Internal flow subjected to an axial variation of the external heat transfer coefficient

• Main Author: Beale, James H.
• Other Authors: Mechanical Engineering
• Format: Others
• Language: en_US
• Published: Virginia Polytechnic Institute and State University 2019
• Subjects: LD5655.V855 1987.B399; Heat > Transmission; Laminar flow; Eigenvalues
• Online Access: http://hdl.handle.net/10919/91162

A theoretical investigation of internal flow subjected to an axial variation of the external convection coefficient is presented. Since the variable boundary condition parameter causes the problem to become nonseparable, conventional techniques do not apply. Instead, the Green's function technique is used to convert the governing partial differential equations into a singular Volterra integral equation for the temperature of the fluid at the wall. The integral equation is resolved numerically by the trapezoid rule with the aid of a singularity subtraction procedure. The solution methodology is developed in terms of a fully turbulent flow which is shown to contain fully laminar and slug flow as special cases. Before examining the results generated by numerical solution of the integral equation, a thorough study is made of each of the building blocks required in the solution procedure. A comparison of the respective dimensionless velocity profiles and dimensionless total diffusivities for each of the flow models is presented. Next, an analysis of the eigenvalue problem for each flow model is presented with consideration given to the normalized eigenfunctions and the eigenvalues themselves. Finally, the singular nature of the Green's function is examined showing the effect of the parameters Ho, Re and Pr. The technique is applied to study the heat transfer from a finned tube. A parameter study is presented to examine the effects of the external finning and the flow model. The effect of external finning is examined through specific variations of the external convection coefficient, while the flow model is selected through the velocity profile and eddy diffusivity. In examining turbulent flow, the effects of the parameters, Re and Pr, are considered. === M.S.