Transient Natural Convection in Partitioned Enclosures

In this paper, the natural convection flow in a cavity heated differentially with a partition placed in the middle of the hot wall is numerically simulated. The aspect ratio of the geometry, Prandtl number are fixed at 0.24, 6.64, respectively, for different partitions lengths; however the Rayleigh number values were ranging from 106 to 3.77 × 109 in order to observe the transition regime. The fluid flow and the heat transfer described in terms of continuity, linear momentum and energy equations were predicted by using the finite volume method. To approach the physical reality experience, calculations were performed in a cavity with the same size and same priority of the fluid with an average temperature Tm imposed on the cooled wall, also another simulation with an average temperature Tm imposed on the horizontal wall.Time evolution, isotherms and mean Nusselt number are presented for all investigated values. Representative results illustrating the effects of the partition length for the heat transfer and the thermal boundary layer are also reported and discussed. The results indicate that the flow and heat transfer properties are altered by the presence of the partition, especially in the initial stage. In a certain sense, the partition blocks the flow and forces it to come off the hot wall. Since the partition parameters are critical for the transient natural convection flow in the cavity, different partition lengths on the warm wall have been studied.

Vector eigenfunction expansion in the integral transform solution of transient natural convection

Purpose The purpose of this work is to revisit the integral transform solution of transient natural convection in differentially heated cavities considering a novel vector eigenfunction expansion for handling the Navier-Stokes equations on the primitive variables formulation. Design/methodology/approach The proposed expansion base automatically satisfies the continuity equation and, upon integral transformation, eliminates the pressure field and reduces the momentum conservation equations to a single set of ordinary differential equations for the transformed time-variable potentials. The resulting eigenvalue problem for the velocity field expansion is readily solved by the integral transform method itself, while a traditional Sturm–Liouville base is chosen for expanding the temperature field. The coupled transformed initial value problem is numerically solved with a well-established solver based on a backward differentiation scheme. Findings A thorough convergence analysis is undertaken, in terms of truncation orders of the expansions for the vector eigenfunction and for the velocity and temperature fields. Finally, numerical results for selected quantities are critically compared to available benchmarks in both steady and transient states, and the overall physical behavior of the transient solution is examined for further verification. Originality/value A novel vector eigenfunction expansion is proposed for the integral transform solution of the Navier–Stokes equations in transient regime. The new physically inspired eigenvalue problem with the associated integmaral transformation fully shares the advantages of the previously obtained integral transform solutions based on the streamfunction-only formulation of the Navier–Stokes equations, while offering a direct and formal extension to three-dimensional flows.