2023/11/19 by Brian Straughan, Straughan, Brian, A. Barletta +1
Computer Science · Engineering · #35Q35 #37N10 #76E06 #76E15 #76E30 #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Nanofluid Flow and Heat Transfer
paper · pdf · doi:10.48550/arxiv.2311.11264
openalex publication_date 2023/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We investigate the fully nonlinear model for convection in a Darcy porous material where the diffusion is of anomalous type as recently proposed by Barletta. The fully nonlinear model is analysed but we allow for variable gravity or penetrative convection effects which result in spatially dependent coefficients. This spatial dependence usually requires numerical solution even in the linearized case. In this work we demonstrate that regardless of the size of the Rayleigh number the perturbation solution will decay exponentially in time for the superdiffusion case. In addition we establish a similar result for convection in a bidisperse porous medium where both macro and micro porosity effects are present. Moreover, we demonstrate a similar result for thermosolutal convection.