Three-dimensional convective cooling in a vertical channel with protruding heat sources

Three-dimensional thermal convection in a vertical channel with spatially-periodic, uniform flux, protruding heat sources mounted on one vertical wall is investigated numerically. A Boussinesq fluid of Prandtl number, Pr = 0.71 is assumed throughout this study and the non-dimensional channel reference temperature is kept constant at Θ₀ = 0.17. The flow and heat transfer characteristics are presented for Grashof numbers within the range 1 ≤ Gr ≤ 7 × 10⁴ based on the channel width. The governing equations with the appropriate boundary conditions are solved by a spectral element method. Integration in time is based on conventional finite difference techniques. All numerical solutions are obtained using a time-accurate integration scheme. For given aspect ratios, and for sufficiently small Grashof numbers, the solution evolves to a unique, time-independent state that exhibits the maximum symmetry consistent with the boundary conditions. For time-dependent solutions (Gr ≥ Gr_c) the symmetry of the flow and temperature fields breaks down. Data on maximum temperature rise, local and average Nusselt number distributions and time-oscillatory behavior are presented, and their implications to design are discussed.