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Abstract
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 foukou, 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. This includes the computation of a zeroth-order accurate singular perturbation asymptotic expansion of the solution, as the angular velocity of the skewer tends to infinity, as well as an analytic expression for the theoretical cooking time (time it takes for the meat to reach the desired cooking temperature), which we validate via numerical simulations using the Python spectral solver library, Dedalus. We then 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", which leads to a heat equation with rotating Robin boundary conditions, simulating 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 elaborate setting, we again produce in the same manner a zeroth-order accurate singular perturbation asymptotic expansion of the solution and a theoretical cook-through time, as the angular velocity grows unboundedly, using a first Fourier mode approximation attributed to the sparse spectrum. 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 heat transfer Taylor-Couette flow setting, which is driven by a combination of multiple time scales inside and outside the meat, fluid and temperature damping scales, and boundary layers developing at the meat surface.
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