Natural Element Method For Coupled Radiation-conduction Heat Transfer And Inverse Geometry Design

Heating devices with considering coupled radiation-conduction heat transfer isan important heat transfer equipment in engineering, they are not only used for tradi-tional boiler, but also get important applications in high-precision special materialprocessing and modeling, special materials drying, electronic components package. Tomeet special requirement of engineering, pre-design of heating devices need to beconducted. Geometric inverse design for heating devices with considering coupledradiation-conduction heat transfer involve changing boundaries. To solve these prob-lems, the traditional methods must suffer from the drawbacks of repeatedly meshingand remeshing. Natural element method is a kind of meshless method based on natu-ral neighbor interpolation, it don’t rely on mesh, and has great advantage in solvingproblem involve changing boundaries.In this dissertation, natural element method has been employed to solve the radi-ative heat transfer problems in participating media. The theory of natural elementmethod, the properties of shape function and numerical characteristics are introduced.The natural element method solution of pure radiative heat transfer, coupled radia-tion-conduction heat transfer is investigated. Natural element method is also extendedto solve inverse geometry design of heating devices with considering coupled radia-tion-conduction heat transfer.The main work includes the following five aspects of investigations.1) The difference of shape function constructed by the two natural neighbor interpo-lation is examined, and both of the interpolations are compared to the linear finiteelement. The numerical characteristics of the natural neighbor interpolation aredeeply investigated.2) Based on the discrete ordinate equations, the natural element meshless methodapproach for pure radiative heat transfer and coupled heat transfer are established.Using this method to solve pure radiative heat transfer of participating media inrectangle and trapezoid, correctness of the result is validated by comparison withliterature data.3) The natural element meshless method approach for coupled radiation-conductionheat transfer of participating media is investigated. Thesis studies steady coupledradiation-conduction heat transfer in rectangle and annulus containing participat-ing medium. While for transient condition, the coupled radiation-conduction heattransfer in rectangle containing participating medium is investigated. Correctness of the natural element method results is validated by comparison with the litera-ture data.4) The natural element method is applied to solve coupled radiation-conduction heattransfer involve the second and third heat transfer boundary condition. The naturalelement discretization equation of semitransparent and opaque boundary condi-tions is derived. Correctness of the processing scheme is validated by comparisonwith the literature data. On this basis, the coupled radiation-conduction heat trans-fer problems in rectangle are investigated.5) The natural element method has been extended to solve inverse geometry designwith considering coupled radiation-conduction heat transfer. The coupled heattransfer is solved by the least square natural element method. The modified con-jugate gradient method is used to minimize the object function. In the inverse de-sign progress, the height of the adiabatic surfaces and the geometric shape of theheating surface are constantly adjusted, finally the design requirement of thepre-specified total heat flux distribution on the pre-appointed region of heatedsurface is satisfied. Correctness of the natural element method solution of thisphysical model is validated by comparison with the literature data. On this basis,the inverse geometry design is investigated, the influences of the number of designpoints, scattering albedoes on coupled radiation-conduction parameters on the de-sign results are examined.