scholarly journals Optimal Estimation of Thermal Diffusivity in a Thermal Energy Transfer Problem with Heat Generation, Convection Dissipation and Lateral Heat Flow

2021 ◽  
Vol 16 ◽  
pp. 222-231
Author(s):  
Guillermo F. Umbricht ◽  
Diana Rubio
Keyword(s):  
Thermal Diffusivity ◽  
Optimal Design ◽  
Heat Generation ◽  
Transfer Problem ◽  
Optimal Estimation ◽  
Dirichlet Condition ◽  
Heat Transfer Process ◽  
Relative Errors ◽  
Moving Fluid ◽  
Lateral Heat

This work focuses on determining the coefficient of thermal diffusivity in a one-dimensional heat transfer process along a homogeneous and isotropic bar, embedded in a moving fluid with heat generation. A first type (Dirichlet) condition is imposed on one boundary and a third type (Robin) condition is considered at the other one. The parameter is estimated by minimizing the squared errors where noisy observations are numerically simulated at different positions and instants. The results are evaluated by means of the relative errors for different levels of noise. In order to enhance the estimation performance, an optimal design technique is chosen to select the most informative data. Finally, the improvement of the estimate is discussed when an optimal design is used.

Thermal Properties of Thin Metallic Layer Deposited on Insulators: Effect of the Interface on the Independent Determination of the Thermal Diffusivity and Conductivity of the Layer

2008 ◽  
Author(s):  
Danie`le Fournier ◽  
Jean Paul Roger ◽  
Christian Fretigny
Keyword(s):  
Thermal Conductivity ◽  
Thermal Properties ◽  
Thermal Diffusivity ◽  
Thermal Resistance ◽  
Thermal Contact ◽  
Heat Diffusion ◽  
Metallic Layer ◽  
Good Thermal Contact ◽  
Lateral Heat

Lateral heat diffusion thermoreflectance is a very powerful tool for determining directly the thermal diffusivity of layered structures. To do that, experimental data are fitted with the help of a heat diffusion model in which the ratio between the thermal conductivity k and the thermal diffusivity D of each layer is fixed, and the thermal properties of the substrate are known. We have shown in a previous work that it is possible to determine independently the thermal diffusivity and the thermal conductivity of a metallic layer deposited on an insulator, by taking into consideration all the data obtained at different modulation frequencies. Moreover, it is well known that to prevent a lack of adhesion of a gold film deposited on substrates like silica, an intermediate very thin (Cr or Ti) layer is deposited to assure a good thermal contact. We extend our previous work: the asymptotic behaviour determination of the surface temperature wave at large distances from the modulated point heat source for one layer deposited on the substrate to the two layers model. In this case (very thin adhesion coating whose thermal properties and thickness are known), it can be establish that the thermal diffusivity and the thermal conductivity of the top layer can still be determined independently. It is interesting to underline that the calculus can also be extended to the case of a thermal contact resistance which has often to be taken into account between two solids. We call thermal resistance a very thin layer exhibiting a very low thermal conductivity. In this case, the three parameters we have to determine are the thermal conductivity and the thermal diffusivity of the layer and the thermal resistance. We will show that, in this case, the thermal conductivity of the layer is always obtained independently of a bound of the couple thermal resistance – thermal diffusivity, the thermal diffusivity being under bounded and the thermal resistance lower bounded. Experimental results on thin gold layers deposited on silica with and without adhesion layers are presented to illustrate the method. Discussions on the accuracy will also be presented.

Lateral heat flow method for thickness independent determination of thermal diffusivity

2007 ◽  
Vol 102 (8) ◽  
pp. 083522 ◽  
Author(s):  
Nilesh Tralshawala ◽  
Donald R. Howard ◽  
Bryon Knight ◽  
Yuri Plotnikov ◽  
Harry I. Ringermacher
Keyword(s):  
Thermal Diffusivity ◽  
Heat Flow ◽  
Flow Method ◽  
Independent Determination ◽  
Thickness Independent ◽  
Lateral Heat

Independent Determination of the Thermal Diffusivity and Conductivity of a Thin Metallic Layer Deposited on Silica

2008 ◽  
Author(s):  
Christian Fretigny ◽  
Jean Paul Roger ◽  
Li Liu ◽  
Danie`le Fournier
Keyword(s):  
Thermal Diffusivity ◽  
Careful Analysis ◽  
Thin Layers ◽  
Heat Diffusion ◽  
Bulk Materials ◽  
Thermal Insulator ◽  
Independent Determination ◽  
Lateral Temperature ◽  
Lateral Heat

It is well known that the thermal parameters of materials confined in thin layers may significantly differ from their bulk value. Lateral heat diffusion thermoreflectance experiment is a very powerful tool for determining directly the thermal diffusivity of bulk materials and of layered structure. Nevertheless, in the latter case, experimental data are fitted with the help of a heat diffusion model in which the layer thermal conductivity and thermal diffusivity are taken together into consideration. In this paper, we show that both parameters can be determined independently, in the case of a thermal conductive layer deposited on a thermal insulator, with a careful analysis of the amplitude and the phase of the lateral temperature field associated to a point source.

