scholarly journals Mathematical apparatus for determination of homogenous scalar medium thermal resistance

Vestnik MGSU ◽  
2019 ◽  
pp. 1037-1045
Author(s):  
Tatiana A. Musorina, ◽  
Michail R. Petritchenko ◽  
Daria D. Zaborova
Keyword(s):  
Thermal Conductivity ◽  
Heat Flow ◽  
Thermal Resistance ◽  
Heat Conducting ◽  
Heat Flow Rate ◽  
Conductivity Equation ◽  
Total Thermal Resistance ◽  
Active Resistance ◽  
One Dimensional

Introduction: the article suggests a method for determining a thermal resistance of small and large-sized areas (one-dimensional and multidimensional problems) of wall enclosure. The subject of the study is the thermal resistance of homogeneous scalar medium (homogeneous wall enclosure). The aim is the determination of thermal resistance of a wall structure for areas of arbitrary dimension (by the coordinates xi, where 1 ≤ i ≤ d and d is the area dimension) filled with a scalar (homogeneous and isotropic) heat-conducting medium. Materials and methods: the article used the following physical laws: Fourier law (the value of the heat flow when transferring heat through thermal conductivity) and continuity condition for the heat flow rate leading to the thermal conductivity equation. Results: this method extends the standard definition of thermal resistance. The research proved that the active thermal resistance does not increase with increasing of the area dimension (for example, when switching from a thin shell or plate to a rectangle with length and width of the same order of magnitude). That is the sense of geometric inclusion, i.e., increase of the dimension of an area filled with a homogeneous isotropic medium. Evident expressions are obtained for the determination of active, reactive, and total thermal resistance. It is proved that the total resistance is higher than the active resistance since the reactive resistance is positive, and the wall possesses an ability to suppress the temperature fluctuations and accumulate/give up the heat. Conclusions: the appearance of an additional wall dimension (comparable length-to-thickness ratio) does not increase its active resistance. In the general case, the total thermal resistance exceeds the active thermal resistance no more than four times. Geometric inclusions must be considered in the calculation of wall enclosures that are variant from one-dimensional bodies.

Cylindrical probe with a variable heat flow rate: A new method for the determination of formation thermal conductivity

2013 ◽  
Vol 5 (4) ◽  
Author(s):  
Lev Eppelbaum ◽  
Izzy Kutasov
Keyword(s):  
Thermal Conductivity ◽  
Heat Flow ◽  
Flow Rate ◽  
Dry Density ◽  
Heat Flow Rate ◽  
Cylindrical Probe ◽  
Variable Heat ◽  
Variable Heat Flow

AbstractThe thermal conductivity of a geological formation is one of the important petrophysical parameters which are preferable to study in situ in geophysical well logs. A new technique for the determination of formation thermal conductivity has been developed. We assumed that formation dry density, porosity, and pore fluids saturations could be determined from core samples or cuttings. In this case the specific heat and density of a formation can be quantitatively estimated. It is also assumed that the instantaneous heat flow rate and time data are available for a cylindrical probe with a variable heat flow rate placed in a wellbore. A semi-theoretical equation describing the temperature of the probe’s wall is used to determine in situ the formation conductivity as a function of the temperature increase. The formation thermal diffusivity is also calculated. A field example is presented.

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.

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.

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