A STUDY OF THE DIFFERENTIAL EQUATIONS OF COUPLED VIBRATIONS AND FREE CONVECTION FROM A HEATED HORIZONTAL CYLINDER
Abstract
The basic equations and the boundary conditions which govern the problem of coupled transverse vibrations and free convection from a heated horizontal cylinder are presented. By applying a method developed by C. C. Lin, (Proc. 9th Inter. Congr. Appl. Mech., 139, 1959), it is shown: (1) that the presence of harmonic oscillations modify the steady-flow solution only when pressure gradients are present; (2) that the modifying forces have their most pronounced effect on the fluid closest to the surface; and (3) that the product of a and the circular frequency of rotation (af) is a measure of the magnitude of the modifying forces. The use of the quantity (af) as a measure of the magnitude of the influence of vibrations on free convection agrees with experimental correlations. By transforming the differential equations into dimensionless form, it is shown that four dimensionless parameters are needed to fully describe the flow. A perturbation method is applied to one set of equations, and the zeroth-order solution is obtained. This zeroth-order solution, which corresponds to free convection, agrees with Hermann's analysis for a heated horizontal cylinder.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1961
- Accession Number
- AD0275770
Entities
People
- R. M. Fand
- R. S. Dougall
- T. Chiang
Organizations
- Massachusetts Institute of Technology