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Natural convection in an enclosure with localized heating and salting from below. (English) Zbl 1143.80338
Summary: Two-dimensional, double diffusion, natural convection in a rectangular enclosure filled with binary fluid saturating porous media is investigated numerically. Multiple motions are driven by the external temperature and concentration differences imposed across horizontal walls with the simultaneous presence of discrete heat and contaminant sources. The general Brinkman-extended Darcy model is adopted to formulate the fluid flow in the cavity. The fluid, heat and moisture transport through the isotropic porous layer are analyzed using the streamlines, heatlines and masslines, and the heat and mass transfer potentials are also explained by the variations of overall Nusselt and Sherwood numbers. The numerical simulations presented here span a wide range of the main parameters (thermal Rayleigh numbers, strip pitches and Darcy number) in the domain of destabilizing solutal buoyancy forces. It is shown that the heat and mass transfer potential can be promoted or inhibited, depending strongly on the permeability of porous medium, the strip pitch, the thermal and solutal Rayleigh numbers.
##### MSC:
 80A20 Heat and mass transfer, heat flow 76R10 Free convection (fluid mechanics) 76S05 Flows in porous media; filtration; seepage 76M12 Finite volume methods (fluid mechanics)
##### References:
 [1] Turner, J. S.: Multi-component convection, Ann. rev. Fluid mech. 17, 11-44 (1985) [2] Viskanta, R.; Bergman, T. L.; Incropera, F. P.: Double diffusive natural convection, Natural convection: fundamentals and applications, 1075-1099 (1985) [3] Bejan, A.: Convection heat transfer, (1995) [4] Turner, J. S.: The behavior of a stable salinity gradient heated from below, J. fluid mech. 33, 183-200 (1968) [5] Wee, H. K.; Keey, R. B.; Cunningham, M. J.: Heat and moisture transfer by natural convection in a rectangular cavity, Int. J. Heat mass transfer 32, 1765-1778 (1989) [6] Chen, F.; Chen, C. F.: Double-diffusive fingering convection in a porous medium, Int. J. Heat mass transfer 36, 793-807 (1993) · Zbl 0764.76021 · doi:10.1016/0017-9310(93)80055-Y [7] Trevisan, O. V.; Bejan, A.: Natural convection with combined heat and mass transfer buoyancy effects in a porous medium, Int. J. Heat mass transfer 28, 1597-1611 (1985) [8] Trevisan, O. V.; Bejan, A.: Mass and heat transfer by natural convection in a vertical slot filled with porous medium, Int. J. Heat mass transfer 29, 403-415 (1986) · Zbl 0591.76152 · doi:10.1016/0017-9310(86)90210-3 [9] Trevisan, O. V.; Bejan, A.: Combined heat and mass transfer by natural convection in a vertical enclosure, ASME J. Heat transfer 109, 104-112 (1987) [10] Lin, T. F.; Huang, C. C.; Chang, T. S.: Transient binary mixture natural convection in square enclosures, Int. J. Heat mass transfer 33, 287-299 (1990) [11] Beghein, C.; Haghighat, F.; Allard, F.: Numerical study of double-diffusive natural convection in a square cavity, Int. J. Heat mass transfer 35, 833-846 (1992) [12] Costa, V. A. F.: Double diffusive natural convection in a square enclosure with heat and mass diffusive walls, Int. J. Heat mass transfer 40, 4061-4071 (1997) · Zbl 0930.76084 · doi:10.1016/S0017-9310(97)00061-6 [13] Costa, V. A. F.: Double-diffusive natural convection in parallelogrammic enclosures filled with fluid-saturated porous media, Int. J. Heat mass transfer 47, 2699-2714 (2004) · Zbl 1079.76640 · doi:10.1016/j.ijheatmasstransfer.2003.11.031 [14] Costa, V. A. F.: Double-diffusive natural convection in parallelogrammic enclosures, Int. J. Heat mass transfer 47, 2913-2926 (2004) · Zbl 1079.76065 · doi:10.1016/j.ijheatmasstransfer.2004.03.008 [15] Chamkha, A. J.; Al-Naser, H.: Double-diffusive convection in an inclined porous enclosure with opposing temperature and concentration gradients, Int. J. Therm. sci. 40, 227-244 (2001) [16] Chamkha, A. J.: Double-diffusive convection in a porous enclosure with cooperating temperature and concentration gradients and heat generation or absorption effects, Numer. heat transfer, part A 41, 65-87 (2002) [17] Chamkha, A. J.; Al-Naser, H.: Hydromagnetic double-diffusive convection in a rectangular enclosure with opposing temperature and concentration gradients, Int. J. Heat mass transfer 45, 2465-2483 (2002) · Zbl 1101.76055 · doi:10.1016/S0017-9310(01)00344-1 [18] Chamkha, A. J.; Al-Naser, H.: Hydromagnetic double-diffusive convection in a rectangular enclosure with uniform side heat and mass fluxes and opposing temperature and concentration gradients, Int. J. Therm. sci. 41, 936-948 (2002) [19] Zhao, F. Y.; Liu, D.; Tang, G. F.: Application issues of the streamline, heatline and massline