On the stability of the flow over a shrinking cylinder with prescribed surface heat flux

Izyan Syazana Awaludin ^a,b, Rokiah Ahmad ^b, Anuar Ishak ^b,*

a. Faculty of Management, Multimedia University, 63100 Cyberjaya, Selangor, Malaysia
         b. Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

Abstract: This study investigates the steady stagnation point flow and heat transfer passes a horizontal shrinking permeable cylinder. The free stream velocity and the prescribed surface heat flux are assumed to vary linearly with the distance from a fixed point on the cylinder. The partial differential equations governing the flow and heat transfer are transformed into a system of ordinary differential equations via similarity transformation. These equations are solved numerically for several values of the governing parameters, such as suction parameter s, curvature parameter γ, and shrinking parameter λ. The equations are solved numerically by employing the boundary value problem solver package available in MATLAB software, bvp4c. The effects of the governing parameters on the skin friction coefficient, surface temperature, velocity, and temperature profiles are examined. Given the existence of dual solutions in the present study for a certain range of the curvature parameter, stability analysis is carried out to determine which one of the solutions is stable as time passes. The outcome of the stability analysis demonstrates that only the first solution, with lower boundary layer thickness, appeared to be stable and thus physically reliable, while the other is not. It is also discovered that the boundary layer separation is delayed by reducing the curvature parameter.

Keywords: Stagnation point flow; Heat transfer; Shrinking cylinder; Prescribed surface heat flux; Stability analysis