Bifurcation in steady laminar mixed convection flow in uniformly heated inclined tubes

The fully developed laminar mixed convection flow in inclined tubes subject to axially and circumferentially uniform heat flux has been studied numerically for a Boussinesq fluid. Dual solutions characterized by a two‐ and a four‐vortex secondary flow structure in a cross‐section normal to the tube’s longitudinal axis have been found for different combinations of the Grashof number Gr and of the tube inclination α for all Prandtl numbers between 0.7 and 7. In the two‐parameter space defined by Gr and α dual solutions occur: at a given α, if the Grashof number exceeds a critical value Gr_ℓ (for horizontal tubes Gr_ℓ is approximately 5.5 × 10⁵, 1.7 × 10⁵ and 1.7 × 10⁴ respectively for Pr = 0.7, 7 and 70); at a given Gr, if the tube inclination is below a critical value α_c (for Gr = 10⁶ this critical angle is approximately 62.5° and 83.5° respectively for Pr = 0.7 and 7). Numerical experiments carried out for developing flows indicate that the two‐vortex solution is the only stable flow structure.