer mediated, non-thermodynamic limited, freezing delay on non-wetting surfaces for a variety of characteristic length scales, Lc (volume/surface area, 3 mm &amp;lt; Lc &amp;lt; 6 mm) using carefully designed freezing experiments in a temperature-controlled, zero-humidity environment on thin water slabs. To probe the effect of surface wettability, we investigated the total time for room temperature water to completely freeze into ice on superhydrophilic (θaapp→ 0°), hydrophilic (0° &amp;lt; θa &amp;lt; 90°), hydrophobic (90° &amp;lt; θa &amp;lt; 125°), and superhydrophobic (θaapp→ 180°) surfaces. Our results show that at macroscopic length scales, heat conduction through the bulk water/ice layer dominates the freezing process when compared to heat conduction through the functional coatings or nanoscale gaps at the superhydrophobic substrate-water/ice interface. In order to verify our findings, and to determine when the surface structure thermal resistance approaches the water/ice resistance, we fabricated and tested the additional substrates coated with commercial superhydrophobic spray coatings, showing a monotonic increase in freezing time with coating thickness. The added thermal resistance of thicker coatings was much larger than that of the nanoscale superhydrophobic features, which reduced the droplet heat transfer and increased the total freezing time. Transient finite element method heat transfer simulations of the water slab freezing process were performed to calculate the overall heat transfer coefficient at the substrate-water/ice interface during freezing, and shown to be in the range of 1–2.5 kW/m2K for these experiments. The results shown here suggest that in order to exploit the heat-transfer mediated freezing delay, thicker superhydrophobic coatings must be deposited on the surface, where the coating resistance is comparable to the bulk water/ice conduction resistance.

Thermal Resistance Approach: An Engineering Tool for Improvement of Conductive Constructal Configurations

In the last decade, various conductive networks for cooling heat generating bodies have been proposed, analyzed, and optimized. Nevertheless, many of these studies have not been based on an analytical or mathematical formulation of the effective parameters. In this trend, a new geometry is assumed and analyzed (by analytical or numerical methods) hoping to decrease the total thermal resistance of the system. Therefore, the objective of the present paper is to illustrate how to analyze a conductive cooling network and improve it using the analytical procedures based on the general formulation of thermal resistance. As an example, the conventional rectangular elemental volumes with I shaped conductive link is modified to V shaped and pencil shaped designs and optimized analytically. Moreover, general expressions for optimum local thickness and thermal resistance of the links with variable cross section in an arbitrary network are provided. It is shown that improvements up to 50% can be achieved easily by simple geometrical changes if the designer is equipped with a profound knowledge of the important governing parameters.

Thermal Assessment of Forced Convection Through Metal Foam Heat Exchangers

Using a thermal resistance approach, forced convection heat transfer through metal foam heat exchangers is studied theoretically. The complex microstructure of metal foams is modeled as a matrix of interconnected solid ligaments forming simple cubic arrays of cylinders. The geometrical parameters are evaluated from existing correlations in the literature with the exception of ligament diameter which is calculated from a compact relationship offered in the present study. The proposed, simple but accurate, thermal resistance model considers: the conduction inside the solid ligaments, the interfacial convection heat transfer, and convection heat transfer to (or from) the solid bounding walls. The present model makes it possible to conduct a parametric study. Based on the generated results, it is observed that the heat transfer rate from the heated plate has a direct relationship with the foam pore per inch (PPI) and solidity. Furthermore, it is noted that increasing the height of the metal foam layer augments the overall heat transfer rate; however, the increment is not linear. Results obtained from the proposed model were successfully compared with experimental data found in the literature for rectangular and tubular metal foam heat exchangers.

Theoretical Analysis of Natural Convection in an Enclosure Filled with Disconnected Conducting Square Solid Blocks

Two different approaches have been implemented to interpret the existing data in Merrikh and Lage (2005a, in: Pop, Ingham, Transport Phenomena in Porous Media, Elsevier, Oxford) pertinent to the pore-scale simulation of natural convection in a laterally heated square enclosure filled with a fluid bathing discrete, disconnected and conducting solid blocks. Mathematical analysis of the problem based on the least squares method leads us to a Nu-Ra correlation with the solid-to-fluid thermal conductivity ratio and the porous medium permeability as the controlling parameters. In this study, while the porosity is fixed, the permeability is varied by changing either the block size or the number of blocks. Hence, three independent variables N, Ra, and κ being the number of blocks, Rayleigh number, and the conductivity ratio between the solid and the fluid, respectively, affect the overall heat transfer process. Based on a simplified thermal resistance approach, an alternative correlation is proposed to predict the Nusselt number as a function of the aforementioned parameters. Detailed analysis of the results and the expected errors are presented.

