Transient energy growth modulation by temperature dependent transport properties in a stratified plane Poiseuille flow

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We investigate the effect of temperature dependent thermal conductivity $\lambda$ and isobaric specific heat $c_P$ on the transient amplification of perturbations in a thermally stratified laminar plane Poiseuille flow. It is shown that for decreasing thermal conductivity the maximum transient energy growth is amplified with respect to the $\lambda=1$ case, while the opposite occurs for increasing $\lambda$. A reversed mechanism is induced by a variable $c_p$. Substantial maximum growth enhancement/suppression is found in the range of Prandtl numbers $Pr$ which encompasses most fluids of practical interest. The relative growth modulation shows an optimum $Pr$ under spanwise perturbations. For energy amplifying property distributions a speed-up of the transient to reach the maximum energy growth is observed at low $Pr$, while a slow-down is found at large $Pr$. The opposite is true when the property variations suppress the growth of perturbations.