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Rayleigh Benard Convergence in Square Cavity Enclosure

Posted 27 feb 2026, 09:49 GMT-5 Heat Transfer 0 Replies

Chongyue Liang

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I am currently modelling 2D natural convection in a square cavity using the Boussinesq approximation and have encountered an issue when switching from a vertically differentially heated cavity (left wall hot, right wall cold) to a Rayleigh–Bénard configuration (bottom wall hot, top wall cold, vertical walls adiabatic). The fluid assigned is a nanofluid which the effective properties have been derived through the correct relationships and have been made in global parameters. Model setup: • Geometry: 2D square cavity • Physics: Laminar Flow (spf) + Heat Transfer in Fluids (ht) + Nonisothermal Flow • Coupling: Boussinesq approximation implemented via Volume force as no tick box for boussinesq approximation • Boundary conditions: – Bottom wall: isothermal hot – Top wall: isothermal cold – Vertical walls: adiabatic – All walls: no-slip • Density in Laminar Flow: constant (rho0) • Buoyancy implemented as a Volume Force: Fy = -rho0 * g_eff * beta * (ht.T - Tref) • Rayleigh number varied by defining: g_eff = Ra * nu * alpha / (beta * dT * L^3) and performing a parametric sweep over Ra. Issue: For all Rayleigh numbers tested (10^3 to 10^6): • Velocity magnitude remains the same across each Rayleigh number • Temperature field remains nearly linear (conduction profile) • Hot-wall heat flux does not change • Nusselt number remains exactly 1 across all Rayleigh values which is definitely incorrect All parameters (Ra, g_eff, buoyancy force magnitude) are confirmed to change between parametric steps via Global Evaluation. The buoyancy force expression is non-zero and applied to the fluid domain. Interestingly, when I revert to the vertically differentially heated configuration (left hot, right cold), the model behaves correctly: velocity develops and Nusselt number increases with Ra. This suggests the model is converging to the conduction branch in the Rayleigh–Bénard case for all Rayleigh numbers, even above the expected critical value.

I would appreciate guidance on best practice for obtaining the physically correct convective solution branch in this configuration. I believe all my physics are correct in my model and buoyancy is active and the above image shows the velocity plot for all Rayleigh values (it doesnt change). Below is my mph file of it and velocity plot picture which doenst change for any Rayleigh value - so definently incorrect.

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