for conjugate heat and mass transfer, Int. J. Heat mass transfer 50, 320-334 (2007) · Zbl 1120.80006 · doi:10.1016/j.ijheatmasstransfer.2006.06.026 [20] Lee, J.; Hyun, M. T.; Kang, Y. S.: Confined natural convection due to lateral heating in a stably stratified solution, Int. J. Heat mass transfer 33, 869-875 (1990) [21] Lee, J. W.; Hyun, J. M.: Time-dependent double diffusion in a stably stratified fluid under lateral heating, Int. J. Heat mass transfer 34, 2409-2421 (1991) [22] Lee, J. W.; Hyun, J. M.: Double-diffusive convection in a cavity under a vertical solutal gradient and a horizontal temperature gradient, Int. J. Heat mass transfer 34, 2423-2427 (1991) [23] Newell, T. A.; Hull, J. R.: Depth sounding diagnostic measurement of salt gradient solar ponds, J. solar energy eng. 107, 160-164 (1985) [24] Bergman, T. L.; Ungan, A.: Experimental and numerical investigation of double-diffusive convection induced by a discrete heat source, Int. J. Heat mass transfer 29, 1695-1709 (1986) [25] Chen, W.; Zhao, F. Y.; Tang, G. F.; Liu, D.: Transportation of indoor double diffusive mixed convection coupled with diffusion in solid walls, J. hv&AC 36, 12-18 (2006) [26] Zhao, F. Y.; Liu, D.; Tang, G. F.: Multiple steady flows in confined gaseous double diffusion with discrete thermosolutal sources, Phys. fluids 19, No. 10, 107103 (2007) · Zbl 1182.76872 · doi:10.1063/1.2770518 [27] Zhao, F. Y.; Liu, D.; Tang, G. F.: Natural convection in a porous enclosure with a partial heating and salting element, Int. J. Therm. sci. (2007) [28] Zhao, F. Y.; Liu, D.; Tang, G. F.: Free convection from one thermal and solute source in a confined porous medium, Transport porous media (2007) [29] Liu, D.; Zhao, F. Y.; Tang, G. F.: Thermosolutal convection in a saturated porous enclosure with concentrated energy and solute sources, Energy convers. Manage. 49, 16-31 (2008) [30] Heindel, T. J.; Incropera, F. P.; Ramadhyani, S.: Enhancement of natural convection heat transfer from an array of discrete heat sources, Int. J. Heat mass transfer 39, 479-490 (1996) [31] Tou, S. K. W.; Tso, C. P.; Zhang, X.: 3-D numerical analysis of natural convective liquid cooling of $3×3$ heater array in rectangular enclosures, Int. J. Heat mass transfer 42, 3231-3244 (1999) · Zbl 0973.76610 · doi:10.1016/S0017-9310(98)00379-2 [32] Tou, S. K. W.; Zhang, X. F.: Three-dimensional numerical simulation of natural convection in an inclined liquid-filled enclosure with an array of discrete heaters, Int. J. Heat mass transfer 46, 127-138 (2003) · Zbl 1018.76532 · doi:10.1016/S0017-9310(02)00253-3 [33] Tso, C. P.; Jin, L. F.; Tou, S. K. W.; Zhang, X. F.: Flow pattern evolution in natural convection cooling from an array of discrete heat sources in a rectangular cavity at various orientations, Int. J. Heat mass transfer 47, 4061-4073 (2004) [34] Da Silva, A. K.; Lorente, S.; Bejan, A.: Optimal distribution of discrete heat sources on a wall with natural convection, Int. J. Heat mass transfer 47, 203-214 (2004) · Zbl 1041.76560 · doi:10.1016/j.ijheatmasstransfer.2003.07.007 [35] Da Silva, A. K.; Lorenzini, G.; Bejan, A.: Distribution of heat sources in vertical open channels with natural convection, Int. J. Heat mass transfer 48, 1462-1469 (2005) · Zbl 1189.76569 · doi:10.1016/j.ijheatmasstransfer.2004.10.019 [36] Jin, L. F.; Tou, S. K. W.; Tou, C. P.: Effects of rotation on natural convection cooling from three rows of heat sources in a rectangular cavity, Int. J. Heat mass transfer 48, 3982-3994 (2005) · Zbl 1188.76252 · doi:10.1016/j.ijheatmasstransfer.2005.04.013 [37] He, Y. L.; Yang, W. W.; Tao, W. Q.: Three-dimensional numerical study of natural convective heat transfer of liquid in a cubic enclosure, Numer. heat transfer, part A 47, 917-934 (2005) [38] Zhao, F. Y.; Liu, D.; Tang, G. F.: Resonant response of fluid flow subjected to discrete heating elements, Energy convers. Manage. 48, 2461-2472 (2007) [39] Zhao, F. Y.; Liu, D.; Tang, G. F.: Conjugate heat transfer in square enclosures, Heat mass transfer 43, 907-922 (2007) [40] Zhao, F. Y.; Tang, G. F.; Liu, D.: Conjugate natural convection in enclosures with external and internal heat sources, Int. J. Eng. sci. 44, 148-165 (2006) [41] Liu, D.; Zhao, F. Y.; Tang, G. F.: Conjugate heat transfer in an enclosure with a centered conducting body imposed sinusoidal temperature profiles on one side, Numer. heat transfer, part A 53, No. 2, 204-223 (2008) [42] Patankar, S. V.: Numerical heat transfer and fluid flow, (1980) · Zbl 0521.76003 [43] Hayase, T.; Humphrey, J. A. C.; Greif, R.: A consistently formulated QUICK scheme for fast and stable convergence using finite-volume iterative calculation procedure, J. comput. Phys. 98, 108-118 (1992) · Zbl 0743.76054 · doi:10.1016/0021-9991(92)90177-Z