Effective conductivity of heterogeneous systems with disordered structure

Zarichnyak, Yu. P.; Novikov, V. V.

doi:10.1007/bf00860269

Cited by 9 publications

(5 citation statements)

References 2 publications

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“…The reason for the strong deviation between some literature reports [3,12,[28][29][30] and the results of the present study (up to a 2000% increase expected in literature [3] vs. a 68% increase to be expected upon an increase of the core conductivity from silica to gold) is that these few available literature reports are mainly based on a simple model that was reported in a series of models by Zarichnyak and Novikov [31]. This particular model was originally developed for heterogeneous materials and assumes the material consists of two types of cubical zones, resp.…”

Section: Limitations Of the Zarichnyak-model And Improved Modellingcontrasting

confidence: 88%

Numerical and analytical investigation of the possibilities to enhance the thermal conductivity of core-shell particle packed beds

Deridder

Smits

Benkahla

et al. 2018

Journal of Chromatography A

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Section: Limitations Of the Zarichnyak-model And Improved Modellingcontrasting

confidence: 88%

Numerical and analytical investigation of the possibilities to enhance the thermal conductivity of core-shell particle packed beds

Deridder

Smits

Benkahla

et al. 2018

Journal of Chromatography A

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“…The parameters a 1 and b 2 were obtained from the experimental data given in ref 21 measured between 283.15 and 328.15 K, and are listed in Appendix Table A2. Finally, the variation of the volume heat capacity with the temperature, which is required in the differential equation 4 is (23) with…”

Section: Theorymentioning

confidence: 99%

“…The particles are not homogeneous but made of a silica core covered with a bonded layer of C 18 alkyl groups. The heat conductivity of the column bed when the flow rate is zero (u e ) 0) was estimated after the results of Zarichnyak et al 23 These authors proposed a model that predicts the effective thermal conductivity of twocomponent heterogeneous systems that have a chaotic structure. This model applies to packed beds impregnated with a stagnant liquid.…”

mentioning

confidence: 99%

Complete Temperature Profiles in Ultra-High-Pressure Liquid Chromatography Columns

2008

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The temperature profiles were calculated along and across seven packed columns (lengths 30, 50, 100, and 150 mm, i.d., 1 and 2.1 mm, all packed with Acquity UPLC, BEH-C 18 particles, average d(p) approximately 1.7 microm) and their stainless steel tubes (o.d. 4.53 and 6.35 mm). These columns were kept horizontal and sheltered from forced air convection (i.e., under still air conditions), at room temperature. They were all percolated with pure acetonitrile, either under the maximum pressure drop (1034 bar) or at the maximum flow rate (2 mL/min) permitted by the chromatograph. The heat balance equation of chromatographic columns was discretized and solved numerically with minimum approximation. Both the compressibility and the thermal expansion of the eluent were taken into account. The boundary conditions were determined from the experimental measurements of the column inlet pressure and of the temperature profile along the column wall, which were made with a precision better than +/-0.1 K. These calculation results provide the 3-D temperature profiles along and across the columns. The axial and radial temperature gradients are discussed in relationship with the experimental conditions used. The temperature map obtained permits a prediction of the chromatographic data obtained under a very high pressure gradient.

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“…However, a comparison of the values of A3d, A~d, and the experimental data contradicts this conclusion, which indicates that there are internal contradictions in this method for the determination of A (as n ~ ~, the value of And ~ 0 for any concentration of the components mi < i). This is partially solved in [29].…”

Section: Methods Taking Account Of the Disordered Distribution Of The Componentsmentioning

confidence: 98%

Methods for the analytic determination of the effective conductivities of heterogeneous systems

Dul'nev

Novikov

1981

Journal of Engineering Physics

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Closure of Transfer Equations in Heterogeneous SystemsHeterogeneous systems with a disordered structure (composite and granular materials, eutectie alloys and their melts, composites, metal ceramics, solutions, etc.) constitute macroscopic uniform systems made up of small nonuniform regions (components) and delimited interfaces.The dimension of the nonuniformity, d, is much smaller than the characteristic dimension L of the specimen, but much larger than the length of the free path A 0 of the carriers of heat flux, electricity, etc., i.e., A 0 << d << L.

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Effective conductivity of heterogeneous systems with disordered structure

Cited by 9 publications

References 2 publications

Numerical and analytical investigation of the possibilities to enhance the thermal conductivity of core-shell particle packed beds

Numerical and analytical investigation of the possibilities to enhance the thermal conductivity of core-shell particle packed beds

Complete Temperature Profiles in Ultra-High-Pressure Liquid Chromatography Columns

Methods for the analytic determination of the effective conductivities of heterogeneous systems

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