Effect of Tollmien Schlichting wave on convective heat transfer in a wavy channel. Part I: Linear analysis

Abstract Hydrodynamic instabilities in wavy channels and their effect on the convective heat transfer are investigated using both linear stability analysis and integration of the time dependent Navier–Stokes and energy equations. The linear stability of the fully developed flow is determined from a generalized eigenvalue problem resulting from a Galerkin approach using divergence free Chebychev basis functions and trigonometric polynomials. Several axial periodicity lengths to geometry length ratios have been considered. For our geometry, the instability is found to set in as a Tollmien Schlichting wave, at a Reynolds number approximately equal to 90. The dynamics of the detachment and reattachment points and of temperature field for constant wall temperature are examined under the assumption of small amplitude fluctuations. It is shown that, although the average heat transfer remains almost constant, large amplitude variations of the local heat transfer coefficient can be observed, this effect is increasing with increasing Prandtl number.