Mixed convection phenomenon in packed beds: A comprehensive review

Kaviany, 1995 Carbonell, 1998, Heat and mass transfer in porous media, 121 Quintard, 1993, One- and two-equation models for transient diffusion processes in two-phase systems, Adv. Heat Transf., 23, 369, 10.1016/S0065-2717(08)70009-1 Vafai, 1998, Non-darcian effects in confined forced convective flows, 313 Nield, 2006 Darcy, 1856 Forchheimer, 1901, Wasserbewegung durch boden, Zeitschrift Vereines Deutscher Ingenieure, 45, 1782 Brinkmann, 1949, A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Appl. Sci. Res., 1, 27, 10.1007/BF02120313 Wooding, 1957, Steady state free thermal convection of liquid in a saturated permeable medium, J. Fluid Mech., 2, 273, 10.1017/S0022112057000129 Schumann, 1929, Heat transfer: A liquid flowing through a porous prism, J. Franklin Inst. B, 208, 405, 10.1016/S0016-0032(29)91186-8 Gamson, 1943, Heat, mass and momentum transfer in the flow of gases through granular solids, Trans. AIChE, 39, 1 Dixon, 1979, Theoretical prediction of effective heat transfer parameters in packed beds., AIChE J., 25, 663, 10.1002/aic.690250413 Wakao, 1979, Effect of fluid dispersion coefficients on particle-to-fluid heat transfer coefficients in packed beds- correlation of nusselt numbers, Chem. Eng. Sci., 34, 325, 10.1016/0009-2509(79)85064-2 Achenbach, 1995, Heat and flow characteristics of packed beds, Exp. Therm. Fluid Sci., 10, 17, 10.1016/0894-1777(94)00077-L Kuwahara, 2001, A numerical study of interfacial convective heat transfer coefficient in two-energy equation model for convection in porous media, Int. J. Heat Mass Transfer, 44, 1153, 10.1016/S0017-9310(00)00166-6 Moghari, 2008, A numerical study of non-equilibrium convective heat transfer in porous media, J. Enhanc. Heat Transf., 15, 81, 10.1615/JEnhHeatTransf.v15.i1.60 Yagi, 1957, Studies on effective thermal conductivities in packed beds, Chem. Eng. Prog., 3, 373 Yagi, 1959, Heat and mass transfer from wall to fluid in packed beds, AIChE J., 5, 79, 10.1002/aic.690050118 Yagi, 1960, Studies on axial effective thermal conductivities in packed beds, AIChE J., 6, 543, 10.1002/aic.690060407 Cheng, 1981, Thermal dispersion effects in non-Darcian convective flows in a saturated porous medium, Lett. Heat Mass Transf., 8, 267, 10.1016/0094-4548(81)90041-2 Levec, 1985, Longitudinal and lateral thermal dispersion in packed beds. Part II: Comparison between theory and experiment, AIChE J., 31, 591, 10.1002/aic.690310409 Cheng, 1988, Transverse thermal dispersion and wall channelling in a packed bed with forced convective flow, Chem. Eng. Sci., 43, 2523, 10.1016/0009-2509(88)85186-8 S.M. Kuo, C.L. Tien, Transverse dispersion in packed-sphere beds, in: ASME Proceedings of the Heat Transfer Conference, Vol. 96, New York, NY, USA, 1988, pp. 629–634. Hsu, 1990, Thermal dispersion in a porous medium, Int. J. Heat Mass Transfer, 33, 1587, 10.1016/0017-9310(90)90015-M Ingham, 1998 Nield, 1999 Hadim, 2000, Overview of current computational studies of heat transfer in porous media and their applications-forced convection and multiphase heat transfer, Adv. Num. Heat Transf., 2, 291 Vafai, 2000, Overview of current computational studies of heat transfer in porous media and their applications-natural and mixed convection and multiphase heat transfer, Adv. Num. Heat Transf., 2, 331 Vafai, 2000 Pop, 2001 Bejan, 2003 Ingham, 2004 Bergles, 1981, Applications of heat transfer augmentation, 883 Gupta, 1986 Webb, 1994 Palm, 1972, On steady convection in a porous medium, J. Fluid Mech., 54, 153, 10.1017/S002211207200059X