Natural convection flow in a vertical annulus with time-periodic thermal boundary conditions

Basant K. Jha, Michael O. Oni ^*

Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria

Abstract: This paper presents an analytical solution for natural convection flow in a vertical annulus due to time-periodic heating of annulus surfaces. Closed-form expressions for velocity, temperature, skin-friction, mass flow rate and rate of heat transfer which is expressed as Nusselt number are obtained by solving the present mathematical model after separating into steady component and periodic regime. The effects of pertinent parameters such as Strouhal number (St), Prandtl number (Pr) and radius ratio (λ) are shown with the aid of contour and line graphs. Results indicate that the role of Strouhal number and Prandtl number is to decrease fluid velocity, temperature and skin-friction. Furthermore, increase in Strouhal number increases the temperature phase-lag.

Keywords: Natural convection; Fully developed flow; Time-periodic heating; Vertical annulus; Strouhal number