Numerical Study of Double Diffusive Convection in Partially Heated Vertical Open Ended Cylindrical Annulus (Advances in Applied Mathematics and Mechanics, 2021)
A numerical investigation of laminar natural double diffusive convection inan open ended vertical cylindrical annulus with unheated entry and unheatedexit is performed. Both boundary conditions of uniform wall temperature/uniformwall concentration (UWT/UWC) and uniform heat flux/uniform mass flux (UHF/UMF)are considered. Results of dimensionless induced volume rate $Q$, average Nusseltnumber $\overline{Nu}$ and Sherwood number $\overline{Sh}$ are obtained for airflow under various buoyancy ratio $N$, Grashof numbers due to heat and mass transfer$Gr_T$ and $Gr_M$, Schmidt number $Sc$ and combinations of unheated entry, heatedsection and unheated exit length. Since the flow under consideration is a boundarylayer type, the governing partial differential equations was discretized to a linearsystem of equations by the use of an implicit finite difference method. The nonlinearconvective terms are approximated by second upwind difference method for the numericalstability. The numerical results reveal that the presence of unheated entry and unheatedexit severely affects the heat and mass transfer rates. The numerical solutions are foundto approach asymptotically the closed form solutions for fully developed flow. Further,the present numerical results are validated with the existing solutions for pure thermalconvection and are found to be in good agreement.