Chandrasekhara, 1979, Flow model for velocity distribution in fixed porous beds under isothermal conditions, Wärme- Und Stoffübertragung, 12, 105, 10.1007/BF01002325 Bear, 1982 Wooding, 1960, Rayleigh Instability of a thermal boundary layer in flow through a porous medium, J. Fluid Mech., 9, 183, 10.1017/S0022112060001031 Wooding, 1963, Convection in a saturated porous medium at large Rayleigh number or péclet number, J. Fluid Mech., 15, 527, 10.1017/S0022112063000434 Prats, 1966, The effect of horizontal fluid flow on thermally induced convection currents in porous mediums, J. Geophys. Res., 71, 4835, 10.1029/JZ071i020p04835 Sutton, 1970, Onset of convection in a porous channel with net through flow, Phys. Fluids, 13, 1931, 10.1063/1.1693188 Homsy, 1976, Convective instabilities in porous media with through flow, AIChE J., 22, 168, 10.1002/aic.690220121 Combarnous, 1971, Combined free and forced convection porous media, Soc. Pet. Eng. J., 11, 399, 10.2118/3192-PA Cheng, 1977, Combined free and forced convection flow about inclined surfaces in porous media, Int. J. Heat Mass Transfer, 20, 807 Cheng, 1977, Similarity solutions for mixed convection from horizontal impermeable surfaces in saturated porous media, Int. J. Heat Mass Transfer, 20, 893, 10.1016/0017-9310(77)90059-X Cheng, 1978, Convective heat transfer in porous layers by integral methods, Lett. Heat Mass Transf., 5, 243, 10.1016/0094-4548(78)90031-0 Hsu, 1980, Onset of longitudinal vortices in mixed convective flow over an inclined surface in a porous medium, J. Heat Transfer, 102, 544, 10.1115/1.3244338 Hsu, 1980, Vortex instability of mixed convective flow in a semi-infinite porous medium bounded by a horizontal surface, Int. J. Heat Mass Transfer, 23, 789, 10.1016/0017-9310(80)90033-2 Minkowycz, 1984, Non-similar boundary layer analysis of mixed convection about a horizontal heated surface in a fluid-saturated porous medium, Int. Commun. Heat Mass Transf., 11, 127, 10.1016/0735-1933(84)90017-4 Chandrasekhara, 1985, Mixed convection in the presence of horizontal impermeable surfaces in saturated porous media with variable permeability, Wärme- Und Stoffübertragung, 19, 195, 10.1007/BF01403756 Nakayama, 1987, General similarity transformation for combined free and forced-convection flows within a fluid-saturated porous medium, J. Heat Transfer, 109, 1041, 10.1115/1.3248180 Nakayama, 1991, Unified similarity transformation for free, forced and mixed convection in Darcy and non-Darcy porous media, Int. J. Heat Mass Transfer, 34, 357, 10.1016/0017-9310(91)90256-E Aldoss, 1993, Nonsimilarity solutions for mixed convection from horizontal surfaces in a porous medium-variable surface heat flux, Int. J. Heat Mass Transfer, 36, 463, 10.1016/0017-9310(93)80021-L Aldoss, 1993, Nonsimilarity solutions for mixed convection from horizontal surfaces in a porous medium-variable wall temperature, Int. J. Heat Mass Transfer, 36, 471, 10.1016/0017-9310(93)80022-M Aldoss, 1994, Mixed convection over nonisothermal horizontal surfaces in a porous medium: The entire regime, Numer. Heat Transf.: Part A: Applications, 25, 685, 10.1080/10407789408955973 Haajizadeh, 1984, Combined natural and forced convection in a horizontal porous channel, Int. J. Heat Mass Transfer, 27, 799, 10.1016/0017-9310(84)90001-2 F.C. Lai, F.A. Kulacki, V. Prasad, Mixed convection in horizontal porous layers: effects of thermal boundary conditions, in: ASME Proceedings of the Heat Transfer Conference, Vol. 84, New York, NY, USA, 1987, pp. 91–96. F.C. Lai, V. Prasad, F.A. Kulacki, Effects of the size of heat source