On the stability analysis of thermally stratified channel flow with a compliant boundary

In this work we investigate the linear viscous stability of thermally stratified plane Poiseuille channel flow over a compliant surface. This problem is posed as an ‘Orr–Sommerfeld-like’ eigenvalue problem which is coupled to an energy equation. The Chebyshev collocation spectral method is used to solve the eigenvalue system. The critical Reynolds numbers, wavenumbers, wavespeeds, and curves of neutral stability are obtained for a wide range of compliant wall parameters and buoyancy parameters. These results are discussed and compared with results from related studies on thermally stratified flow between rigid flat plates (plane Poiseuille flow).