Accurate Thermal Diffusivity Measurements Using a Modified Ångström's Method With Bayesian Statistics

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Yuan Hu ◽  
Timothy S. Fisher
Keyword(s):  
Thermal Diffusivity ◽  
Probability Distribution Function ◽  
Transfer Problem ◽  
Temperature Fluctuations ◽  
Infinite Medium ◽  
One Dimension ◽  
Ambient Conditions ◽  
Diffusivity Measurements ◽  
Inverse Heat Transfer ◽  
Inverse Heat Transfer Problem

Abstract This work reports a custom instrument that employs a modified Ångström's method to measure the thermal diffusivity of foil-like materials in which heat propagates in one dimension. This method does not require a semi-infinite medium assumption as compared to the original Ångström's method, which also has been typically performed in vacuum. However, in this work, temperature measurements are performed in laboratory ambient conditions, which are more convenient for most experiments. To quantify and reduce uncertainties due to temperature fluctuations in noisy ambient conditions, a Bayesian framework and Metropolis algorithm are employed to solve the inverse heat transfer problem and to obtain a probability distribution function for thermal diffusivity. To demonstrate the effectiveness of the custom instrument, the thermal diffusivity of a copper 110 foil (25.0 mm long, 7.0 mm wide, and 76.2 μm thick) was measured in ambient conditions, and the results match well with previous studies performed in vacuum conditions on much longer samples.

Experimental Study on Transient Heat Transfer for Helium Gas Flowing in a Minichannel

2020 ◽  
Author(s):  
Feng Xu ◽  
Qiusheng Liu ◽  
Satoshi Kawaguchi ◽  
Makoto Shibahara
Keyword(s):  
Heat Transfer ◽  
Heat Generation ◽  
Heat Transfer Process ◽  
Test Tube ◽  
Generation Rate ◽  
Transient Heat Transfer ◽  
Heat Generation Rate ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Helium Gas

Abstract The blanket modules of first wall need bear tremendous heat flux due to the very high temperature of plasma in the nuclear fusion reactor. Therefore, it is significant to clarify the knowledge of transient heat transfer process for helium gas flowing in the tubes installed in the blanket modules. In this research, the transient heat transfer process of turbulent forced convection for helium gas flowing in a horizontal minichannel was experimentally investigated. The test tube made of platinum with the inner diameter of 1.8 mm, the wall thickness of 0.1 mm and the effective length of 90 mm was heated by a direct current from power source. The heat generation rate of the test tube, Q̇, was raised with an exponential function, Q̇ = Q0 exp(t/τ), where Q0 is the initial heat generation rate, t is time, and τ is e-folding time of heat generation rate. The heat generation rates of the test tube were controlled and measured by a heat input control system. The flow rates were adjusted by the bypass of gas loop and measured by the turbine flow meter. The experiment was conducted under the e-folding time of heat generation rate ranged from 40 ms to 15 s. Based on experimental data, it is obvious that the heat flux and temperature difference between surface temperature of test tube and bulk temperature of helium gas increased with the exponentially increasing of heat generation rate. At the same flow velocity, the heat transfer coefficients approached constant values when the e-folding time is longer than about 1 s (quasi-steady state), but increased with a decrease of e-folding time when the e-folding time is smaller than about 1 s (transient state). The heat transfer coefficients increased with the increase in flow velocities but showed less dependent on flow velocities at shorter e-folding time. Furthermore, the Nusselt number under quasi-steady and transient condition was affected by the Reynolds number and the Fourier number.

scholarly journals Thermal Diffusivity Identification of Distributed Parameter Systems to Sea Ice

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Liqiong Shi ◽  
Zhijun Li ◽  
Enmin Feng ◽  
Yila Bai ◽  
Yu Yang
Keyword(s):  
Optimal Control ◽  
Thermal Diffusivity ◽  
Sea Ice ◽  
Transfer Problem ◽  
Control Model ◽  
Performance Criterion ◽  
Distributed Parameter Systems ◽  
Parabolic Partial Differential Equation ◽  
Distributed Parameter ◽  
Computational Errors

A method of optimal control is presented as a numerical tool for solving the sea ice heat transfer problem governed by a parabolic partial differential equation. Taken the deviation between the calculated ice temperature and the measurements as the performance criterion, an optimal control model of distributed parameter systems with specific constraints of thermal properties of sea ice was proposed to determine the thermal diffusivity of sea ice. Based on sea ice physical processes, the parameterization of the thermal diffusivity was derived through field data. The simulation results illustrated that the identified parameterization of the thermal diffusivity is reasonably effective in sea ice thermodynamics. The direct relation between the thermal diffusivity of sea ice and ice porosity is physically significant and can considerably reduce the computational errors. The successful application of this method also explained that the optimal control model of distributed parameter systems in conjunction with the engineering background has great potential in dealing with practical problems.

Thermal Diffusivity Determination of High-Temperature Levitated Oblate Spheroidal Specimen by a Flash Method

1998 ◽  
Vol 120 (3) ◽  
pp. 777-781 ◽  
Author(s):  
F. Shen ◽  
J. M. Khodadadi
Keyword(s):  
Thermal Diffusivity ◽  
Transfer Problem ◽  
Oblate Spheroid ◽  
Single Step ◽  
Flash Method ◽  
Conduction Heat Transfer ◽  
Oblate Spheroidal ◽  
Flash Technique ◽  
Transient Conduction

In extending the range of applicability of a recently developed method, a single-step containerless flash technique for determining the thermal diffusivity of levitated oblate spheroidal oblate spheroidal samples is proposed. The flash method is modeled as an axisymmetric transient conduction heat transfer problem within the oblate spheroid. It is shown that by knowing the sample geometric parameters and recording the temperature rise history at least at two different points on the surface simultaneously, the thermal diffusivity can be determined without knowing needed for determining the thermal diffusivity of oblate spheroidal samples are provided.

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