on mixed convection in horizontal porous layers heated from below, in: 2nd ASME/JSME Proceedings of Thermal Engineering Joint Conference, Vol. 2, New York, NY, USA, 1987, pp. 413–419. Prasad, 1988, Mixed convection in horizontal porous layers heated from below, J. Heat Transf. Trans. ASME, 110, 395, 10.1115/1.3250498 Oosthuizen, 1988, Mixed convective heat transfer from a heated horizontal plate in a porous medium near an impermeable surface, J. Heat Transf. Trans. ASME, 110, 390, 10.1115/1.3250497 Lai, 1990, Free and mixed convection in horizontal porous layers with multiple heat sources, J. Thermophys. Heat Trans., 4, 221, 10.2514/3.167 F.C. Lai, F.A. Kulacki, Transient mixed convection in horizontal porous layers locally heated from below, in: ASME Proceedings of the Heat Transfer Conference, Vol. 96, Houston, TX, USA, 1988, pp. 353–364. Lai, 1991, Oscillatory mixed convection in horizontal porous layers locally heated from below, Int. J. Heat Mass Transfer, 34, 887, 10.1016/0017-9310(91)90134-Z Lai, 1991, Experimental study of free and mixed convection in horizontal porous layers locally heated from below, Int. J. Heat Mass Transfer, 34, 525, 10.1016/0017-9310(91)90271-F Chao, 1991, Laminar mixed convection in rectangular darcy porous channels with the effect of aspect ratio, J. Chin. Soc. Mech. Eng., 12, 580 Buretla, 1976, Convective heat transfer in a liquid saturated porous layer, ASME J. Appl. Mech., 47, 249, 10.1115/1.3423818 Islam, 1986, Multiple solutions for buoyancy-induced flow in saturated porous media for large péclet numbers, J. Heat Transfer, Transactions ASME, 108, 866, 10.1115/1.3247025 Chao, 1992, Laminar mixed convection in a horizontal rectangular Darcy porous channel, J. Chin. Soc. Mech. Eng., 13, 430 Saeid, 2006, Periodic mixed convection in horizontal porous layer heated from below by isoflux heater, Arab J. Sci. Eng ., 31, 153 Saeid, 2006, Jet impingement cooling of a horizontal surface in a confined porous medium: Mixed convection regime, Int. J. Heat Mass Transfer, 49, 3906, 10.1016/j.ijheatmasstransfer.2006.03.044 Sivasamy, 2010, Jet impingement cooling of a constant heat flux horizontal surface in a confined porous medium: Mixed convection regime, Int. J. Heat Mass Transfer, 53, 5847, 10.1016/j.ijheatmasstransfer.2010.07.063 Saeid, 2015, Mixed convection jet impingement cooling of a rectangular solid heat source immersed in a porous layer, J. Porous Media, 8, 401, 10.1615/JPorMedia.v18.i4.40 Sphaier, 2014, Unstable mixed convection in a heated horizontal porous channel, Int. J. Therm. Sci., 78, 77, 10.1016/j.ijthermalsci.2013.12.002 Barletta, 2020, Wavepacket instability in a rectangular porous channel uniformly heated from below, Int. J. Heat Mass Transfer, 147, 10.1016/j.ijheatmasstransfer.2019.118993 Ozgen, 2019, Numerical study of mixed convection in a channel filled with a porous medium, Appl. Sci., 9 Parang, 1987, Boundary effects in laminar mixed convection flow through an annular porous medium, J. Heat Transfer, 109, 1039, 10.1115/1.3248179 Lai, 1988, Aiding and opposing mixed convection in a vertical porous layer with a finite wall heat source, Int. J. Heat Mass Transfer, 31, 1049, 10.1016/0017-9310(88)90093-2 Pop, 2004, Mixed convection flow in a narrow vertical duct filled with a porous medium, Int. J. Therm. Sci., 43, 489, 10.1016/j.ijthermalsci.2003.09.004 Saeid, 2005, Mixed convection from two thermal sources in a vertical porous layer, Int. J. Heat Mass Transfer, 48, 4150, 10.1016/j.ijheatmasstransfer.2005.04.023 Mahmud, 2006, Mixed convection in a square vented enclosure filled with