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Oscillating pressure-driven slip flow and heat transfer through an elliptical microchannel. (English) Zbl 1485.76028

Summary: This paper studies the transient slip flow and heat transfer of a fluid driven by the oscillatory pressure gradient in a microchannel of elliptic cross section. The boundary value problem for the thermal-slip flow is formulated based on the assumption that the fluid flow is fully developed. The semi-analytical solutions of velocity and temperature fields are then determined by the Ritz method. These solutions include some existing known examples as special cases. The effects of the slip length and the ratio of minor to major axis of the elliptic cross section on the velocity and temperature distribution in the microchannel are investigated.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
76N15 Gas dynamics (general theory)
76R05 Forced convection
76R10 Free convection
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[1] Ahuja, A.S.: Measurement of thermal conductivity of stationary blood by unsteady-state method. J. Appl. Physiol. 37(5), 765-770 (1997) · doi:10.1152/jappl.1974.37.5.765
[2] Akyildiz, F.T., Siginer, D.A.: Exact solution of forced convection gaseous slip flow in corrugated microtubes. Int. J. Heat Mass Transf. 112, 553-558 (2017) · doi:10.1016/j.ijheatmasstransfer.2017.01.101
[3] Avcci, M., Aydin, O., Arici, M.E.: Conjugate heat transfer with viscous dissipation in a microtube. Int. J. Heat Mass Transf. 55, 5302-5308 (2012) · doi:10.1016/j.ijheatmasstransfer.2012.05.038
[4] Azih, C., Brinkerhoff, J.R., Yaras, M.I.: Direct numerical simulation of convective heat transfer in a zero-pressure-gradient boundary layer with supercritical water. J. Therm. Sci. 21(1), 49-59 (2012). https://doi.org/10.1007/s11630-012-0518-5 · doi:10.1007/s11630-012-0518-5
[5] Balaj, M., Roohi, E., Akhlaghi, H., Myong, R.S.: Investigation of convective heat transfer through constant wall heat flux micro/nano channels using DSMC. Int. J. Heat Mass Transf. 71, 633-638 (2014) · doi:10.1016/j.ijheatmasstransfer.2013.12.053
[6] Body (Human) Heat Transfer. http://www.thermopedia.com/content/587/
[7] Chuchard, P., Orankitjaroen, S., Wiwatanapataphee, B.: Study of pulsatile pressure-driven electroosmotic flows through an elliptic cylindrical microchannel with the Navier slip condition. Adv. Differ. Equ. 2017, 160 (2017). https://doi.org/10.1186/s13662-017-1209-z · Zbl 1422.76036 · doi:10.1186/s13662-017-1209-z
[8] Das, S.K., Tahmouresi, F.: Analytical solution of fully developed gaseous slip flow in elliptic microchannel. Int. J. Adv. Appl. Math. Mech. 3(3), 1-15 (2016) · Zbl 1367.76052
[9] Duan, Z., Muzychka, Y.S.: Slip flow in elliptic microchannels. Int. J. Therm. Sci. 46, 1104-1111 (2007) · doi:10.1016/j.ijthermalsci.2007.01.026
[10] Hemadri, V., Biradar, G.S., Shah, N., Garg, R., Bhandarkar, U.V., Agrawal, A.: Experimental study of heat transfer in rarefied gas flow in a circular tube with constant wall temperature. Exp. Therm. Fluid Sci. 93, 326-333 (2018) · doi:10.1016/j.expthermflusci.2017.12.030
[11] Kuddusi, L.: Prediction of temperature distribution and Nusselt number in rectangular microchanels at wall slip condition for all versions of constant wall temperature. Int. J. Therm. Sci. 46, 998-1010 (2007) · doi:10.1016/j.ijthermalsci.2006.12.006
[12] Kuddusi, L., Çetegen, E.: Thermal and hydrodynamic analysis of gaseous flow in trapezoidal silicon microchannels. Int. J. Therm. Sci. 48, 353-362 (2009) · doi:10.1016/j.ijthermalsci.2008.02.004
[13] Maurer, J., Tabeling, P., Joseph, P., Willaime, H.: Second-order slip flows in micro channels for helium and nitrogen. Phys. Fluids 15(9), 2613-2621 (2003) · Zbl 1186.76356 · doi:10.1063/1.1599355
[14] Neutrium. Hydraulic diameter, https://neutrium.net/fluid-flow/hydraulic-diameter/
[15] Spiga, M., Vocale, P.: Slip flow in elliptic microducts with constant heat flux. Adv. Mech. Eng. (2012). https://doi.org/10.1155/2012/481280 · doi:10.1155/2012/481280
[16] van Rij, J., Ameel, T., Harman, T.: The effect of viscous dissipation and rarefaction on rectangular microchannel convection heat transfer. Int. J. Therm. Sci. 48, 271-281 (2009) · doi:10.1016/j.ijthermalsci.2008.07.010
[17] Wang, C.Y.: Slip flow in ducts. Can. J. Chem. Eng. 81, 1058-1061 (2003) · doi:10.1002/cjce.5450810517
[18] Wang, C.Y.: Ritz method for slip flow in super-elliptic ducts. Eur. J. Mech. B, Fluids 43, 85-89 (2014) · Zbl 1297.76052 · doi:10.1016/j.euromechflu.2013.07.004
[19] Wiwatanapataphee, B., Wu, Y.H., Hu, M., Chayantrakom, K.: A study of transient flows of Newtonian fluids through micro-annuals with a slip boundary. J. Phys. A, Math. Theor. 42, 065206 (2009). https://doi.org/10.1088/1751-8113/42/6/065206 · Zbl 1168.76014 · doi:10.1088/1751-8113/42/6/065206
[20] Wu, Y.H., Wiwatanapataphee, B., Hu, M.: Pressure-driven transient flows of Newtonian fluids through microtubes with slip boundary. Phys. A, Stat. Mech. Appl. 387(24), 5979-5990 (2008) · doi:10.1016/j.physa.2008.06.043
[21] Yu, S., Ameel, T.A.: Slip-flow heat transfer in rectangular microchannels. Int. J. Heat Mass Transf. 44, 4225-4234 (2001) · Zbl 1014.76085 · doi:10.1016/S0017-9310(01)00075-8
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