scholarly journals Avoiding Being Trapped in False Analogical Modeling of Composite Wall Thermal Resistance

2018 ◽  
Vol 1 (2) ◽  
pp. 69-77
Author(s):  
Mohammed Aliedeh*
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Flow ◽  
Thermal Resistance ◽  
Detailed Calculation ◽  
True Value ◽  
Parallel Wall ◽  
Composite Wall ◽  
The Difference ◽  
Composite Walls

Because Analogy is considered as a double-edged sword, thermal engineers should be cautious in analogical maneuvering between electrical and thermal domains in order not to be slipped into building misconceptions about thermal resistance concept. Composite wall thermal resistance (CWTR) modeling is one of the practical examples that illustrates the probability of misusing analogy. Heat transfer undergraduate textbooks coverage of CWTR suffers a lean towards “cookbook” coverage that reports concise statements that lack deep clarification and illustration. Transparent Thinking Approach (TTA) is employed to present a detailed calculation and illustration of a typical CWTR modeling based on isothermal and adiabatic assumptions. The calculation of a typical CWTR for different values of wall thermal conductivities shows that the difference in parallel walls thermal conductivity is creating a large discrepancy that may reach 80% between heat flows calculated based on isothermal and adiabatic assumptions. It is found that for a series-parallel arrangement of composite walls with high difference in parallel wall thermal conductivity values, the true value of heat flow is bracketed between the isothermal and adiabatic heat flow values. The transparent way of presenting CWTR modeling can be readily included in any standard heat transfer textbook and result in greatly enhancing CWTR modeling coverage.

Theoretical Investigation on Effective Thermal Conductivity of a Disk-Shaped Composite System

2010 ◽  
Author(s):  
Yasushi Koito ◽  
Toshio Tomimura ◽  
Shuichi Torii
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Effective Thermal Conductivity ◽  
Composite System ◽  
Microsoft Excel ◽  
Resistance Network ◽  
Estimation Equations ◽  
The Difference ◽  
Wiring Board

This paper addresses the methodology to estimate the effective thermal conductivity of the wiring board, where the metal wiring network is very complicated and then the thermal conductivity of the metal wiring is more than 1000 times higher than that of the resign board. Based on the concept of analogy between the electric and the thermal resistance network, two types of estimation equations are derived by dividing the composite system parallel or perpendicular to the heated/cooled surface. When the ratio of higher to lower thermal conductivities is less than 10, the estimated values by these equations agree with each other. However, the difference is clearly found between them when the ratio is larger than 100. The estimated values are moreover compared with the exact solutions, which are obtained by numerical simulation of heat transfer using Microsoft Excel, and then the applicability of the present estimation methodology is discussed. It is found that the thermal resistance network obtained by dividing the composite system perpendicular to the heated/cooled surface is effective to estimate the effective thermal conductivity of the composite system.

Heat transfer in liquid helium below 1°K

1955 ◽  
Vol 231 (1187) ◽  
pp. 545-555 ◽  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Flow ◽  
Temperature Gradient ◽  
Thermal Resistance ◽  
Specific Heat ◽  
Liquid Helium ◽  
Practical Importance ◽  
Heat Pulses

The thermal conductivity of liquid helium has been measured between 0.2 and 1.0° K. Below 0.6° K the heat flow is exactly proportional to the temperature gradient and the thermal conductivity is proportional to the specific heat and the diameter of the specimen. Thus the sole mechanism of heat transfer appears to be by phonons which are scattered only at the boundaries of the specimen. These results are in satisfactory accord with previous theoretical discussions and with measurements of the propagation of heat pulses in the liquid. The experiment also afforded the opportunity of making subsidiary measurements of the thermal resistance of the boundary between a metal and liquid helium. Besides being of practical importance, the results show that some modification is called for in the existing theoretical treatments.

scholarly journals Thermal conductivity of sandstones from Biot’s coefficient

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. D173-D185 ◽  
Author(s):  
Tobias Orlander ◽  
Eirini Adamopoulou ◽  
Janus Jerver Asmussen ◽  
Adam Andrzej Marczyński ◽  
Harald Milsch ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Flow ◽  
Cross Section ◽  
Geometric Mean ◽  
Well Log ◽  
Biot’S Coefficient ◽  
Model Predictions ◽  
The Cross ◽  
Rock Texture

