Development length of fluids modelled by the gPTT constitutive differential equation

• Autor(a) principal: Bertoco, Juliana
• Data de Publicação: 2021
• Outros Autores: Leiva, Rosalía T., Ferrás, Luís Jorge Lima, Afonso, Alexandre M., Castelo, Antonio
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/75239
• topic: viscoelastic fluids; finite-differences; development length; generalised PTT model; Ciências Naturais::Matemáticas; Engenharia e Tecnologia::Engenharia Mecânica; Science & Technology; Indústria, inovação e infraestruturas

In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach 99% of its fully-developed value) of a pressure-driven viscoelastic fluid flow (between parallel plates) modelled by the generalised Phan–Thien and Tanner (gPTT) constitutive equation. The governing equations are solved using the finite-difference method, and, a thorough analysis on the effect of the model parameters α and β is presented. The numerical results showed that in the creeping flow limit (Re=0), the development length for the velocity exhibits a non-monotonic behaviour. The development length increases with Wi. For low values of Wi, the highest value of the development length is obtained for α=β=0.5; for high values of Wi, the highest value of the development length is obtained for α=β=1.5. This work also considers the influence of the elasticity number.