a porous medium, Int. J. Heat Mass Transfer, 49, 2190, 10.1016/j.ijheatmasstransfer.2005.11.022 Cimpean, 2009, Fully developed mixed convection flow between inclined parallel plates filled with a porous medium, Transp. porous Med., 77, 87, 10.1007/s11242-008-9264-2 Barletta, 2013, Instability of mixed convection in a vertical porous channel with uniform wall heat flux, Phys. Fluids, 25, 10.1063/1.4819121 Barletta, 2016, Instability of combined forced and free flow in an inclined porous channel, Int. J. Comput. Methods, 13, 10.1142/S0219876216400016 Barletta, 2017, Instability of fully developed mixed convection with viscous dissipation in a vertical porous channel, Transp. porous Med., 117, 337, 10.1007/s11242-017-0836-x Celik, 2015, Effect of an inserted porous layer on heat and fluid flow in a vertical channel with mixed convection, Therm. Sci., 19, 1005, 10.2298/TSCI121001056C Vafai, 1981, Boundary and inertia effects on flow and heat transfer in porous media, Int. J. Heat Mass Transfer, 24, 195, 10.1016/0017-9310(81)90027-2 Ergun, 1952, Fluid flow through packed columns, Chem. Eng. Prog., 48, 89 Lai, 1987, Non-Darcy convection from horizontal impermeable surfaces in saturated porous media, Int. J. Heat Mass Transfer, 30, 2189, 10.1016/0017-9310(87)90096-2 Kodah, 1998, Non-Darcy mixed convection from a vertical plate in saturated porous media-variable surface heat flux, Wärme- Und Stoffübertragung, 33, 377, 10.1007/s002310050204 Islam, 1988, Mixed convection heat transfer in porous media in the non-Darcy regime, Can. J. Chem. Eng., 66, 68, 10.1002/cjce.5450660110 Ibrahim, 2000, Non-Darcy mixed convection flow along a vertical plate embedded in a non-Newtonian fluid saturated porous medium with surface mass transfer, Int. J. Numer. Method H., 10, 397, 10.1108/09615530010327387 Rami, 2001, Darcy-Forchheimer mixed convection heat and mass transfer in fluid saturated porous media, Int. J. Numer. Method H., 11, 600 Barletta, 2019, Unstable mixed convection flow in a horizontal porous channel with uniform wall heat flux, Transp. porous Med., 129, 385, 10.1007/s11242-019-01294-y Al-Hadhrami, 2002, Combined free and forced convection in vertical channels of porous media, Transp. porous Med., 49, 265, 10.1023/A:1016290505000 Wong, 2009, Numerical study of mixed convection on jet impingement cooling in a horizontal porous layer-using Brinkman-extended Darcy model, Int. J. Therm. Sci., 48, 96, 10.1016/j.ijthermalsci.2008.03.006 Sivasamy, 2010, Mixed convection on jet impingement cooling of a constant heat flux horizontal porous layer, Int. J. Therm. Sci., 49, 1238, 10.1016/j.ijthermalsci.2010.01.010 Umavathi, 2014, Mixed convection flow in a vertical channel filled with a fluid-saturated porous medium divided by a perfectly conductive baffle, Int. J. Microscale Nanoscale Therm. Fluid Transp. Phenom., 5, 127 Vajravelu, 2014, Mixed convection heat transfer in an anisotropic porous medium with oblique principal axes, J. Mech., 30, 327, 10.1017/jmech.2014.38 Basant, 2015, Mixed convection in an inclined channel filled with porous material having time-periodic boundary conditions: Steady-periodic regime, Transp. porous Med., 109, 495, 10.1007/s11242-015-0533-6 Basant, 2016, Role of heat generation/absorption on mixed convection flow in a vertical tube filled with porous material having time-periodic boundary condition: Steady-periodic regime, Transp. porous Med., 111, 681, 10.1007/s11242-015-0620-8 Tayari, 2015, Second law analysis in mixed convection through an inclined porous channel, Int. J. Thermophys., 36, 2881, 10.1007/s10765-015-1925-0 