On the influence of the size and packing of non-heat-conducting spherical pores on the thermal conductivity of porous bodies
Abstract Generated abstract
This article investigates how the size and spatial arrangement of non-heat-conducting spherical pores affect the effective thermal conductivity of porous bodies. Using the electrothermal analogy method, the authors modeled heat conduction through plane electrical specimens with pores of different diameters arranged in corridor, staggered, and arbitrary patterns, comparing their dimensionless electrical conductivity with the corresponding dimensionless thermal conductivity. The experimental results, plotted as conductivity versus porosity, showed only limited scatter attributed to measurement errors. The study concludes that, for the modeled conditions, the thermal conductivity of porous bodies depends on porosity but not on the size or packing arrangement of the non-heat-conducting pores.
Full Text
On the Influence of the Size and Packing of Non-Heat-Conducting Spherical Pores on the Thermal Conductivity of Porous Bodies
G. M. Serykh; T. A. Grechkina; A. I. Gnatyuk
(Presented by Prof. G. I. Fuks, Doctor of Technical Sciences)
In the heat-transfer laboratory of the Department of Theoretical Foundations of Heat Engineering at the Tomsk Polytechnic Institute, studies are being carried out on the thermal conductivity of porous materials. Some communications on this question are given in works [1], [2].
The present article sets forth the results of investigations into the influence of the size and packing of pores on the thermal conductivity of porous bodies in the case of non-heat-conducting pores of spherical form.
The investigation of this question is, above all, of theoretical significance. In addition, in engineering practice a number of porous bodies may, with sufficient approximation, be regarded as bodies with non-heat-conducting pores. Such bodies are porous bodies in which the thermal conductivity of the principal material is considerably greater than the thermal conductivity of the medium filling the pores.
The solution of the problem was carried out experimentally. The formal analogy between the processes of propagation of heat and of electricity in bodies described by identical differential equations makes it possible to study the phenomenon of thermal conductivity by means of the method of electrothermal analogies (ETA). In work [1] an experimental dependence between volume and plane porosity is given, which makes it possible to carry out electrical modeling of thermal processes in porous bodies on a plane electrical model.
Experimental Setup
The experiments were carried out on an apparatus for plane modeling, a description of which is given in work [1].
Measurements of the resistances of the specimens were made by a bridge circuit. A battery with an e.m.f. equal to 3 V was used as the power source; a sensitive galvanometer with a constant \(C = 1.8 \cdot 10^{-9}\) A was used as the null instrument. The constant of the bridge ratio arms was taken equal to \(1/10000\). The size of the model was \(432 \times 300\) mm. A part of the model measuring \(300 \times 300\) mm was taken as the specimen. During the experiments a constant temperature of the specimen and a constant e.m.f. of the power source were maintained.
Conduct of the Experiments
According to the ETA method, the ratio of the electrical conductivity of a porous specimen \(\mathcal{E}_{\mathrm{p}}\) to the electrical conductivity of a specimen without pores \(\mathcal{E}_{\mathrm{bp}}\) was regarded as the ratio of the thermal conductivity of the porous specimen \(\lambda_{\mathrm{p}}\) to the thermal conductivity of the specimen without pores \(\lambda_{\mathrm{bp}}\)
\[ \mathcal{E}=\frac{\mathcal{E}_{\mathrm{p}}}{\mathcal{E}_{\mathrm{bp}}} =\frac{\lambda_{\mathrm{p}}}{\lambda_{\mathrm{bp}}} =\Lambda, \]
where \(\mathcal{E}\) and \(\Lambda\) are, respectively, the dimensionless electrical conductivity and thermal conductivity.
The first series of experiments was carried out with specimens having a corridor arrangement of pores with diameters of 10, 20, 30, 40, and 50 mm.
A flat model without pores was inserted into the apparatus, the uniformity of the electric field was checked, and its resistance was measured. Then, in the working part of the model \((300 \times 300\ \mathrm{mm})\), pores of a specified diameter were cut out, located at the corners of squares (corridor arrangement), and the resistance of the model was measured.
The resistance of the specimen without pores was calculated from the expression
\[ R_{\mathrm{ob}}^{\mathrm{bp}}=K R_{\mathrm{m}}^{\mathrm{bp}}, \]
where \(R_{\mathrm{ob}}^{\mathrm{bp}}\) is the resistance of the specimen \((300 \times 300\ \mathrm{mm})\) without pores,
\(K\) is the proportionality coefficient, equal to the ratio of the linear dimensions of the specimen and the model, \(K=0.696\),
\(R_{\mathrm{m}}^{\mathrm{bp}}\) is the resistance of the model without pores.
The resistance of the porous specimen was calculated from the expression
\[ R_{\mathrm{ob}}^{\mathrm{p}}=R_{\mathrm{m}}^{\mathrm{p}}-R_{\mathrm{oc}}, \]
where \(R_{\mathrm{ob}}^{\mathrm{p}}\) is the resistance of the porous specimen;
\(R_{\mathrm{m}}^{\mathrm{p}}\) is the resistance of the model with pores;
\(R_{\mathrm{oc}}\) is the resistance of the model after subtracting the resistance of the specimen without pores;
\[ R_{\mathrm{oc}}=R_{\mathrm{m}}^{\mathrm{bp}}-R_{\mathrm{ob}}^{\mathrm{bp}}. \]
The second series of experiments was carried out in the same way with specimens having a staggered arrangement of pores with diameters of 10, 20, 30, and 40 mm.
The third series of experiments was carried out with specimens having an arbitrary arrangement of pores with diameters of 10, 30, and 50 mm. The results of all experiments are presented in Fig. 1 in the coordinates \(m\)—\(\Lambda\), where \(m\) is porosity.
Fig. 1. Relationship between thermal conductivity and porosity for non-thermally conductive pores. The first symbols for each of the sizes correspond to the corridor arrangement, the second to the staggered arrangement, and the third to the arbitrary arrangement of pores.
The deviation of individual points from a certain mean curve is on average 1–5%, and the maximum deviations are 12.4%. These deviations are explained by the unavoidable errors of the experiment, caused by various factors (fluctuations in the temperature of the specimen, inaccuracies in the pore dimensions, etc.).
Brief Conclusions
The results presented from experimental investigations aimed at determining the influence of the size and packing of non-thermally conductive pores of spherical shape in porous bodies on the thermal conductivity of the latter make it possible to draw the following conclusions.
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The thermal conductivity of porous bodies does not depend on the size of the non-thermally conductive pores.
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The thermal conductivity of porous bodies does not depend on the packing of the non-thermally conductive pores in the body.
REFERENCES
- Serykh G. M. Izvestiya TPI, vol. 101, 1958.
- Serykh G. M., Ponomarev O. A. Izvestiya TPI, vol. 101, 1958.