Algebraically explicit analytical solutions of two-buoyancy natural convection in porous media

Heatandmasstransferinporousmediaisanim portantprocessinmanyfieldssuchasin petroleumandgeothermalreservoirengineering ,thermaltech niqueinbuilding ,nuclearreactordesign ,environ mentprotection ,castingtechnology ,dryingtechnol ogyandsoforth .Itisnecessarytoresearchsuchphe nomenaindepth .Thetwo buoyancynaturalconvectioninporousmediawithbothtemperatureandconcentrationgradi entsisstudiedinthispaper.Suchphenomenonhasnotyetbeenresearchedindetail.Thesteadygeomet rically 2 Dgoverningequationsetsofsu…

Algebraically explicit analytical solutions of two-buoyancy natural convection in porous media

Analytical solutions of governing equations of various physical phenomena have their own irreplaceable theoretical meaning. In addition, they can also be the benchmark solutions to verify the outcomes and codes of numerical solution, and to develop various numerical methods such as their differencing schemes and grid generation skills as well. In order to promote the development of the discipline of natural convection, three simple algebraically explicit analytical solution sets are derived for a non-linear simultaneous partial differential equation set with five dependent unknown variables, which represents the natural convection in porous media with both temperature and concentration gradients. An extraordinary method separating variables with addition is applied in this paper to deduce solutions.