Tayari, 2016, Second law analysis through a porous Poiseuille–Benard channel flow, J. Heat Transfer, ASME, 138, 10.1115/1.4031731 Avramenko, 2018, Mixed convection in vertical flat and circular porous microchannels, Transp. porous Med., 124, 919, 10.1007/s11242-018-1104-4 Manish, 2021, Instability of mixed convection in a differentially heated channel filled with porous medium: A finite amplitude analysis, Phys. Fluids, 33 Shankar, 2021, Numerical investigation of the stability of mixed convection in a differentially heated vertical porous slab, Appl. Math. Comput., 389 Hwang, 1992, Effects of wall conduction and Darcy number on laminar mixed convection in a horizontal square porous channel, J. Heat Transfer Trans. ASME, 114, 614, 10.1115/1.2911325 Hadim, 1994, Numerical study of non-Darcy mixed convection in a vertical porous channel, J. Thermophys. Heat Trans., 8, 371, 10.2514/3.549 Hadim, 1994, Non-darcy mixed convection in a vertical porous channel with discrete heat sources at the walls, Int. Commun. Heat Mass Transf., 21, 377, 10.1016/0735-1933(94)90006-X Aldoss, 1996, Mixed convection from a vertical cylinder embedded in a porous medium: non-Darcy model, Int. J. Heat Mass Transfer, 39, 1141, 10.1016/0017-9310(95)00211-1 Chen, 2000, Non-Darcy mixed convection in a vertical channel filled with a porous medium, Int. J. Heat Mass Transfer, 43, 2421, 10.1016/S0017-9310(99)00299-9 Umavathi, 2005, Mixed convection in a vertical porous channel, Transp. porous Med., 61, 315, 10.1007/s11242-005-0260-5 Kumar, 2010, Influence of inertia and drag terms on the stability of mixed convection in a vertical porous-medium channel, Int. J. Heat Mass Transfer, 53, 5261, 10.1016/j.ijheatmasstransfer.2010.07.033 Kumar, 2011, Non-Darcy mixed convection in a vertical pipe filled with porous medium, Int. J. Therm. Sci., 50, 725, 10.1016/j.ijthermalsci.2010.11.018 Umavathi, 2012, Non-Darcy mixed convection in a vertical porous channel with boundary conditions of third kind, Transp. porous Med., 95, 111, 10.1007/s11242-012-0035-8 Adeniyan, 2016, Mixed convection radiating flow and heat transfer in a vertical channel partially filled with a Darcy-forchheimer porous substrate, Gen. Math. Notes, 32, 80 Sharma, 2018, Linear stability of mixed convection in a differentially heated vertical channel filled with high permeable porous-medium, Int. J. Therm. Sci., 134, 622, 10.1016/j.ijthermalsci.2018.08.027 Sharma, 2018, Finite amplitude analysis of non-isothermal parallel flow in a vertical channel filled with a highly permeable porous medium: A finite amplitude analysis, J. Fluid Mech., 857, 469, 10.1017/jfm.2018.745 Wong, 2009, Numerical study of non-darcian effects on jet impingement cooling in a horizontal porous layer in the mixed convection regime, Int. Commun. Heat Mass Transf., 36, 45, 10.1016/j.icheatmasstransfer.2008.09.011 Wong, 2009, Unsteady mixed convection of a confined jet in a fluid-superposed high porosity medium, Numer. Heat Transf.: A: Applications, 56, 827, 10.1080/10407780903466543 Saeid, 2018, Effect of the metallic foam heat sink shape on the mixed convection jet impingement cooling of a horizontal surface, J. Porous Media, 21, 295, 10.1615/JPorMedia.v21.i4.10 Dixon, 2017, Mixed convection in fluid-superposed porous layers. Part 1. analysis, Int. J. Heat Mass Transfer, 109, 1289, 10.1016/j.ijheatmasstransfer.2017.01.123 Dixon, 2017, Mixed convection in fluid-superposed porous layers. Part 2. experiments, Int. J. Heat Mass Transfer, 109, 1301, 10.1016/j.ijheatmasstransfer.2017.02.028 B. Buonomo, V. Fardella, O. Manca, S. Nardini, S. Vigna, Investigation