Thermal conductivity of rocks is typically measured on core samples and cannot be directly measured from logs. We have developed a method to estimate thermal conductivity from logging data, where the key parameter is rock elasticity. This will be relevant for the subsurface industry. Present models for thermal conductivity are typically based primarily on porosity and are limited by inherent constraints and inadequate characterization of the rock texture and can therefore be inaccurate. Provided known or estimated mineralogy, we have developed a theoretical model for prediction of thermal conductivity with application to sandstones. Input parameters are derived from standard logging campaigns through conventional log interpretation. The model is formulated from a simplified rock cube enclosed in a unit volume, where a 1D heat flow passes through constituents in three parallel heat paths: solid, fluid, and solid-fluid in series. The cross section of each path perpendicular to the heat flow represents the rock texture: (1) The cross section with heat transfer through the solid alone is limited by grain contacts, and it is equal to the area governing the material stiffness and quantified through Biot’s coefficient. (2) The cross section with heat transfer through the fluid alone is equal to the area governing fluid flow in the same direction and quantified by a factor analogous to Kozeny’s factor for permeability. (3) The residual cross section involves the residual constituents in the solid-fluid heat path. By using laboratory data for outcrop sandstones and well-log data from a Triassic sandstone formation in Denmark, we compared measured thermal conductivity with our model predictions as well as to the more conventional porosity-based geometric mean. For outcrop material, we find good agreement with model predictions from our work and with the geometric mean, whereas when using well-log data, our model predictions indicate better agreement.

scholarly journals The Influence of Burial Depth and Soil Thermal Conductivity on Heat Transfer in Buried CO2 Pipelines for CCS: A Parametric Study

2020 ◽  
Author(s):  
Babafemi Olugunwa ◽  
Julia Race ◽  
Tahsin Tezdogan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Thermal Resistance ◽  
Parametric Study ◽  
Flow Assurance ◽  
Burial Depth ◽  
Soil Thermal Conductivity ◽  
Dense Phase ◽  
Pipeline Transportation

Abstract Pipeline heat transfer modelling of buried pipelines is integral to the design and operation of onshore pipelines to aid the reduction of flow assurance challenges such as carbon dioxide (CO2) gas hydrate formation during pipeline transportation of dense phase CO2 in carbon capture and storage (CCS) applications. In CO2 pipelines for CCS, there are still challenges and gaps in knowledge in the pipeline transportation of supercritical CO2 due to its unique thermophysical properties as a single, dense phase liquid above its critical point. Although the design and operation of pipelines for bulk fluid transport is well established, the design stage is incomplete without the heat transfer calculations as part of the steady state hydraulic and flow assurance design stages. This paper investigates the steady state heat transfer in a buried onshore dense phase CO2 pipelines analytically using the conduction shape factor and thermal resistance method to evaluate for the heat loss from an uninsulated pipeline. A parametric study that critically analyses the effect of variation in pipeline burial depth and soil thermal conductivity on the heat transfer rate, soil thermal resistance and the overall heat transfer coefficient (OHTC) is investigated. This is done using a one-dimensional heat conduction model at constant temperature of the dense phase CO2 fluid. The results presented show that the influence of soil thermal conductivity and pipeline burial depth on the rate of heat transfer, soil thermal resistance and OHTC is dependent on the average constant ambient temperature in buried dense phase CO2 onshore pipelines. Modelling results show that there are significant effects of the ambient natural convection on the soil temperature distribution which creates a thermal influence region in the soil along the pipeline that cannot be ignored in the steady state modelling and as such should be modelled as a conjugate heat transfer problem during pipeline design.

scholarly journals Numerical Simulation of Thermal Conductivity of Foam Glass Based on the Steady-State Method

Materials ◽  
2018 ◽  
Vol 12 (1) ◽  
pp. 54 ◽  
Author(s):  
Zipeng Qin ◽  
Gang Li ◽  
Yan Tian ◽  
Yuwei Ma ◽  
Pengfei Shen
Keyword(s):  
Thermal Conductivity ◽  
Steady State ◽  
Heat Flow ◽  
Thermal Resistance ◽  
Thermal Insulation ◽  
Foam Glass ◽  
Orthogonal Experimental Design ◽  
Carbonate Content ◽  
Steady State Method ◽  
State Method

