Influence of the thermal load on the characteristics of a~flow with evaporation
Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 2, pp. 83-92.

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We study two-layer flows of liquid and gas in a horizontal channel under given gas flow rate. Evaporation is taken into account on the thermocapillary interface. An exact solution is constructed to Navier–Stokes equations in the Boussinesq approximation taking into account the Dufour effect in the gas-vapor layer. In the framework of the linear theory, we study the stability of the obtained solutions and the characteristics of the arising perturbations. The influence of the width of the liquid layer and the longitudinal temperature gradient on the strucuture of the principal flow and the perturbations is studied.
Mots-clés : exact solution, Dufour effect, thermocapillary interface
Keywords: stability.
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E. V. Rezanova; I. A. Shefer. Influence of the thermal load on the characteristics of a~flow with evaporation. Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 2, pp. 83-92. http://geodesic.mathdoc.fr/item/SJIM_2017_20_2_a8/

[1] Lyulin Yu. V., Kabov O. A., “Izmerenie massovoi skorosti ispareniya v gorizontalnom sloe zhidkosti, chastichno otkrytom v dvizhuscheisya gaz”, Pisma v ZhTF, 39:17 (2013), 88–94

[2] Lyulin Y., Kabov O., “Evaporative convection in a horizontal liquid layer under shear-stress gas flow”, Internat. J. Heat and Mass Transfer, 70 (2014), 599–609 | DOI

[3] Mizev A. A., “Eksperimentalnoe issledovanie vliyaniya tolschiny gazovoi fazy na ustoichivost i strukturu techeniya v dvukhsloinoi sisteme zhidkost-gaz”, Prikl. mekhanika i tekhn. fizika, 45:6 (2004), 14–18 | Zbl

[4] Kabov O. A., Kabova Yu. O., Kuznetsov V. V., “Isparenie neizotermicheskoi plenki zhidkosti v mikrokanale pri sputnom potoke gaza”, Dokl. AN, 446:5 (2012), 522–526 | MR

[5] Andreev V. K., Kuznetsov V. V., “Dvizhenie zhidkoi plenki i gazovogo potoka v mikrokanale s ispareniem”, Teplofizika i aeromekhanika, 2013, no. 1, 17–28

[6] Iorio C. S., Goncharova O. N., Kabov O. A., “Study of evaporative convection in an open cavity under shear stress flow”, Microgravity Sci. Technol., 21 (2009), 313–319 | DOI

[7] Iorio C. S., Goncharova O. N., Kabov O. A., “Heat and mass transfer control by evaporative thermal pattering of thin liquid layers”, Comput. Thermal Sci., 4:3 (2011), 333–342 | DOI

[8] Kuznetsov V. V., “Teplomassoobmen na poverkhnosti razdela zhidkost-par”, Mekhanika zhidkosti i gaza, 2011, no. 5, 97–107 | Zbl

[9] Goncharova O. N., “Modelirovanie techenii v usloviyakh teplo- i massoperenosa na granitse”, Izv. AltGU, 73:1 (2012), 12–18

[10] Birikh R. V., “O termokapillyarnoi konvektsii v gorizontalnom sloe zhidkosti”, Prikl. mekhanika i tekhn. fizika, 7:3 (1966), 69–72

[11] Napolitano L. G., “Plane Marangoni–Poiseulle flow of two immiscible fluids”, Acta Astronautica, 7:4 (1980), 461–478 | DOI | Zbl

[12] Aristov S. N., Shvarts K. G., Vikhrevye techeniya advektivnoi prirody vo vraschayuschemsya sloe zhidkosti, Izd-vo Perm. un-ta, Perm, 2006

[13] Bekezhanova V. B., “Konvektivnaya neustoichivost techeniya Marangoni–Puazeilya pri nalichii prodolnogo gradienta temperatury”, Prikl. mekhanika i tekhn. fizika, 52:1 (2011), 92–100 | MR | Zbl

[14] Aristov S. N., Prosviryakov E. Yu., “O sloistykh techeniyakh ploskoi svobodnoi konvektsii”, Nelineinaya dinamika, 9:4 (2013), 651–657

[15] Shliomis M. A., Yakushin V. A., “Konvektsiya v dvukhsloinoi binarnoi sisteme s ispareniem”, Uchenye zapiski Perm. gos. un-ta. Ser. Gidrodinamika, 1972, no. 4, 129–140

[16] Goncharova O. N., Rezanova E. V., “Primer tochnogo resheniya statsionarnoi zadachi o dvukhsloinykh techeniyakh s ispareniem na granitse razdela”, Prikl. mekhanika i tekhn. fizika, 55:2 (2014), 68–79 | MR | Zbl

[17] Goncharova O. N., Hennenberg M., Rezanova E. V., Kabov O. A., “Modeling of the convective fluid flows with evaporation in the two-layer systems”, Interfacial Phenomena and Heat Transfer, 3:1 (2013), 317–338 | DOI

[18] Goncharova O. N., Rezanova E. V., Lyulin Yu. V., Kabov O. A., “Modelirovanie dvukhsloinykh techenii zhidkosti i gaza s uchetom ispareniya”, Teplofizika i aeromekhanika, 2015, no. 5, 655–661

[19] Andreev V. K., Cheremnykh E. N., “Sovmestnoe polzuschee dvizhenie trekh vyazkikh zhidkostei v ploskom sloe: apriornye otsenki i skhodimost k statsionarnomu rezhimu”, Sib. zhurn. industr. matematiki, 19:1 (2016), 3–17 | DOI | MR | Zbl

[20] De Groot S. R., Termodinamika neobratimykh protsessov, Gostekhizdat, M., 1956

[21] De Groot S., Neravnovesnaya termodinamika, Mir, M., 1964

[22] Gebhart B., Jaluria Y., Mahajan R. L., Sammakia B., Bouyancy-induced Flows and Transport, Springer Verl., N.Y., 1988

[23] Ostroumov G. A., Svobodnaya konvektsiya v usloviyakh vnutrennei zadachi, Gostekhizdat, M., 1952 | MR

[24] Lyulin Y., Kabov O., Iorio C. S., Chikov S., Glushchuk A., Marchuk I., Queeckers P., Liquidscandidates for CIMEX-1 experiments on ISS, CIMEX Meeting, Bruxelles, 2009, May 15

[25] Godunov S. K., “O chislennom reshenii kraevykh zadach dlya sistem lineinykh obyknovennykh uravnenii”, Uspekhi mat. nauk, 16:3(99) (1961), 171–174 | MR | Zbl

[26] Gaponov S. A., Maslov A. A., Razvitie vozmuschenii v szhimaemykh potokakh, Nauka, Novosibirsk, 1980 | MR