Volumetric Heat Capacity Enhancement in Thin Films of Amorphous Fluorocarbon Polymers

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Hongxiang Tian ◽  
Marc G. Ghossoub ◽  
Oksen T. Baris ◽  
Jun Ma ◽  
Murli Tirumala ◽  
...  
Keyword(s):  
Heat Capacity ◽  
Film Thickness ◽  
Heat Diffusion ◽  
Volumetric Heat Capacity ◽  
Dimensional Solution ◽  
Heat Diffusion Equation ◽  
Adhesion Promoters ◽  
Capacity Enhancement ◽  
Ultrathin Layers ◽  
Transient Heat Diffusion

Plasma deposited amorphous fluorocarbon polymers find use in biopassivation, and as low-friction coatings, adhesion promoters, and interlayer dielectrics. Here, we exploit their ease of deposition into ultrathin layers (<50 nm thick) to explore their potential as thermal storage elements. We design and fabricate a microcalorimeter for measuring the heat capacity of thin fluorocarbons. Conventional thin film calorimetry assumes adiabatic conditions that lead to large errors as film thickness decreases. We propose a new data analysis procedure that incorporates a one-dimensional solution of the transient heat diffusion equation to account for conduction losses. The data for films with thicknesses in the range 12–27 nm reveal a lowering of the melting point and an increase in the volumetric heat capacity with decreasing thickness. We attribute this to change in the carbon to fluorine ratio in the films’ composition. The volumetric heat capacity approximately doubles at room temperature as the film thickness decreases from 27 nm to 12 nm.

scholarly journals Evaluation of the reliability of building energy performance models for parameter estimation

2019 ◽  
Author(s):  
  Жулиан Берже ◽  
  Денис Дутых
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Capacity ◽  
Parameter Estimation ◽  
Heat Transfer Coefficient ◽  
Diffusion Equation ◽  
Heat Diffusion ◽  
Unknown Parameters ◽  
Heat Diffusion Equation ◽  
The Heat Transfer Coefficient

The fidelity of a model relies both on its accuracy to predict the physical phenomena and its capability to estimate unknown parameters using observations. This article focuses on this second aspect by analyzing the reliability of two mathematical models proposed in the literature for the simulation of heat losses through building walls. The first one, named DF, is the classical heat diffusion equation combined with the DuFort-Frankel numerical scheme. The second is the so-called RC lumped approach, based on a simple ordinary differential equation to compute the temperature within the wall. The reliability is evaluated following a two stages method. First, samples of observations are generated using a pseudo-spectral numerical model for the heat diffusion equation with known input parameters. The results are then modified by adding a noise to simulate experimental measurements. Then, for each sample of observation, the parameter estimation problem is solved using one of the two mathematical models. The reliability is assessed based on the accuracy of the approach to recover the unknown parameter. Three case studies are considered for the estimation of ( i ) the heat capacity, ( ii ) the thermal conductivity or ( iii ) the heat transfer coefficient at the interface between the wall and the ambient air. For all cases, the DF mathematical model has a very satisfactory reliability to estimate the unknown parameters without any bias. However, the RC model lacks of fidelity and reliability. The error on the estimated parameter can reach 40% for the heat capacity, 80% for the thermal conductivity and 450% for the heat transfer coefficient.

Convergence and error analysis of an automatically differentiated finite volume based heat conduction code

2019 ◽  
Vol 29 (7) ◽  
pp. 2389-2406
Author(s):  
Christopher DeGroot
Keyword(s):  
Heat Conduction ◽  
Finite Volume ◽  
Automatic Differentiation ◽  
Heat Diffusion ◽  
Reconstruction Method ◽  
Heat Diffusion Equation ◽  
Content Type ◽  
Discretization Schemes ◽  
Transient Heat Diffusion ◽  
Volume Method

Purpose This paper aims to investigate the convergence and error properties of a finite volume-based heat conduction code that uses automatic differentiation to evaluate derivatives of solutions outputs with respect to arbitrary solution input(s). A problem involving conduction in a plane wall with convection at its surfaces is used as a test problem, as it has an analytical solution, and the error can be evaluated directly. Design/methodology/approach The finite volume method is used to discretize the transient heat diffusion equation with constant thermophysical properties. The discretized problem is then linearized, which results in two linear systems; one for the primary solution field and one for the secondary field, representing the derivative of the primary field with respect to the selected input(s). Derivatives required in the formation of the secondary linear system are obtained by automatic differentiation using an operator overloading and templating approach in C++. Findings The temporal and spatial discretization error for the derivative solution follows the same order of accuracy as the primary solution. Second-order accuracy of the spatial and temporal discretization schemes is confirmed for both primary and secondary problems using both orthogonal and non-orthogonal grids. However, it has been found that for non-orthogonal cases, there is a limit to the error reduction, which is concluded to be a result of errors in the Gauss-based gradient reconstruction method. Originality/value The convergence and error properties of derivative solutions obtained by forward mode automatic differentiation of finite volume-based codes have not been previously investigated.

scholarly journals Steady-state heat conduction in a medium with spatial non-singular fading memory: Derivation of Caputo-Fabrizio space-fractional derivative from Cattaneo concept with Jeffrey`s Kernel and analytical solutions

