64 citations · 563 across the 39 of their papers we have counts for
11 papers · 1 filter
Internal heating profiles for which downward conduction is impossible
Ali Arslan, Giovanni Fantuzzi, John Craske +1
We consider an internally heated fluid between parallel plates with fixed thermal fluxes. For a large class of heat sources that vary in the direction of gravity, we prove that $\l…
Rigorous scaling laws for internally heated convection at infinite Prandtl number
Ali Arslan, Giovanni Fantuzzi, John Craske +1
New bounds are proven on the mean vertical convective heat transport, , for uniform internally heated (IH) convection in the limit of infinite Prandt…
Analytical bounds on the heat transport in internally heated convection
Anuj Kumar, Ali Arslan, Giovanni Fantuzzi +2
We obtain an analytical bound on the mean vertical convective heat flux between two parallel boundaries driven by uniform internal heating. We consider two co…
The background method: Theory and computations
Giovanni Fantuzzi, Ali Arslan, Andrew Wynn
The background method is a widely used technique to bound mean properties of turbulent flows rigorously. This work reviews recent advances in the theoretical formulation and numeri…
Bounds for internally heated convection with fixed boundary heat flux
Ali Arslan, Giovanni Fantuzzi, John Craske +1
We prove a new rigorous bound for the mean convective heat transport , where and are the nondimensional vertical velocity and temperature, in internall…
Bounds on heat transport for convection driven by internal heating
Ali Arslan, Giovanni Fantuzzi, John Craske +1
The mean vertical heat transport in convection between isothermal plates driven by uniform internal heating is investigated by means of rigorous bounds. These…
New bounds on the vertical heat transport for Bénard-Marangoni convection at infinite Prandtl number
Giovanni Fantuzzi, Camilla Nobili, Andrew Wynn
We prove a new rigorous upper bound on the vertical heat transport for Bénard-Marangoni convection of a two- or three-dimensional fluid layer with infinite Prandtl number. Precisel…
Bounds for Rayleigh-Bénard convection between free-slip boundaries with an imposed heat flux
Giovanni Fantuzzi
We prove the first rigorous bound on the heat transfer for three-dimensional Rayleigh-Bénard convection of finite-Prandtl-number fluids between free-slip boundaries with an imposed…
Bounds on heat transfer for Bénard-Marangoni convection at infinite Prandtl number
Giovanni Fantuzzi, Anton Pershin, Andrew Wynn
The vertical heat transfer in Bénard-Marangoni convection of a fluid layer with infinite Prandtl number is studied by means of upper bounds on the Nusselt number as a function…
Exact energy stability of Bénard-Marangoni convection at infinite Prandtl number
Giovanni Fantuzzi, Andrew Wynn
Using the energy method we investigate the stability of pure conduction in Pearson's model for Bénard-Marangoni convection in a layer of fluid at infinite Prandtl number. Upon exte…
Optimal bounds with semidefinite programming: an application to stress driven shear flows
G. Fantuzzi, A. Wynn
We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the backgr…