A novel heat transfer switch using the yield stress

Abstract

International audienceWe 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 heattransfer. Practically, this type of control can be actuated with electro-rheological ormagneto-rheological fluids. We demonstrate that above a given critical yield stressvalue only static steady regimes are possible, i.e. a purely conductive unyielded fluidfills the cavity. We show that this limit is governed by a balance of yield stressand buoyancy stresses, here described by B. With proper formulation the criticalstate can be described as a function of the domain geometry, and is independent ofother 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 perturbationsfrom a static regime decay to zero. Assuming stability, we show that the kineticenergy of the perturbed field decays to zero in a finite time, and give estimatesfor the stopping time, t0. This allows us to predict the response of the system insuppressing advective heat transfer. The unconditional stability is also considered forthe first time, illustrating the role of yield stress. We focus on the hydrodynamiccharacteristics of Bingham fluids in transition between conductive and convectivelimits. We use computational simulations to resolve the Navier–Stokes and energyequations for different yield stresses, and for different imposed controls. We showthat depending on the initial conditions, a yield stress less than the critical value canresult in temporary arrest of the flow. The temperature then develops conductivelyuntil the fluid yields and the flow restarts. We provide estimates of the hydrodynamictimescales of the problem and examples of flow transitions. In total, the theoreticaland computational results establish that this methodology is feasible as a control, atleast from a hydrodynamic perspective

Flow, onset and stability: Qualitative analysis of yield stress fluid flow in enclosures

“…3c. This seems to be a common feature among the steady state regimes as B → B cr or transient regimes whent →t e (see [7] for more examples). …”

“…In the situations explored 415 the difference comes from the (slow) evolution of the temperature field which changes the body force. Stability of the flows in §5 has not been considered here, but follows along similar lines as explored in [7,8]. Static steady states A C C E P T E D M A N U S C R I P T are generally stable but conditionally so.…”

“…These numerical and analytical estimates of b c are identified and explained in more detail in [7]. The computational procedure that is used for the numerical solution is also described in [7].…”

“…The computational procedure that is used for the numerical solution is also described in [7]. Time evolution of |u| is illustrated at various…”

“…Whether time-invariant or not, and whether coupled to the flow or independently prescribed, the body force determines how the momentum balance is affected by purely viscous stresses, yield stress and the body force, and hence allows for different dynamic behaviours; e.g. recent studies have illustrated the possibility of delayed flow 55 onset when the driving force is the buoyancy due to temperature differences in the domain [6,7,8]. In naturally convecting flows, the forcing is coupled with the flow field.…”