Local heating of an unbounded orthotropic plate through a circular and annular domain

Model-based and Signal-Based Inverse Methods

“…The grid convergence study led to the selection of three mesh layers through the plate's thickness dimension, 9,780 total elements, and 45,983 degrees of freedom. Agreement between the final the direct model solution and the closed-form solution Kozlov et al [1989] is acceptable with mean absolute error less than 0.5K.…”

“…Mesh refinement is accomplished using all of the predefined free mesh sizes available in the direct model starting with the coarsest mesh and proceeding to the finest mesh. Grid convergence is achieved with 13,256 elements and 26,628 degrees of freedom, however the solution does not agree with an analytical solution of heating through a circular domain without convection Kozlov et al [1989] as illustrated in Figure 16. Element sizes from the converged 3D free mesh were used to create an extruded mesh which does agree the analytic solution (Figure 16).…”

Using Ultrasound and the Extended Kalman Filter for Characterizing Aerothermodynamic Environments

“…The grid convergence study led to the selection of a single mesh layer through the plate's thickness, a maximum element size in the rectangular heated area of 0.1 (dimensionless), 596 elements, and 3759 degrees of freedom. Independent verification of the numerical model was performed using a closed-form, analytical solution of heating through a circular domain without convection or radiation [17]. The areas of the heated zone for the circle model and the rectangle model were equal.…”

Optimum Thickness of a Cooled Wall in Local Pulse-Periodic Heating

“…Thus, in particular, for a heat flux with a Gaussian-type intensity the problem of determination of the "optimal thickness of the wall subjected local heating" has been solved [16] and also sufficient conditions of the existence of the optimum thickness of a cooled coated wall being pulse-periodically heated have been determined [17]. As far as the present authors are aware, for concentrated heat fluxes similar results are absent, which can be explained by the specific properties of the process of formation of corresponding temperature fields [18,19].…”

“…Thus, in particular, for a heat flux with a Gaussian-type intensity the problem of determination of the "optimal thickness of the wall subjected local heating" has been solved [16] and also sufficient conditions of the existence of the optimum thickness of a cooled coated wall being pulse-periodically heated have been determined [17]. As far as the present authors are aware, for concentrated heat fluxes similar results are absent, which can be explained by the specific properties of the process of formation of corresponding temperature fields [18,19].In the present work, we consider a plane isotropic wall of constant thickness h, one of the surfaces of which is exposed to the influence of both the surrounding medium with a constant temperature T c 0 and heat-transfer coefficient α 0 and a concentrated axisymmetrical heat flux q(r) in a pulse-periodic regime and the other surface of which is cooled by the external medium with a constant temperature T c h and heat-transfer coefficient α h . The main aim of the investigations carried out is analysis of the characteristic features of a stationary temperature field in the cooled wall on its exposure to a concentrated axisymmetric heat flux.…”