Convective Instability in the Thermal Entrance Region of a Horizontal Parallel-Plate Channel Heated from Below

摘要: An investigation is carried out to determine the conditions marking onset of longitudinal vortex rolls due buoyant forces in thermal entrance region a horizontal parallel-plate channel where lower plate heated isothermally and upper cooled isothermally. Axial heat conduction included an analytical solution for Graetz problem with fully developed laminar velocity profile. Linear-stability theory based on Boussinesq approximation employed derivation perturbation equations. iterative procedure using high-order finite-difference applied solve equations comparison made against conventional second-order approximation. It found that Pr ≥ 0.7 flow more stable than region, but situation just opposite small Prandtl number, say ≤ 0.2. Graphical results critical Rayleigh numbers corresponding disturbance wavenumbers are presented case Pe → ∞ number as parameter air (Pr = 0.7) Peclet range dimensionless axial distance from between x 0.001 4 × 10−1 .