Ruelle--Takens--Newhouse and degenerate period-doubling routes to chaos in a wavy-channel flow under mixed convection*

We numerically investigate the effects of mixed convection on the nonlinear dynamics and heat transfer of the flow through a two-dimensional wavy channel with varying degrees of symmetry at Reynolds numbers ranging from 100 to 2200.  Our findings reveal that the introduction of mixed convection significantly alters the routes to chaos of the system compared to its isothermal counterpart.  We demonstrate that (i) a symmetric channel can host both the Ruelle--Takens--Newhouse and degenerate period-doubling routes to chaos, (ii) an asymmetric channel can host only the latter route, and (iii) a semi-wavy channel can host no routes to chaos under the present conditions.  Crucially, the Pomeau--Manneville intermittency route to chaos,  previously observed in the isothermal system, is absent under mixed convection. Furthermore, our analysis of the heat transfer characteristics reveals quadratic and cubic relationships for the Nusselt number and the thermal performance factor, respectively, as functions of the Reynolds number.  This study provides valuable insights for understanding and manipulating chaotic flow in wavy channels under mixed convection, with potential applications for enhancing the performance of thermal management devices.

Funding Acknowledgement: 

This work was funded by the Research Grants Council of Hong Kong (project nos. 16200220 and 16215521).