2017 ◽  
Vol 21 (2) ◽  
pp. 827-839 ◽  
Author(s):  
Jordan Hristov
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Fractional Derivative ◽  
Heat Diffusion ◽  
Fading Memory ◽  
Heat Diffusion Equation ◽  
Back Ground ◽  
Time Fractional Derivative ◽  
Steady State Heat ◽  
Transient Heat Diffusion

Starting from the Cattaneo constitutive relation with a Jeffrey's kernel the derivation of a transient heat diffusion equation with relaxation term expressed through the Caputo-Fabrizio time fractional derivative has been developed. This approach allows seeing the physical back ground of the newly defined Caputo-Fabrizio time fractional derivative and demonstrates how other constitutive equations could be modified with non-singular fading memories.

Fractional-Diffusion Solutions for Transient Local Temperature and Heat Flux

1999 ◽  
Vol 122 (2) ◽  
pp. 372-376 ◽  
Author(s):  
V. V. Kulish ◽  
J. L. Lage
Keyword(s):  
Heat Flux ◽  
Diffusion Equation ◽  
Local Time ◽  
Simple Relation ◽  
Solution Procedure ◽  
Heat Diffusion ◽  
Time Varying ◽  
Infinite Domain ◽  
Heat Diffusion Equation ◽  
Transient Heat Diffusion

Applying properties of the Laplace transform, the transient heat diffusion equation can be transformed into a fractional (extraordinary) differential equation. This equation can then be modified, using the Fourier Law, into a unique expression relating the local value of the time-varying temperature (or heat flux) and the corresponding transient heat flux (or temperature). We demonstrate that the transformation into a fractional equation requires the assumption of unidirectional heat transport through a semi-infinite domain. Even considering this limitation, the transformed equation leads to a very simple relation between local time-varying temperature and heat flux. When applied along the boundary of the domain, the analytical expression determines the local time-variation of surface temperature (or heat flux) without having to solve the diffusion equation within the entire domain. The simplicity of the solution procedure, together with some introductory concepts of fractional derivatives, is highlighted considering some transient heat transfer problems with known analytical solutions. [S0022-1481(00)01002-1]

Mathematical modelling of temperature profile of volcanic soils affected by an external thermal impact

Soil Research ◽  
2006 ◽  
Vol 44 (1) ◽  
pp. 57 ◽  
Author(s):  
Mónica Antilén ◽  
Olivier Fudym ◽  
Alvaro Vidal ◽  
Juan E. Foerster ◽  
Nelson Moraga ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Soil Temperature ◽  
Temperature Profile ◽  
Soil Surface ◽  
Heat Diffusion ◽  
Volcanic Soils ◽  
Heat Diffusion Equation ◽  
Transient Heat Diffusion ◽  
Relative Errors ◽  
The Mathematical Model

In this work, the soil temperature at depth was measured in the laboratory, and a mathematical model to fit the temperature profile in volcanic soils classified as Ultisols and Andisols was used. The mathematical model considered the transient heat diffusion equation, and a numerical discrete method was used to solve the equations system. The soil surface was heated for 2500 s and the temperature rose close to 700°C; the soil temperature decreased with depth; the temperature v. time curves showed a constant value when the temperature reached around 100°C, associated with water phase change and related to the water content of soils. The model was corrected by including the heat volumetric formulation. The observed relative errors are close to 10% in all fitted curves with respect to experimental data, showing the quality of the parametrisation chosen in the mathematical model. The fitting curve deviations were reduced when the actual position of thermocouples was considered, showing the sensitivity of the mathematical model. The simplified mathematical transient diffusion model proposed, which considers 2 ranges of thermal conductivity of soils and the surface temperature, was able to describe the experimental temperature profile in volcanic soils with wide differences in mineralogy, organic matter, and moisture contents.

scholarly journals Testing a Gypsum Composite Based on Raw Gypsum with a Direct Admixture of Paraffin and Polymer to Improve Thermal Properties

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3241
Author(s):  
Krzysztof Powała ◽  
Andrzej Obraniak ◽  
Dariusz Heim
Keyword(s):  
Thermal Conductivity ◽  
Heat Capacity ◽  
Thermal Properties ◽  
Phase Change ◽  
Large Scale ◽  
Building Materials ◽  
Residential Buildings ◽  
Energy Performance ◽  
Polymer Content ◽  
Volumetric Heat Capacity

The implemented new legal regulations regarding thermal comfort, the energy performance of residential buildings, and proecological requirements require the design of new building materials, the use of which will improve the thermal efficiency of newly built and renovated buildings. Therefore, many companies producing building materials strive to improve the properties of their products by reducing the weight of the materials, increasing their mechanical properties, and improving their insulating properties. Currently, there are solutions in phase-change materials (PCM) production technology, such as microencapsulation, but its application on a large scale is extremely costly. This paper presents a solution to the abovementioned problem through the creation and testing of a composite, i.e., a new mixture of gypsum, paraffin, and polymer, which can be used in the production of plasterboard. The presented solution uses a material (PCM) which improves the thermal properties of the composite by taking advantage of the phase-change phenomenon. The study analyzes the influence of polymer content in the total mass of a composite in relation to its thermal conductivity, volumetric heat capacity, and diffusivity. Based on the results contained in this article, the best solution appears to be a mixture with 0.1% polymer content. It is definitely visible in the tests which use drying, hardening time, and paraffin absorption. It differs slightly from the best result in the thermal conductivity test, while it is comparable in terms of volumetric heat capacity and differs slightly from the best result in the thermal diffusivity test.

