Asymptotic analysis of boundary layer of a thermo-dependent fluid flow

• Published in: International journal of non-linear mechanics 2023-01, Vol.148, p.104252, Article 104252
• Main Authors: Amtout, Tarik, Cheikhi, Adil, Er-Riani, Mustapha, Lahrouz, Aadil, El Jarroudi, Mustapha, Settati, Adil
• Format: Article
• Language: English
• Subjects: Asymptotic modeling; Boundary layer; Heat transfer; Shear-thinning fluids; Thermal dependency properties
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2022.104252

In this work, we applied the asymptotic analysis method based on a large Prandtl number for a boundary layer flow over a flat plate, of a thermo-dependent fluid obeying a power law. In order to make sense to the notion of boundary layer, we have to assume that the fluid is shear-thinning. The governing equations of the thermal boundary layer do not admit self-similar solutions but the asymptotic model derived in this work admits one. This approach was also employed to obtain a Nusselt number correlation as a function of the ratio K(T∞)/K(Tw), where K is the consistency index, T∞ and Tw are respectively the free stream and the wall temperature. In particular, we have shown that the shear-thinning nature of the fluid accentuates the effect of thermo-dependence and amplifies the heat transfer at the wall. •Boundary layer flow of a thermo-dependent fluid obeying a power law is studied.•Asymptotic analysis method based on a large generalized Prandtl number is given.•Discussion on the role of different Prandtl numbers.•Correlations of the Nusselt number are provided.