The effects of fly ash, sodium carbonate content, foaming temperature and foaming time on foam glass aperture sizes and their distribution were analyzed by the orthogonal experimental design. Results from the steady-state method showed a normal distribution of the number of apertures with change in average aperture, which ranges from 0.1 to 2.0 mm for more than 93% of apertures. For a given porosity, the thermal conductivity decreases with the increase of the aperture size. The apertures in the sample have obvious effects in blocking the heat flow transmission: heat flow is quickly diverted to both sides when encountered with the aperture. When the thickness of the sample is constant, the thermal resistance of the foam glass sample increases with increasing porosity, leading to better thermal insulation. Furthermore, our results suggest that the more evenly distributed and orderly arranged the apertures are in the foam glass material, the larger the thermal resistance of the material and hence, the better the thermal insulation.

Effective Thermal Conductivity of Submicron Powders: A Numerical Study

2016 ◽  
Vol 846 ◽  
pp. 500-505
Author(s):  
Wei Jing Dai ◽  
Yi Xiang Gan ◽  
Dorian Hanaor
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Effective Thermal Conductivity ◽  
Granular Materials ◽  
Gas Phase ◽  
Numerical Study ◽  
Transfer Model ◽  
Size Of Particles ◽  
Contact Unit

Effective thermal conductivity is an important property of granular materials in engineering applications and industrial processes, including the blending and mixing of powders, sintering of ceramics and refractory metals, and electrochemical interactions in fuel cells and Li-ion batteries. The thermo-mechanical properties of granular materials with macroscopic particle sizes (above 1 mm) have been investigated experimentally and theoretically, but knowledge remains limited for materials consisting of micro/nanosized grains. In this work we study the effective thermal conductivity of micro/nanopowders under varying conditions of mechanical stress and gas pressure via the discrete thermal resistance method. In this proposed method, a unit cell of contact structure is regarded as one thermal resistor. Thermal transport between two contacting particles and through the gas phase (including conduction in the gas phase and heat transfer of solid-gas interfaces) are the main mechanisms. Due to the small size of particles, the gas phase is limited to a small volume and a simplified gas heat transfer model is applied considering the Knudsen number. During loading, changes in the gas volume and the contact area between particles are simulated by the finite element method. The thermal resistance of one contact unit is calculated through the combination of the heat transfer mechanisms. A simplified relationship between effective thermal conductivity and loading pressure can be obtained by integrating the contact units of the compacted powders.

scholarly journals Change in Conductive–Radiative Heat Transfer Mechanism Forced by Graphite Microfiller in Expanded Polystyrene Thermal Insulation—Experimental and Simulated Investigations

Materials ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 2626
Author(s):  
Aurelia Blazejczyk ◽  
Cezariusz Jastrzebski ◽  
Michał Wierzbicki
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Thermal Insulation ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Expanded Polystyrene ◽  
Transfer Mechanism ◽  
Total Thermal Conductivity ◽  
Heat Transfer Mechanism

This article introduces an innovative approach to the investigation of the conductive–radiative heat transfer mechanism in expanded polystyrene (EPS) thermal insulation at negligible convection. Closed-cell EPS foam (bulk density 14–17 kg·m−3) in the form of panels (of thickness 0.02–0.18 m) was tested with 1–15 µm graphite microparticles (GMP) at two different industrial concentrations (up to 4.3% of the EPS mass). A heat flow meter (HFM) was found to be precise enough to observe all thermal effects under study: the dependence of the total thermal conductivity on thickness, density, and GMP content, as well as the thermal resistance relative gain. An alternative explanation of the total thermal conductivity “thickness effect” is proposed. The conductive–radiative components of the total thermal conductivity were separated, by comparing measured (with and without Al-foil) and simulated (i.e., calculated based on data reported in the literature) results. This helps to elucidate why a small addition of GMP (below 4.3%) forces such an evident drop in total thermal conductivity, down to 0.03 W·m−1·K−1. As proposed, a physical cause is related to the change in mechanism of the heat transfer by conduction and radiation. The main accomplishment is discovering that the change forced by GMP in the polymer matrix thermal conduction may dominate the radiation change. Hence, the matrix conduction component change is considered to be the major cause of the observed drop in total thermal conductivity of EPS insulation. At the microscopic level of the molecules or chains (e.g., in polymers), significant differences observed in the intensity of Raman spectra and in the glass transition temperature increase on differential scanning calorimetry(DSC) thermograms, when comparing EPS foam with and without GMP, complementarily support the above statement. An additional practical achievement is finding the maximum thickness at which one may reduce the “grey” EPS insulating layer, with respect to “dotted” EPS at a required level of thermal resistance. In the case of the thickest (0.30 m) panels for a passive building, above 18% of thickness reduction is found to be possible.