on thermal and fluid dynamic behaviours in mixed convection in horizontal channels with aluminium foam and heated from below, in: E3S Web of Conferences, Section of Heat Transfer and Fluid Dynamics, Vol. 197, Roma, 81031 Aversa (CE), Italy, 2020, p. 10006. Mohammed, 2021, Heat transfer enhancement with pressure drop optimisation in a horizontal porous channel locally heated from below, Therm. Sci. Eng. Prog., 26 Vafai, 1984, Convective flow and heat transfer in variable porosity media, J. Fluid Mech., 147, 233, 10.1017/S002211208400207X Cheng, 1986, Fully-developed, forced convective flow through an annular packed-sphere bed with wall effects, Int. J. Heat Mass Transfer, 29, 1843, 10.1016/0017-9310(86)90003-7 Chen, 1996, Non-Darcy mixed convection along nonisothermal vertical surfaces in porous media, Int. J. Heat Mass Transfer, 39, 1157, 10.1016/0017-9310(95)00213-8 Chen, 1998, Mixed convection heat transfer from a horizontal plate with variable surface heat flux in a porous medium, Wärme- Und Stoffübertragung, 34, 1, 10.1007/s002310050224 Chou, 1995, Effect of stagnant conductivity on non-Darcian mixed convection in horizontal square packed channels, Numer. Heat Transf.: A: Applications, 27, 195, 10.1080/10407789508913696 Chang, 2004, Mixed convection in a horizontal square packed-sphere channel under axially uniform heating peripherally uniform wall temperature, Numer. Heat Transf.: A: Applications, 45, 791, 10.1080/10407780490269102 Saeid, 2004, Analysis of mixed convection in a vertical porous layer using non-equilibrium model, Int. J. Heat Mass Transfer, 47, 5619, 10.1016/j.ijheatmasstransfer.2004.07.033 Ahmed, 2011, Study of mixed convection in an annular vertical cylinder filled with saturated porous medium, using thermal non-equilibrium model, Int. J. Heat Mass Transfer, 54, 3822, 10.1016/j.ijheatmasstransfer.2011.05.001 Saeid, 2007, Jet impingement interaction with cross flow in horizontal porous layer under thermal non-equilibrium conditions, Int. J. Heat Mass Transfer, 50, 4265, 10.1016/j.ijheatmasstransfer.2007.02.025 Wong, 2009, Numerical study of mixed convection on jet impingement cooling in a horizontal porous layer under local thermal non-equilibrium conditions, Int. J. Therm. Sci., 48, 860, 10.1016/j.ijthermalsci.2008.06.004 Rees, 2011, The effect of local thermal non-equilibrium on the stability of convection in a vertical porous channel, J. Porous Media, 87, 459, 10.1007/s11242-010-9694-5 Wong, 2009, Numerical study of mixed convection on jet impingement cooling in an open cavity filled with porous medium., Int. Commun. Heat Mass Transf., 36, 155, 10.1016/j.icheatmasstransfer.2008.10.008 Kotresha, 2019, Determination of interfacial heat transfer coefficient for the flow assisted mixed convection through brass wire mesh, Int. J. Therm. Sci., 138, 98, 10.1016/j.ijthermalsci.2018.12.043 Khandelwal, 2012, A thermal non-equilibrium perspective on mixed convection in a vertical channel, Int. J. Therm. Sci., 56, 23, 10.1016/j.ijthermalsci.2012.01.014 Buonomo, 2014, Local thermal non-equilibrium mixed convection in channels partially heated at uniform heat flux filed with a porous medium Kotresha, 2020, Numerical simulations of flow-assisted mixed convection in a vertical channel filled with high porosity metal foams, Heat Transf. Eng., 41, 739, 10.1080/01457632.2018.1564208 Leela, 2020, Effect of asymmetrical wall heat flux and wall temperature ratio on mixed convection in a vertical micro-porous-channel with internal heat generation, Propuls. Power Res., 9, 394, 10.1016/j.jppr.2020.10.003