Geodesic
Mathematical model of heating of plane porous heat exchanger of heat surface cooling system in the starting mode
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 11 (2018) no. 4, pp. 136-145
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Based on the conjugate Darcy–Brinkman–Forchheymer hydrodynamic model and Schumann thermal model with boundary conditions of the second kind, a model with lumped parameters was proposed by means of geometric 2D averaging to identify the integral kinetics of the temperature fields of a porous matrix and a Newtonian coolant without phase transitions. The model was adapted for a heat-stressed surface by means of a porous compact heat exchanger with uniform porosity and permeability, obeying the modified Kozeny–Carman relation, in the form of a Cauchy problem, the solution of which was obtained in the final analytical representation for the average volume temperatures of the coolant and the porous matrix. The possibility of harmonic damped oscillations of the temperature fields and the absence of coolant overheating in the starting condition of the cooling system were shown. For the dimensionless time of establishing the stationary functioning of the porous heat exchanger, an approximate estimate was obtained correlating with the known data of computational and full-scale experiments.
Keywords: flat porous heat exchanger, heat-stressed surface, boundary conditions of the second kind, time to settle a stationary warm regime. 
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     title = {Mathematical model of heating of plane porous heat exchanger of heat surface cooling system in the starting mode},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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V. I. Ryazhskikh; D. A. Konovalov; S. V. Dakhin; Yu. A. Bulygin; V. P. Shatskiy. Mathematical model of heating of plane porous heat exchanger of heat surface cooling system in the starting mode. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 11 (2018) no. 4, pp. 136-145. http://geodesic.mathdoc.fr/item/VYURU_2018_11_4_a9/

[1] Kandlikar S. G., Garimella S., Li D., King M. R., Heat Transfer and Fluid Flow in Minichannels and Microchannels, Elsevier, N.Y., 2014

[2] Hutter G. W., “The Status of World Geothermal Power Generation”, Procceding World Geothermal Congress (2000), 23–37

[3] Advani S. G., Sczer M., Process Modeling in Composite Manufacturing, CRC Press, N.Y., 2002

[4] Howell J. R., Hall M. J., Ellzey J. L., “Combustion of Hydrocarbon Fuels Within Porous Inert Media”, Progress in Energy and Combustion Science, 22 (1996), 121–145 | DOI

[5] Bees M. A., Hill N. A., “Wavelengths of Bioconvection Patterns”, The Journal of Experimental Biology, 200 (1997), 1515–1526

[6] Nield D. A., Bejan A., Convection in Porous Media, Springer, N.Y., 1999 | MR | Zbl

[7] Alazmi B., Vafai K., “Analysis of Variants Within the Porous Media Transport Models”, Journal of Heat Transfer, 122 (2000), 303–326 | DOI

[8] Hsu C. T., Cheng P., “Thermal Dispersion in Porous Medium”, International Journal of Heat and Mass Transfer, 33:8 (1990), 1587–1597 | DOI | Zbl

[9] Guo Z., Kim S. Y., Sung H. J., “Pulsating Flow and Heat Transfer in a Pipe Partially Filled with a Porous Medium”, International Journal of Heat and Mass Transfer, 40:17 (1997), 4209–4218 | DOI

[10] Vafai K., Alkire R. I., Tien C. L., “An Experimental Investigation of Heat Transfer in Variable Porosity Media”, International Journal of Heat and Mass Transfer, 107 (1985), 642–647

[11] Renken K. J., Poulikakos D., “Experiment and Analysis of Forced Convection Heat Transfer in a Packed Led of Spheres”, International Journal of Heat and Mass Transfer, 31 (1988), 1399–1408 | DOI

[12] Teruel F. E., “Validity of the Macroscopic Energy Equation Model for Laminar Flows Through Porous Media: Developing and Fully Developed Regions”, International Journal of Thermal Sciences, 112 (2017), 439–449 | DOI | MR

[13] Ryazhskih V. I., Konovalov D. A., Slyusarev M. I., Drozdov I. G., “Analysis of Mathematical Model Heat Removal from the Flat Surface by the Laminar Moving Refrigerant through Conjugation Porous Medium”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 9:3 (2016), 68–81 (in Russian) | DOI | Zbl

[14] Ingham D. B., “Governing Equations for Laminar Flows Through Porous Media”, Emerging Technologies and Techniques in Porous Media, 134, Springer Science+Business Media, Dordrecht, 2004, 1–11 | DOI | MR

[15] Popov I. A., Hydrodynamics and Heat Transfer in Porous Heat Exchange Elements and Apparatus, Center Informacionnyih Thenologii, Kazan, 2007 (in Russian)

[16] Bear J., Bachmat Y., Introduction to Modeling of Transport Phenomena in Porous Media, Kluwer Academic Publishers, Dordrecht, 1991 | DOI | Zbl

[17] Amiri A., Vafai K., “Analysis of Dispersion Effects and Non-Thermal Equilibrium, Non-Darsian Variable Porosity Incompressible flow Through Porous Media”, Journal Heat and Mass Transfer, 37:6 (1994), 939–954 | DOI

[18] Dech G., A Guide to the Practical Application of the Laplace Transform and the z-Transform, Nauka, M., 1971 (in Russian)

[19] Dehghan M., Valipour M. S., Saedodin S., Mahmoudi Y., “Investigation of Forced Convection Through Entrance Region of a Porous-Filled Microchannel: An Analytical Study Based on the Scale Analysis”, Applied Thermal Engineering, 99 (2016), 446–454 | DOI