Mathematical Modelling Of Heat Transfer Processes With Particular Application To Lighting Fittings

In this thesis the heat transfer processes which are present in a lighting fitting are described and modelled. The coupling of these processes is also studied. All (of the models have been made as general as possible and could be applied to other heat transfer situations, ranging from solar collectors to production of semiconductor crystals, with little amendment. The main interest in the work is in two areas: firstly, in the solution of the coupled nonlinear partial differential equations which describe natural convection and secondly in the study of the coupling of radiation and convection in the lighting fitting, together with external heat transfer effects. The governing equations for natural convection were solved using a finite element method and various results were obtained in this area. The coupled problem was described by two models =: one involving a simple model of the internal convection and the other using a finite element model of this mechanism. The solution of coupled radiation and convection using finite elements has not been done before, although there has been some simultaneous work in this area. The inclusion of external heat transfer effects in the study of coupled radiation and convection in a cavity is also a new field: the only previous work on this subject used finite difference methods and was concerned with rectangular cavities ; here finite element methods are used and the geometry is axisymmetric. The coupled models were applied to the lighting fitting and temperatures at the shade of the fitting were predicted ; these predictions were compared with experiment and reasonable agreement was found. The models described here represent an improvement over previous work on prediction of temperatures in fittings; this improvement is due to the fact that the natural convection was modelled in a more detailed way than previously.