Computation of thermo-solutal convection with soret-dufour cross diffusion in a vertical duct containing carbon/metallic nanofluids

Duct flows constitute an important category of modern thermal engineering. Optimizing efficiency has become a significant objective in the 21st century in, for example, heating ventilation and air-conditioning (HVAC), coolant or heat transfer fluid flows in a nuclear power reactor, heat exchanger design etc., and this has been achieved by either new materials (improved thermal insulation properties) constituting the duct walls, novel geometric designs, or improved working fluids. Nanotechnology has infiltrated into duct design in parallel with many other fields of mechanical, medical, and energy engineering. Motivated by the excellent potential of nanofluids, a subset of materials engineered at the nanoscale, in the present work, a new mathematical model is developed for natural convection in a rectangular vertical duct containing nanofluid. The left and right walls of the duct are maintained at constant and unequal temperatures, while the front and rear walls of the duct are insulated. Thermo-solutal (double-diffusive) natural convection of aqueous nanofluid containing various metallic nanoparticles (e. g., copper and titanium oxide) or carbon-based nanoparticles (e. g., diamond and silicon oxide) is simulated. The Tiwari–Das nanoscale volume fraction model is used in addition to the Brinkman and Maxwell models for defining the properties of the nanofluid. The partial differential conservation equations for mass, momentum and energy are non-dimensionalized via appropriate transformations and the resulting boundary value problem is solved with a second-order accurate implicit finite difference technique employing Southwell-Over-Relaxation (SOR). Mesh independence tests are conducted. Extensive visualization of the solutions for velocity, temperature, and nanoparticle concentration (volume fraction) are presented for five different nanoparticles (silicon oxide, diamond, copper, titanium oxide, and silver), thermal Grashof number, nanoparticle species (solutal) Grashof number, volume fraction of nanoparticles (i.e., percentage doping), Dufour number, Soret number, Prandtl number, Schmidt number, and duct aspect ratio. It is observed that the heat transfer rate (Nusselt number) at both the walls is maximized for diamond nanoparticles and minimized for silicon oxide nanoparticles. Further, the heat transfer rate for clear fluid is lower when compared with nanofluid, confirming that nanoparticles achieve the desired thermal enhancement at the boundaries also. The mass transfer at both walls (Sherwood number), however, is not significantly influenced by any particular type of nanoparticle, thermal and concentration Grashof number and is depleted with higher values of Dufour, Prandtl, Soret, and Schmidt numbers in addition to aspect ratio. However, Sherwood numbers at both the left and right duct walls are substantially boosted with greater solid volume fraction of nanoparticles.