Effects of viscous dissipation on the stability of a liquid film flowing down a heated inclined plane (Q581141)

The author has studied the linear stability of the flow of a fluid down a heated inclined plate, by considering the viscous dissipation effects. Assuming the dissipation parameter to be small \((<1)\), the author has derived the correction \(Ra_ 1\) to the neutral \(Ra_ 0\), where Ra is the Rayleigh number. However, it is well-known that the viscous dissipation effects mainly depend upon the Prandtl number of the fluid and hence the stability of such a fluid flow is still governed by the Prandtl number of the fluid. In this paper, one more aspect of the stability has not been considered by the author. If the dissipation parameter \(Di>1\), what is the effect of this parameter on the stability of the flow on an inclined plane? This question has remained unanswered. It is worth studying. Mechanical engineers with find this paper most useful.