Mapping Thickness Dependent Thermal Conductivity of GaN

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Elbara Ziade ◽  
Jia Yang ◽  
Gordie Brummer ◽  
Denis Nothern ◽  
Theodore Moustaks ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Pump Beam ◽  
Continuous Wave ◽  
High Electron Mobility Transistors ◽  
Heat Diffusion ◽  
Phase Lag ◽  
High Electron ◽  
Heat Diffusion Equation ◽  
Phase Images ◽  
Gan Film

Frequency domain thermoreflectance (FDTR) is used to create quantitative maps of thermal conductivity and thickness for a thinning gallium nitride (GaN) film on silicon carbide (SiC). GaN was grown by molecular beam epitaxy on a 4H-SiC substrate with a gradient in the film thickness found near the edge of the chip. The sample was then coated with a 5 nm nickel adhesion layer and a 85 nm gold transducer layer for the FDTR measurement. A piezo stage raster scans the sample to create phase images at different frequencies. For each pixel, a periodically modulated continuous-wave laser (the red pump beam) is focused to a Gaussian spot, less than 2 um in diameter, to locally heat the sample, while a second beam (the green probe beam) monitors the surface temperature through a proportional change in the reflectivity of gold. The pump beam is modulated simultaneously at six frequencies and the thermal conductivity and thickness of the GaN film are extracted by minimizing the error between the measured probe phase lag at each frequency and an analytical solution to the heat diffusion equation in a multilayer stack of materials. A scanning electron microscope image verifies the thinning GaN. We mark the imaged area with a red box. A schematic of the GaN sample in our measurement system is shown in the top right corner, along with the two fitting properties highlighted with a red box. We show the six phase images and the two obtained property maps: thickness and thermal conductivity of the GaN. Our results indicate a thickness dependent thermal conductivity of GaN, which has implications of thermal management in GaN-based high electron mobility transistors.

Fast Fluid Thermodynamics Simulation by Solving Heat Diffusion Equation

2021 ◽  
Vol 11 (04) ◽  
pp. 1-11
Author(s):  
Wanwan Li
Keyword(s):  
Diffusion Equation ◽  
Real Time ◽  
Stokes Equations ◽  
Fluid Simulation ◽  
Heat Diffusion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Heat Diffusion Equation ◽  
Acceleration Techniques ◽  
Speed Up

In mechanical engineering educations, simulating fluid thermodynamics is rather helpful for students to understand the fluid’s natural behaviors. However, rendering both high-quality and realtime simulations for fluid dynamics are rather challenging tasks due to their intensive computations. So, in order to speed up the simulations, we have taken advantage of GPU acceleration techniques to simulate interactive fluid thermodynamics in real-time. In this paper, we present an elegant, basic, but practical OpenGL/SL framework for fluid simulation with a heat map rendering. By solving Navier-Stokes equations coupled with the heat diffusion equation, we validate our framework through some real-case studies of the smoke-like fluid rendering such as their interactions with moving obstacles and their heat diffusion effects. As shown in Fig. 1, a group of experimental results demonstrates that our GPU-accelerated solver of Navier-Stokes equations with heat transfer could give the observers impressive real-time and realistic rendering results.

scholarly journals Impact of spineless cactus cultivation (O. Ficus-indica) on the thermal characteristics of soil

2018 ◽  
Vol 13 (1) ◽  
pp. 1
Author(s):  
Willames De Albuquerque Soares
Keyword(s):  
Heat Capacity ◽  
Thermal Characteristics ◽  
Thermal Characterization ◽  
Biological Processes ◽  
Volumetric Heat Capacity ◽  
Average Value ◽  
Brazilian Semiarid ◽  
Cultivation Techniques ◽  
Soil Changes

Temperature is a fundamentally important factor for understanding the physical, chemical, and biological processes that occur in soil. However, there are few studies in the Brazilian semiarid zone that seek to understand how soil degradation affects its thermal characteristics. The objective of this study was to evaluate the influence of cultivation techniques on the thermal characterization of soil, using the model proposed by Johansen. The study was conducted in the Agreste region of the state of Pernambuco, Brazil on two plots of land, one with native vegetation (Caatinga) and the other with spineless cactus (O. ficus - indica). It was observed that the procedures used to prepare the soil for cultivation of spineless cactus caused a reduction in the capacity to transmit the surface temperature to the interior of the soil. Changes in the physical properties of the soil required for cultivation resulted in a reduction in the average value of the volumetric heat capacity of about 22%; an increase of approximately 5% in the average volumetric heat capacity and a 26% increase in the thermal diffusivity of the soil, as well as a reduction of approximately 50% in the heat flux from the surface of the soil.

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