Viscous dissipation effects on convective instability and heat transfer in plane poiseuille flow heated from below

1976 ◽  
Vol 32 (4) ◽  
pp. 327-346 ◽  
Author(s):  
K. C. Cheng ◽  
Ray-Shing Wu
Keyword(s):  
Heat Transfer ◽  
Viscous Dissipation ◽  
Poiseuille Flow ◽  
Convective Instability ◽  
Plane Poiseuille Flow

scholarly journals Onset of Thermal Instabilities in the Plane Poiseuille Flow of Weakly Elastic Fluids: Viscous Dissipation Effects

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 432
Author(s):  
Silvia C. Hirata ◽  
Mohamed Najib Ouarzazi
Keyword(s):  
Linear Stability ◽  
Viscous Dissipation ◽  
Viscoelastic Fluid ◽  
Poiseuille Flow ◽  
Hydrodynamic Instability ◽  
Plane Poiseuille Flow ◽  
Volumetric Heating ◽  
Fluid Elasticity ◽  
Different Temperatures ◽  
Elastic Fluids

The onset of thermal instabilities in the plane Poiseuille flow of weakly elastic fluids is examined through a linear stability analysis by taking into account the effects of viscous dissipation. The destabilizing thermal gradients may come from the different temperatures imposed on the external boundaries and/or from the volumetric heating induced by viscous dissipation. The rheological properties of the viscoelastic fluid are modeled using the Oldroyd-B constitutive equation. As in the Newtonian fluid case, the most unstable structures are found to be stationary longitudinal rolls (modes with axes aligned along the streamwise direction). For such structures, it is shown that the viscoelastic contribution to viscous dissipation may be reduced to one unique parameter: γ=λ1(1−Γ), where λ1 and Γ represent the relaxation time and the viscosity ratio of the viscoelastic fluid, respectively. It is found that the influence of the elasticity parameter γ on the linear stability characteristics is non-monotonic. The fluid elasticity stabilizes (destabilizes) the basic Poiseuille flow if γ<γ* (γ>γ*) where γ* is a particular value of γ that we have determined. It is also shown that when the temperature gradient imposed on the external boundaries is zero, the critical Reynolds number for the onset of such viscous dissipation/viscoelastic-induced instability may be well below the one needed to trigger the pure hydrodynamic instability in weakly elastic solutions.

On the onset of dissipation thermal instability for the Poiseuille flow of a highly viscous fluid in a horizontal channel

2011 ◽  
Vol 681 ◽  
pp. 499-514 ◽  
Author(s):  
A. BARLETTA ◽  
M. CELLI ◽  
D. A. NIELD
Keyword(s):  
Viscous Dissipation ◽  
Poiseuille Flow ◽  
Thermal Instability ◽  
Hydrodynamic Instability ◽  
Normal Modes ◽  
Lower Boundary ◽  
Basic Flow ◽  
Plane Poiseuille Flow ◽  
External Temperature ◽  
Volumetric Heating

The thermal instability of the plane Poiseuille flow as a consequence of the effect of viscous dissipation is investigated. No external temperature difference is assumed in the environment; the lower boundary is considered adiabatic, while the upper boundary is isothermal. Thus, the sole cause of the unstable thermal stratification is the flow rate, through the volumetric heating induced by the viscous dissipation. A linear stability analysis is carried out numerically by the analysis of normal modes perturbing the basic flow with different inclinations. The study of cases with different Prandtl numbers and Gebhart numbers suggests that the most unstable perturbations are the longitudinal rolls, namely the normal modes with a wave vector perpendicular to the basic flow direction. A possible comparison with the hydrodynamic instability of the plane Poiseuille flow, described by the Orr–Sommerfeld eigenvalue problem is proposed. This comparison, when referred to high values of the Prandtl number, reveals that the dissipation instability may be effective at a Reynolds number smaller than that needed for the onset of the hydrodynamic instability.

Sign in / Sign up

Export Citation Format

Share Document