Fractional Derivative Modeling of Free Convective Flow over a Vertical Plate with Stability Analysis

The problem fractional derivative of flow and heat transfer by natural convection from a heated semi-infinite wall immersed in a fluid is studied numerically. The time derivative terms in both the momentum and energy equations are assumed fractional. Fractional derivative is a generalization to the normal derivative and it would be interesting to study its possible effects on both velocity and temperature fields. For accurate implementation, it is important that the results obtained by fractional derivative formulations reduce to the results obtained by normal derivative when the order of differentiation becomes the same. In this work, it is found that both the velocity and temperature profiles using fractional derivatives around first order (i.e., smaller and larger than one) encompass those obtained using first order time derivative. Nusselt number variations as well as friction coefficient profiles follow a similar pattern.