Finite element solution to transient asymmetric heat conduction in multilayer annulus Research
This study investigate the heat transfer and thermal stresses for the time-dependent asymmetric heat conduction in a multilayer annulus by using finite element method. The realistic problem of isotropic multilayer annulus subjected to heat flux with internal heat generation and initial temperature is solved. The results of temperature and thermal stress have been computed numerically, illustrated graphically and interpreted technically. These results may be used in many engineering problem like combustion chamber, electric generator, compressor, hydraulic pumps etc. MSC: 35G30 • 35K20 • 74S05 • 80A20 • 80M10
A Thermal Stability Criterion for Heat Conduction in Multilayer Composite Solids
Excessive heat generation within a body can cause unbounded temperature or thermal instability. In this work, a new stability test is established for heat conduction in one-dimensional multilayer composite solids that have internal heat generation at a rate proportional to the interior temperature. In the development, a spatial state formulation in the Laplace transform domain and a root locus analysis yield a stability criterion. This criterion gives an upper bound of heat source for thermal stability and relates the degree of excessive heat production to the number of unstable (positive) eigenvalues. The proposed stability test does not need any information on system eigenvalues, requests minimum computational effort, and is applicable to composites with thermal resistance at layer interfaces and bodies with nonuniformly distributed parameters. The convenience and efficiency of the stability test are demonstrated in three numerical examples.
Thermal modeling of polymerizing polymethylmethacrylate, considering temperature-dependent heat generation.
A methodology for the modeling of unsteady heat conduction in polymethylmethacrylate (PMMA) during its exothermic polymerization is presented. The emphasis is on the formulation of a model for the volumetric rate of heat generation, including its temperature-dependent characteristics. Three parameters appear in the proposed model. The empirical determination of these parameters using Differential Scanning Calorimetry is demonstrated. The incorporation of the proposed model into finite volume methods is also demonstrated, in the context of unsteady, one-dimensional, radial heat conduction in cylindrical coordinates. In addition, the application of the proposed model to two test problems is presented and discussed. The results are encouraging, and the proposed methodology appears to be applicable to the thermal modeling of exothermic polymerization processes in general.