DURGUN POROZ ORTAMDAN LİNEER VE LİNEER OLMAYAN VİSKOELASTİK AKIŞKANLARIN AKIŞI VE ISI TRANSFERİ İÇİN MATEMATİKSEL MODEL DENKLEMLERİ

GOVERNING EQUATIONS FOR QUASI-LINEAR AND NONLINEAR VISCOELASTIC FLUID FLOWS AND HEAT TRANSFER THROUGH STATIONARY POROUS MEDIA

Özet

Geçirgen heterojen ortamdaki akışkanın matematiksel modellemesi, Resin Transfer Molding, Injection Molding,vs. gibi birçok imalat proseslerinde önemli bir yer tutar. Bu araştırmada, Local Volume Averaging Techniquemetodu ile elde edilen 3 boyutlu, zamana bağlı izotermal olmayan genel bir matematiksel model elde edildi. Model,ortalama hız, basınç, polimerik gerilmeleri ve sıcaklık değerlerini kütle, momentum ve enerji korunum kanunlar ilepolimerik gerilme modellerini kullanarak elde etmektedir. Polimerik akışkan gerilmeleri için lineer (UCM veOldroyd-B modelleri) ve lineer olmayan (Giesekus ve PTT modelleri) modeller kullanılarak polimerik akışkanınviskoelastik karakteristikleri ortaya konulabilir.

Abstract

Mathematical modeling involving porous heterogeneous media is important in a number of compositemanufacturing processes, such as resin transfer molding (RTM), injection molding and the like. In this research, amathematical model by utilizing the local volume averaging technique to establish 3-D, time dependent and nonisothermalgoverning equations is presented. The developments should be able to predict the averaged velocity,pressure, polymeric stress and temperature fields by modeling the conservation laws (e.g. mass, momentum andenergy) of the flow field coupled with constitutive equations for polymeric stress field. The governing equationsof the flow are averaged for the fluid phase. Furthermore, the model target a variety of viscoelastic models (e.g.Newtonian model, Upper-Convected-Maxwell Model, Oldroyd-B model, Giesekus model and PTT modl) toprovide a fundamental understanding of the elastic effects on the flow field. The present research is focused onnon-isothermal considerations and a variety of constitutive models accounting for the viscoelastic flow behaviors

Anahtar kelimeler: Mathematical modeling, porous media, non-isothrmal viscoelastic fluid flows