Natural convection in a parallelogrammic enclosure partially heated from below

الملخص EN

Natural convection in a parallelogrammic enclosure partially heated from below lias investigated numerically.

The side walls are symmetrically cooled, and the upper wall is thermally insulated.

Flow within the enclosure is steady, two-dimensional, and laminar.

The Cartesian velocity components and pressure on a collocated (non-staggered) grid are used as dependent variables in the momentum equations, which discretized by finite volume method ; body fitted coordinates are used to represent the parallelogrammic enclosure, and grid generation technique based on elliptic partial differential equations is employed.

SIMPLE algorithm is used to adjust the velocity field to satisfy the conservation of mass.

The range of Rayleigh number is (103 < Ra < 10s ), the tilt angles of the side walls are (θ = 0°, 30°, 45° and 60°), the dimensionless heat source lengths are (D* = 0.2, 0.4, 0.6 and 0.8), the dimensionless heat source positions are (δ* = 0.2 , 0.5 and 0.8), and Prandtl number is (Pr = 0.7).

The results showed that at Ra = 103, the higher heat transfer occurs for parallelogrammic enclosure at angle (θ = 60°) and the lower heat transfer occurs for square enclosure (θ = 0°) irrespective of heat source length (D*).

At Ra = 105, the higher heat transfer occurs for square enclosure (θ = 0°) and the lower heat transfer occurs for parallelogrammic enclosure at angle (θ = 60°) for heat source length (D* = 0.2, 0.4 and 0.6), while at the heat source length (D* = 0.8) the higher heat transfer occurs at (θ = 60°) and the lower heat transfer occurs at (θ = 30°).

Also at Ra = 105 and constant of the heat source length (D* = 0.2), the average Nusselt number (Nuav) almost constant for all positions of the heat source (δ* = 0.2, 0.5, 0.8) for angles (θ = 0°, 30°, 45°) whereas at angle (θ = 60°) the maximum average Nusselt number (Nuav) is found at the heat source position (δ* = 0.2) and minimum average Nusselt number (Nuav) is found at the heat source position (δ* = 0.5).