The present work relates to a numerical investigation of double diffusive mixed convection around a horizontal annulus with a finned inner cylinder. The solutal and thermal buoyancy forces are sustained by maintaining the inner and outer cylinders at uniform temperatures and concentrations. Buoyancy effects are also considered, with the Boussinesq approximation. The forced convection effect is induced by the outer cylinder rotating with an angular velocity (ω) in an anticlockwise direction. The studies are made for various combinations of dimensionless numbers; buoyancy ratio number (N), Lewis number (Le), Richardson number (Ri) and Grashof number (Gr). The isotherms, isoconcentrations and streamlines as well as both average and local Nusselt and Sherwood numbers were studied. A finite volume scheme is adopted to solve the transport equations for continuity, momentum, energy and mass transfer. The results indicate that the use of fins on the inner cylinder with outer cylinder rotation, significantly improves the heat and mass transfer in the annulus.

A numerical analysis was performed to study the effects of combined double diffusive and viscous dissipation under non-uniform wall boundary conditions on heat and mass transfer for a viscous nanofluid past a semi-infinite vertical plate embedded in porous medium which descriped by Darcy-Forchheimer extension. The mathematical model of nanofluid incorporate the Brownian motion and thermophoresis mechanisms. The nonlinear governing equations are reduced to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by Keller-Box method. A parametric study is achieved and obtained numerical results are presented with the help of graphical illustrations, in order to ride how the governing parameters affects the flow field, temperature, concentration and solide volume fraction profiles. Furthermore, some interesting data for the local Nusselt and Sherwood numbers are also illustrated.

The purpose of this study is to examine the instabilities of a two-dimensional mixed convection boundary layer flow induced by an impinging ascending flow on a heated horizontal cylinder. A significant amount of works is done in recent years on this problem because of its wide range of applications. However, they did not check the stability of the flow in the face of small disturbances that occur in reality. For this, we adopt the linear stability theory by first solving the steady basic flow and then solving the linear perturbed problem. Thus, the governing equations of the basic flow are reduced to two coupled partial differential equations and solved numerically with the Keller-Box method. The corresponding steady solution is obtained, by varying the position along the cylinder’s surface, for different values of Richardson number (λ) and Prandtl number (Pr), up to, respectively, 3000 and 20. To examine the onset of thermal instabilities, the linear stability analysis is done using the normal mode decomposition with small harmonic disturbances. The Richardson number λ is chosen as the control parameter of these instabilities. The resulting eigenvalue problem is solved numerically by the use of the pseudospectral method based on the Laguerre polynomials. The computed results for neutral and temporal growth curves are depicted and discussed in detail through graphs for various parametric conditions. The critical conditions are illustrated graphically to show from which thermodynamic state, the flow begins to become unstable. As a main result, from ξ = 0 to ξ ≈ π/3, we found that forced and mixed convection flow cases are linearly stable in this region. However, in free convection case (λ > 100), it appears that the stagnation zone is the most unstable one and then the instability decreases along the cylinder’s surface up to the limit of its first third, thus giving the most stable zone of the cylinder. Beyond ξ ≈ 1.2, strong instabilities are noted also for low values of Richardson number, and the flow tends to an unstable state even in the absence of thermal effect, i.e., hydrodynamically unstable Ri = 0, probably due to the occurring of the boundary layer separation.

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