A novel heat transfer switch using the yield stress
Bibliographic record
Abstract
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, $\mathit{Ra}$ , and Prandtl number, $\mathit{Pr}$ ). 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, $t_{0}$ . 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.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".