Numerical solution of natural convective heat transfer in parabolic enclosures

Abstract

Laminar free convective heat transfer within parabolic enclosures has been investigated using numerical computation methods. The geometry is a long cavity made up of a parabolic wall bowed over a horizontal wall. Due to symmetry, the analytical model is one-half of a two-dimensional cross-section consisting of a hot parabolic upper-wall, a cold horizontal base and an adiabatic vertical wall. Two cases of heat input from the parabolic upper-wall have been considered, namely (i) isothermal condition on the hot wall, and (ii) constant heat-flux through the hot wall. The base and vertical walls are made isothermal and adiabatic, respectively. A finite difference technique called ‘staggered differencing’ (SD) for both regular and irregular boundaries is applied in the iterative solution of the mass, momentum and energy equations. Steady state solutions have been obtained for the heat transfer to the cold base in the form of local and mean Nusselt numbers for 0.05 ⩽ H/ B ⩽ 1.0, 0 ⩽ Gr B ⩽ 10 9, 0.73 ⩽ Pr ⩽ 20 and 0 < C ft ⩽ 0.33. Results show that in case (i) the heat transfer rate to the cold wall increases with increase in Gr and Pr but decreases with increase in H/B and C ft , except for an anomaly for C ft = 0.33, i.e. the circular profile. In case (ii), the heat transfer rate increases with increase in Gr, H/B, Pr and C ft .