A simple analytical model for calculating the effective thermal conductivity of nanofluids

AbstractA simple mathematical model for calculating the effective thermal conductivity of nanofluids has been developed based on the thermal resistance approach. The model is developed by considering both effects of a solid‐like nanolayer and convective heat transfer caused by Brownian motion which have not been considered simultaneously by most available models in the literature. In addition the correlation of Prasher and Phelan for the convective heat transfer coefficient is modified to take into account the effect of the solid‐like nanolayer. In addition a general value for n (different from the one presented by Tillman and Hill) is introduced to modify the thickness of the solid‐like nanolayer. The latter is done by considering both conduction and convection heat transfer mechanisms. Comparisons with previously published experimental results and other mathematical models show that the presented model could well predict a nanofluids effective thermal conductivity as a function of the nanoparticles mean diameter, volume fraction, and temperature for different kinds of nanofluids. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20290

Correction to “Pāhoehoe Flow Cooling, Discharge and Coverage Rates from Thermal Image Chronometry”

[2] Despite the thermal resistance approach used here being underpinned by an assumption of steady state thermal conditions, the model provides a good match to the field measurements and to previous work. For example, after 60 s equation (7) solves with a surface temperature of 558 °C, consistent with the measured surface temperature after 60 s of 563 °C. This is also consistent with Tsurf predicted by the empirical relationship of Hon et al. [1994] for Hawaiian pahoehoe, i.e., Tsurf = −140 log(t) + 303, which gives 552 °C after 60 s (Table 1). As can be seen from Table 1, the equation (2) model consistently over-estimates the expected surface temperature. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

Lattice-dynamical calculation of phonon scattering at ideal Si–Ge interfaces

Detailed phonon scattering at an ideal Si–Ge interface is studied with a linear lattice dynamics model. Frequency dependent transmission coefficients indicate the significance of acoustic-optical phonon mode conversion at the interface. Applied to multiple interfaces, the method shows how the overall thermal resistance approaches a finite (Bloch mode) limit with the increasing number of interfaces in absence of other scattering mechanisms. The dependence of thermal resistance on the superlattice layer thickness is not significant even in the interface-scattering-only limit we study. We also assess errors incurred by the finite domain size and classical statistics in molecular dynamics simulations of interface thermal resistance. Results suggest that using 6×6 unit cells in the transverse directions, a tractable size for such simulations, will incur only a 5% error in the predicted thermal resistance. Similarly, the error due to the classical (Boltzmann) phonon distribution in molecular dynamics simulations is predicted to be less than 10% for temperatures above 300 K.

Specific features of thermal resistance of silicon in the temperature range 105–130 K

Careful experimental investigations into the behavior of the thermal resistance of single-crystal silicon are carried out in the immediate vicinity of the temperature of an anharmonicity sign inversion (T i =121.1 K), where phonon thermal resistance approaches zero. An anomalous positive deviation of the total thermal resistance (W) from the linear part of the temperature dependence with a maximum at 121.1 K is found in the temperature range 105–130 K. The temperature behavior of W in this range indicates that the mean free path of phonons is limited by a characteristic size of structural defects and that its temperature dependence exhibits specific features in the vicinity of T i . It is established that the character of the temperature dependence of W above and below T i is different. A linear functional relation between the total thermal resistance and the isobaric thermal strain is revealed at positive and negative anharmonicities of atomic vibrations.

Numerical Modeling of Reflux Solar Receivers

Using reflux solar receivers to collect solar energy for dish-Stirling electric power generation systems is presently being investigated by several organizations, including Sandia National Laboratories, Albuquerque, N. Mex. In support of this program, Sandia has developed two numerical models describing the thermal performance of pool-boiler and heat-pipe reflux receivers. Both models are applicable to axisymmetric geometries and they both consider the radiative and convective energy transfer within the receiver cavity, the conductive and convective energy transfer from the receiver housing, and the energy transfer to the receiver working fluid. The primary difference between the models is the level of detail in modeling the heat conduction through the receiver walls. The more detailed model uses a two-dimensional finite control volume method, whereas the simpler model uses a one-dimensional thermal resistance approach. The numerical modeling concepts presented are applicable to conventional tube-type solar receivers, as well as to reflux receivers. Good agreement between the two models is demonstrated by comparing the predicted and measured performance of a pool-boiler reflux receiver being tested at Sandia. For design operating conditions, the receiver thermal efficiencies agree within 1 percent and the average receiver cavity temperature within 1.3 percent. The thermal efficiency and receiver temperatures predicted by the simpler thermal resistance model agree well with experimental data from on-sun tests of the Sandia reflux pool-boiler receiver. An analysis of these comparisons identifies several plausible explanations for the differences between the predicted results and the experimental data.

A Methodology and Tutorial for Thermal Modeling with PC Spreadsheets

Personal computer spreadsheet programs are widely recognized for their business applications but are also well suited for performing numerical thermal analysis. Following a description of the basic steps in numerical thermal modeling, the methodology of implementing spreadsheet solutions is presented. Memory requirements, iteration time, and the structure for parametric studies are discussed. Three techniques for deriving the nodal equations used in numerical thermal modeling are given in detail, Included are the finite-difference approach, the energy balance approach, and the thermal resistance approach. The paper concludes with a detailed example showing how to implement a spreadsheet numerical solution for two-dimensional heat flow through a plate. Heat flux, insulated, isothermal, and convecting boundaries are illustrated.