Two-dimensional Steady Heat Conduction Research Articles

A new analytical model for the conduction shape factor of annulus sectors

Heat transfer devices, such as heat pipes, vapor chambers, thermosiphons, microchannel heat sinks, and Peltier cooling plates, rely on two-dimensional steady heat conduction to thermally manage telecommunications, aerospace, and microelectronics heat-generating components. The conduction shape factor can evaluate these devices’ two-dimensional steady heat conduction. The geometry of the device’s annulus and its mechanical attachment to the heat-generating component can vary. Given the prominence of single-sided heating and cooling, the two-dimensional heat conduction is commonly through an annulus sector. For the first time, an analytical model is developed to predict the conduction shape factor of annulus sectors. The present model is an extension of the previously developed equivalent concentric circular annulus model and applies the equivalent concentric circular annulus sector. The model is validated with results from finite element modeling for parametric boundary geometries, capturing most of the data across a variety of sectors within a relative difference of 10%. The present model provides a simple, closed-form analytical solution for the shape factor of an annulus sector formed between concentric arbitrarily shaped isothermal boundaries. More importantly, it provides a unified platform for designing and optimizing novel heat transfer devices.

Study on AZ91D chip for injection molding (2nd Report, Effect of dimension on effective thermal conductivity after consolidation)

The purpose of this study is to propose an effective model to estimate the effective thermal conductivity of compacts made from magnesium alloy particles, considering the effects of particle size, temperature and pressure. In order to investigate the influence of the particle size, six kinds of particles were prepared in which the cross sectional area was different. The test particles made from AZ91D were poured into a compression vessel and then a given pressure was applied to the piston of vessel for six hours under constant temperature condition. After compression, effective thermal conductivity of compacts were measured by steady state comparative-longitudinal heat flow method. The numerical calculation considering two-dimensional steady heat conduction was also conducted by using the actual cross section of compacts. Test results showed that the effective thermal conductivity of compacts were increased with increase of applied pressure and temperature elevation. Calculation results also revealed that by considering the actual cross section of compacts, the effective thermal conductivity could be well estimated when filling fraction is lower than 0.8. However, when filling fraction is exceed 0.8, the effect of thermal contact resistance between particles on thermal conductivity is not negligible. The experimental equation of effective thermal conductivity of compacts was determined to discuss the effects of cross sectional area of particles.

Two-dimensional steady heat conduction in functionally gradient materials by triple-reciprocity boundary element method

Homogeneous heat conduction can be easily solved by means of the boundary element method. However, domain integrals are generally necessary to solve the heat conduction problem in the functionally gradient materials. This paper shows that the two-dimensional heat conduction problem in the functionally gradient materials can be solved approximately without a domain integral by the triple-reciprocity boundary element method. In this method, the distribution of domain effects is interpolated by integral equations. A new computer program is developed and applied to several problems.