Reconstructing temperature fields for thermally-driven flows under quasi-steady state

This letter introduces a method to reconstruct the temperature field of thermally-driven Boussinesq fluid flows. The technique relies on prescribed boundary conditions and a velocity field measured from particle image velocimetry. This information is then plugged into the heat equation to integrate and map the temperature field in space. We demonstrate the method’s skill by applying it to the problem of thermal convection in Hele-Shaw cells under a quasi-steady state. The limitations and strengths of this approach are discussed in the context of thermally-driven flows in laboratory experiments.