Natural-Convection Heat Transfer in Channels With Isoflux Convex Surfaces

Abstract

Numerical solutions are presented for laminar natural convection heat transfer in channels with convex surfaces that are subjected to a uniform heat flux. Simulations are conducted for several values of Grashof number (10 to 10⁴) and radius of curvature (1 to ∞). The governing elliptic conservation equations are solved in a boundary-fitted coordinate system using a collocated control-volume-based numerical procedure. The results are presented in terms of streamline and isotherm plots, inlet mass flow rates, curved wall temperature profiles, maximum hot wall temperature estimates, and average Nusselt number values. At the lowest radius of curvature, computations reveal the formation of recirculation zones in the exit section for all values of Grashof number considered. For a radius of curvature equal to or greater than 2, recirculation does not occur at any Grashof number. For values of radius of curvature between 1 and 2, the value of Grashof number at which recirculation occurs decreases with increasing values of the former. The variation in the buoyancy-induced volume flow rate is highly nonlinear with respect to the radius of curvature, and the value of the radius of curvature at which the volume flow rate is maximum increases with increasing Grashof number. The value of radius of curvature at which the maximum hot wall temperature is minimized increases with Grashof number. For all configurations studied, the average Nusselt number increases with increasing Grashof number values. Correlations for maximum wall temperature and average Nusselt number are provided.

Acknowledgments

The computational resources provided by the Center for Advanced Mathematical Sciences (CAMS) at the American University of Beirut (AUB) through the “Ibnsina” cluster are gratefully acknowledged.