A novel heat transfer switch using the yield stress
Résumé
We explore the feasibility of a novel method for the regulation of heat transfer across a cavity, by using a controllable yield stress in order to suppress the convective heat
transfer. Practically, this type of control can be actuated with electro-rheological or
magneto-rheological fluids. We demonstrate that above a given critical yield stress
value only static steady regimes are possible, i.e. a purely conductive unyielded fluid
fills the cavity. We show that this limit is governed by a balance of yield stress
and buoyancy stresses, here described by B. With proper formulation the critical
state can be described as a function of the domain geometry, and is independent of
other dimensionless flow parameters (Rayleigh number, Ra, and Prandtl number, Pr).
On the theoretical side, we examine the conditional stability of the static regime.
We derive conservative conditions on disturbance energy to ensure that perturbations
from a static regime decay to zero. Assuming stability, we show that the kinetic
energy of the perturbed field decays to zero in a finite time, and give estimates
for the stopping time, t0. This allows us to predict the response of the system in
suppressing advective heat transfer. The unconditional stability is also considered for
the first time, illustrating the role of yield stress. We focus on the hydrodynamic
characteristics of Bingham fluids in transition between conductive and convective
limits. We use computational simulations to resolve the Navier–Stokes and energy
equations for different yield stresses, and for different imposed controls. We show
that depending on the initial conditions, a yield stress less than the critical value can
result in temporary arrest of the flow. The temperature then develops conductively
until the fluid yields and the flow restarts. We provide estimates of the hydrodynamic
timescales of the problem and examples of flow transitions. In total, the theoretical
and computational results establish that this methodology is feasible as a control, at
least from a hydrodynamic perspective.