Through our paper, thermosolutal convection of viscoplastic materials ‘so called Bingham plastics’ which occurs into a porous matrix with an inner pollutant source has been treated numerically, in the aim to light out the impact of some relevant parameters; such Lewis and porous Rayleigh numbers; as well as the buoyancy ratio and the source dimension one; on a such conjugate phenomenon. To do so, the physical model for the momentum conservation equations is made using the Brinkman extension of the classical Darcy equation. The set of coupled equations is solved using the finite volume method and the SIMPLER algorithm. The heat and solute source within the porous space has taken a circular shape. Simply said, our pollutant source is a transport pipe which presented in 2D. To handle the latter in Cartesian Coordinates; the Cartesian Cut-Cell approach was adopted. After a careful treatment of such double-diffusive convection within the Bingham-porous space; powerful expressions that expect the mean transfer rates in such industrial geometry are set forth as a function of the governing parameters. These correlations, which predicted with ±3% the numerical results, may count as a complement to previous Newtonian-fluid researches. It is to note that the validity of the computing code was ascertained by comparing our results with experimental data and numerical ones, already available in the literature.
thermosolutal convection, bingham plastics, porous medium, circular pollutant source, finite volume approach, cut-cell approach, proposed models
 Nield DA, Bejan A. (1992). Convection in porous media. Springer, Berlin. http://dx.doi.org/10.1007/978-1-4757-2175-1.
 Mamou M, Vasseur P, Bilgen E. (1993). Multiple solution for double-diffusive convection in a vertical porous enclosure. Int. J. Heat Mass Transfer 36: 2479-2498. http://dx.doi.org/10.1016/0017-9310(94)00301-B
 Nithiarasu P, Seetharamo KN, Sundarajan T. (1996). Double-diffusive natural convection in an enclosure filled with fluid-saturated porous medium: A generalized Non-Darcy approach. Num. Heat Transfer Part A. 30: 413-426. http://dx.doi.org/10.1080/10407789608913848
 Ostrach S. (1980). Natural convection with combined driving forces. Phys-Chem. Hydrodynamic 1(04): 233-247. http://dx.doi.org/1980PhChH.1.233O
 Kamotani Y, Wang LW, Ostrach S, Jiang HD. (1985). Experimental study of natural convection in shallow enclosures with horizontal temperature and concentration gradients. Int. J. Heat Mass Transfer 28: 165-173. http://dx.doi.org/1985IJHMT.28.165K
 Lee J, Hyun MT, Kim KW. (1988). Natural convection in confined fluids with combined horizontal temperature and concentration gradients. Int. J. Heat Mass Transfer 31(10): 1969-1977. https://doi.org/10.1016/0017-9310(88)90106-8
 Benard C, Gobin D, Thevenin J. (1989). Thermosolutale natural convection in a rectangular enclosure. Numerical Results. in Heat Transfer in Convective Flows, ASME, R. K. Shah, Ed., New York, 249-254. http://dx.doi.org/1985IJHMT.28.165K
 Han H, Kuehn TH. (1989). A numerical simulation of double diffusive natural convection in a vertical rectangular enclosure, in Heat Transfer in Convective Flows, ASME, R.K. Shah, Ed., New York, 149-154.
 Chang J, Lin TF. (1993). Unsteady thermosolutal opposing convection of liquid-water mixture in a square cavity- II: Flow structure and fluctuation analysis. Int. J. Heat Mass Transfer 36: 1333-1345. https://doi.org/10.1016/S0017-9310(05)80101-2
 Chen F. (1993). Double-diffusive fingering convection in a porous medium. Int. J. Heat Mass Transfer 36: 793-807. https://doi.org/10.1016/0017-9310(93)80055-Y
 Trevisan O, Bejan A. (1987). Heat and mass transfer by high Rayleigh number convection in a porous medium heated from below. Int. J. Heat Mass Transfer 30(11): 2341-2356. https://doi.org/10.1016/0017-9310(87)90226-2
 Lin TF, Huang CC, Chang TS. (1990). Transient binary mixture natural convection in a square enclosure. Int. J. Heat Mass Transfer 33: 287-299. http://dx.doi.org/10.1016/0017-9310(90)90099-G
 Rachid B. (1993). Thermosolutal convection: fluid flow and heat transfer numerical simulations. Ph.D. Thesis, Pierre & Marie Curie, Paris.
 Ragui K, Boutra A, Benkahla YK. (2016). On the validity of a numerical model predicting heat and mass transfer in porous squares with a bottom thermal and solute source: Case of pollutants spreading and fuel leaks. Mech. & Ind. 17: 311. http://dx.doi.org/10.1051/meca/2015109
 Bingham EC. (1916). An investigation of the laws of plastic flow. Bul Bur Standards 13: 309-353. https://archive.org/details/inv133093531916278278unse
 Bingham EC. (1922). Fluidity and plasticity. Mc Graw -Hill, New-York, USA.
