Conjugate effect of fluctuating thermal and mass diffusion on the flow of viscous fluid along flat and cylindrical surfaces

Abstract

Numerical investigations have been carried out to look into the e ect of double-di usion on laminar ow along vertical at and cylindrical surfaces. Conventional convective processes i.e. natural convection, mixed convection and magnetohydrodynamic (MHD) natural convection have been considered and six di erent models are studied deeming oscillating surface temperature and species concentration boundary conditions. In each case, extensive parametric simulations are performed in order to elucidate the e ects of some important parameters i.e. Prandtl number, Schmidt number, buoyancy ratio parameter, Straouhal number, and magnetic parameter on ow eld in conjunction with heat and mass transfer. Di erent numerical techniques are applied to solve the governing equations. Asymptotic solutions for low and high frequencies are obtained for the conveniently transformed governing coupled equations. Solutions are also obtained for wide ranged values of the frequency parameter. At the very outset of this dissertation, natural convection ow along vertical at plate is considered. The surface temperature and species concentrations are assumed to be of small amplitude oscillation. In this study, the similar boundary conditions are imposed for surface temperature and concentration as well as surface heat and mass ux. Finally, comparative study has been made to nd a correlation between these two cases. Comparison between the perturbation solutions and the solutions for the wide ranged values are made in terms of the amplitude and phase of the shear stress, surface heat transfer and surface mass transfer coe cient. It has been found that the amplitudes and phase angles obtained from asymptotic solutions are in good agreement with the nite di erence solutions obtained for wide ranged values of the frequency parameter. This simulated results are validated against some published results. Flow along a vertical wedge is taken into account and the convective process is deemed as mixed convection in the subsequent model study. In this study also, the surface temperature and velocity boundary conditions are assumed to be sinusoidal and amplitude of the oscillation is considered very small. Implicit nite di erence method is used to solve the governing equations of the entire ow eld and results obtained from this method are regions of the ow eld, respectively. To study the parametric e ects on the heat transfer rate, results are calculated in terms of amplitude and phase angles of shear stress and heat transfer coe cient. In the next investigation, the preceding model is extended to study heat and mass transfer simultaneously. In order to take into account the concentration eld, another convection-di usion equation is added with the governing set of equations and corresponding boundary condition is assumed to be similar to surface temperature boundary condition. Wide-ranging parametric studies have been carried out and results are presented in both tabular and graphical forms. Magnetohydrodynamic (MHD) natural convection ow is investigated considering uctuating surface temperature and concentration boundary condition. Results obtained in the present investigation are compared with some other published results and further numerical investigations are accomplished to study the both heat and mass transfer by using implicit nite di erence method. It has been assumed in this study that, in some undisturbed ow region, there is an uniform magnetic eld making a non-zero angle with it. Mixed convection ow along horizontal heated cylinder have been considered in the last two models and full set of Navier-Stokes equations in terms of vorticity and stream function is solved. Parametric studies have been carried out in these cases and heat and mass transfer rates are observed by calculating the Nusselt number and Sherwood number. In the rst investigation of these type of ow, non-uniform surface temperature and concentration are considered with no oscillations. After that, the same problem is studied by allowing small amplitude oscillations in surface velocity, temperature and species concentration. In both the cases, isothermal lines and isoconcentration contours are drawn to visualize the temperature and concentration distribution by varying the relevant parameters. Important ndings are listed after each investigation and nally concluding remarks are brought out based on the overall investigation and understanding. Almost all the cases, the present simulations are validated either qualitatively or quantitatively by comparing with some published results.