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Summary
Souvla, which can be summed up as a chunkier version of the Greek souvlaki, is widely considered to be Cyprus' national dish. Large chunks of lamb or pork meat are pierced with a long metallic skewer and cooked above a rectangular grill, known as a foukou (φουκού), by rotating the skewer using a motor. In this work we model the cooking process by initially solving the heat equation with rotating Dirichlet boundary conditions, used to simulate heat transfer through pure induction. In this setting we compute a zeroth-order accurate singular perturbation asymptotic expansion of the solution as the angular velocity of the skewer tends to infinity. We additionally recover an analytic expression for the theoretical cooking time in this regime (time it takes for the meat to reach the desired cooking temperature) through a leading-order Fourier mode approximation attributed to the sparse spectrum of the solution, which we validate via numerical simulations using the Python spectral solver library, Dedalus. We expand on these findings by extending our model to a Taylor–Couette flow heat transfer model, where the grill now surrounds the meat on one of its "sides". This leads to a heat equation with rotating Robin boundary conditions that simulate heat transfer at the meat boundary through convection (via the Boussinesq approximation of natural convection) and radiation from the grill (after a Stefan–Boltzmann linearisation). In this more elaborate setting, we similarly produce a zeroth-order accurate singular perturbation asymptotic expansion of the solution and a theoretical cook-through time as the angular velocity grows unboundedly. This cook-through time is then compared against numerical results from simulations of the full equations in Dedalus by using a mixture of the Diffuse Domain Method (DDM) and the Volume Penalty Method (VPM) to solve the double domain (meat-outside) heat transfer Taylor–Couette flow model, which is driven by a combination of multiple time scales inside and outside the meat, fluid velocity and temperature damping scales, and boundary layers developing at the meat surface. (This project is work in progress/put on-hold.)
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