Stability Analysis of Two Dimensional Fluid Flow in Rayleigh-Benard Convection Along With Rotation Using DTM-Pade Approximation

H V Gangamani, V Pooja, Achala L Nargund

Rayleigh- Benard convection, vorticity, Differential Transform Method, DTM- Pade approximation, Stability Analysis.

Two dimensional Rayleigh-Benard convection in a Boussinesq fluid is revisited using DTM-Pade approximation. The stationary and oscillatory instability analysis is obtained using critical Rayleigh numbers. We observe that the effect of   increasing the rotational rate is to increase the critical wave number and also the solutions are oscillating more in the horizontal direction as the rotational rate is increased. We have analysed the stability conditions to determine the type of instability at the onset of convection that were dependent on the value of the Taylor number and the Prandtl number. Asymptotic limits reveal that the flow would be comprised of columns of fluid aligned with the rotational axis since as the wave number increases the rotational rate also increases and the critical wave length decreases by setting the onset of convection in the form of tall thin columns. The flow equations are solved to obtain the linearised solutions and Differential Transform Method is applied along with Pade approximation to yield solutions without discretization and linearization and results are displayed in the graphical forms.

https://dx.doi.org/10.31873/IJEAS.7.10.09