 Mitsoulis E, Tsamopoulos J. (2017). Numerical simulations of complex yield-stress fluid flows. Rheol Acta. http://dx.doi.org/10.1007/s00397-016-0981-0
 Pascal H. (1983). Rheological behaviour effect of non-Newtonian fluids on steady and unsteady flow through porous media. Int. J. Num. Anal. Methods Geomech 07: 207-224. http://dx.doi.org/10.1002/nag.1610070303
 Amari B, Vasseur P, Bilgen E. (1994). Natural convection of non-Newtonian fluids in horizontal porous layer. Warme und Stoffubertragung 29: 185-199. https://doi.org/10.1007/BF01548603
 Ragui K, Boutra A, Bennacer R, Benkahla YK. (2016). Heat and mass transfer into a porous annulus found between two horizontal concentric circular cylinders. applied mechanics, behavior of materials, and engineering systems. Book Lect.Notes Mechanical Engineering, Springer. http://dx.doi.org/10.1007/978-3-319-41468-3
 Turan O, Poole RJ, Chakraborty N. (2010). Aspect ratio effects in laminar natural convection of Bingham fluids in rectangular enclosures with differentially heated side walls. J. Non-Newtonian Fluid Mech. 166: 208-230. https://doi.org/10.1016/j.jnnfm.2010.12.002
 Turan O, Chakraborty N, Poole RJ. (2012). Laminar Rayleigh-Bénard convection of yield stress fluids in a square enclosure. J. Non Newtonian Fluid Mech. 171: 83-96. https://doi.org/10.1016/j.jnnfm.2012.01.006
 Hadidi N, Ould Amer Y, Bennacer R. (2013). Bi-layered and inclined porous collector: Optimum heat and mass transfer. Energy 51: 422-430. https://doi.org/10.1016/j.energy.2013.01.012
 Papanastasiou TC. (1987). Flow of materials with yeld J. Rheol. 31: 385-404. https://doi.org/10.1122/1.549926
 Aniri A, Vafai K. (1994). Analysis of dispersion effects and non thermal equilibrium, non-Darcian, variable porosity incompressible flow through porous medium. Int. J. Heat Mass Tranfer 37: 939-954. http://dx.doi.org/0017-9310(93)E0019-D
 Noirot R. (1990). Experimental and parametric studies of soot combustion in a particulate filter: Application to Diesel exhaust gas purifying. PhD Thesis, Haute Alsace University, http://www.theses.fr/1990MULH0147
 Paiola J. (2017). Ecoulement d’un fluide à seuil dans un milieu poreux. Mécanique des fluides [physics.class-ph] Paris-Saclay University, France; NNT: 2017SACLS031. HAL Id: tel-01563941. https://tel.archives-ouvertes.fr/tel-01563941
 Glowinski R, Wachs A. (2011). On the numerical simulation of viscoplastic fluid flow. In PG Ciarlet, JL Lions (eds.), Handbook of numerical analysis. Vol. 16, Num. Meth. Non Newtonian Fluids 06: 483-717. https://doi.org/10.1016/B978-0-444-53047-9.00006-X
 Nebbali R, Bouhadef K. (2006). Numerical study of forced convection in a 3D flow of a non-Newtonian fluid through a porous duct. Int. J. Numer. Methods Heat & Fluid Flow 16(8): 870-889. http://dx.doi.org/10.1108/09615530610702041
 Ragui K, Boutra A, Bennacer R, Benkahla YK. (2018). Progress on numerical simulation of yield stress fluid flows (Part I): Correlating thermosolutal coefficients of Bingham plastics within a porous annulus of a circular shape. Int. J. Heat & Mass Transfer 126: 72-94. https://doi.org/10.1016/j.ijheatmasstransfer.2018.05.010
 Colella P, Graves DT, Keen BJ, Modiano D. (2006). A cartesian grid embedded boundary method for hyperbolic conservation laws. J. Comput. Phys. 211(1): 347-366. http://dx.doi.org/10.1016/j.jcp.2005.05.026
 Patankar SV. (1980). Numerical heat transfer and fluid flow. Mc Grow, New York. ISBN 10: 0891165223 / ISBN 13: 9780891165224
 Ragui K, Benkahla YK, Labsi N, Boutra A. (2015). Natural convection heat transfer in a differentially heated enclosure with adiabatic partitions and filled with a Bingham fluid. J. Heat Transfer Research 08: 765-783. http://dx.doi.org/10.1615/2015007477
 Weaver JA, Viskanta R. (1992). Natural convection in binary gases driven by combined horizontal thermal and vertical solutal gradients. Exp. Thermal Fluid Sci. 05: 57-68. https://doi.org/10.1016/0894-1777(92)90056-B
 Kim BS, Lee DS, Ha MY, Yoon HS. (2008). A numerical study of natural convection in a square enclosure with a circular cylinder at different vertical locations Int. J. Heat Mass Transfer 51: 1888-1906. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2007.06.033
 Sheikholeslami M, Gorji-Bandpy M, Pop I, Soheil S. (2013). Numerical study of natural convection between a circular enclosure and a sinusoidal cylinder using control volume based finite element method. Int. J. Thermal Science 72: 147-158. https://doi.org/10.1016/j.ijthermalsci.2013.05.004
 Cheng P. (1985). Natural Convection in Porous Media: External Flow. in Natural Convection. Fundamentals and Applications. Edited by S. Kakac, W. Aung and R. Viskanta, Martinus Nijhoff Publisher, The Haque, The Netherlands 475-513.
 Beghein C, Haghighat F, Allard F. (1992). Natural study of double-diffusive natural convection in a square cavity. Int. J. Heat Mass Transfer 35-4: 833-846. https://doi.org/10.1016/0017-9310(92)90251-M
 Goyeau B, Songbe JP, Gobin D. (1996). Numerical study of double-diffusive natural convection in a porous cavity using the Darcy-Brinkman formulation. Int. J. Heat Mass Transfer 39-7: 1363-1378. https://doi.org/10.1016/0017-9310(95)00225-1