Investigation of Interfacial Thermal Resistance on Nano-Structures Using Molecular Dynamics Simulations

2010 ◽  
Author(s):  
Navdeep Singh ◽  
Debjyoti Banerjee
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Carbon Nanotubes ◽  
Thermal Resistance ◽  
Md Simulations ◽  
Interfacial Thermal Resistance ◽  
Filler Materials ◽  
Nano Structures ◽  
Dynamics Simulations ◽  
Very High

Due to their very high thermal conductivity carbon nanotubes have been found to be an excellent material for thermal management. Experiments have shown that the heaters coated with carbon nanotubes increase the heat transfer by as much as 60%. Also when nanotubes are used as filler materials in composites, they tend to increase the thermal conductivity of the composites. But the increase in the heat transfer and the thermal conductivity has been found to be much less than the calculated values. This decrease has been attributed to the interfacial thermal resistance between the carbon nanotubes and the surrounding material. MD simulations were performed to study the interfacial thermal resistance between the carbon nanotubes and the liquid molecules. In the simulations, the nanotube is placed at the center of the simulation box and a temperature of 300K is imposed on the system. Then the temperature of the nanotube is raised instantaneously and the system is allowed to relax. From the temperature decay, the interfacial thermal resistance between the carbon nanotube and the liquid molecules is calculated. In this study the liquid molecules under investigation are n-heptane, n-tridecane and n-nonadecane.

scholarly journals Temperature measurements and heat transfer in near-surface snow at the South Pole

1997 ◽  
Vol 43 (144) ◽  
pp. 339-351 ◽  
Author(s):  
Richard E. Brandt ◽  
Stephen G. Warren
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Lower Boundary ◽  
Water Vapor Transport ◽  
South Pole ◽  
Near Surface ◽  
Temperature Changes ◽  
Surface Snow ◽  
Order Of Magnitude ◽  
The Difference

AbstractTo study near-surface heat flow on the Antarctíc ice sheet, snow temperatures were measured at South Pole Station to a depth of 3 m at 15 min intervals during most of 1992. Solar heating and water-vapor transport were negligible during the 6 month Winter, as was inter-grain net thermal radiation, leaving conduction as the dominant heat-transport mechanism. The rate of temperature change at depth over 15 min intervals was smaller than that at the surface, by one order of magnitude at 20 cm depth and two orders of magnitude at 1 m depth. A finite-difference model, with conduction as the only heat-transfer mechanism and measured temperatures as the upper and lower boundary conditions, was applied to foursets of three thermistors each. The thermal conductivity was estimated as that which minimized the difference between modeled and measured 15 min changes in temperatures at the center thermistor. The thermal conductivity obtained at shallow depths (above 40 cm) was lower than that given by existing parameterizations based on density, probably because the snow grains were freshly deposited, cold and poorly bonded. A model using only vertical conduction explains on average 87% ofthe observed 15 min temperature changes at less than 60 cm depth and 92% below 60 cm. The difference between modeled andmeasured temperature changes decreased with depth. The discrepancies between model and observation correlated more strongly with the air-snow temperature difference than with the product of that difference with the square of the wind speed,suggesting that the residual errors are due more to non-vertical conduction and to sub-grid-scale variabilis of the conductivity than to windpumping. The residual heating rate not explained by the model of vertical conduction exceeds 0.2 W m−3only in the top 60 cm of the near-surface snow.

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