Session: 11-16-02: Oscillating Heat Pipes and Thermosiphons

Paper Number: 112692

112692 - Theoretical Study of Counter-Current Liquid-Vapor Flow Under Condensation Conditions Over Non-Isothermal Vertical Wall of Two-Phase Closed Thermosyphon 

This paper outlines a theoretical approach to model liquid falling film condensation in counter-current pure liquid-vapor flow subject to a cooling wall in gravity-assisted heat pipes (or two-phase closed thermosyphons). Determining the falling film thermal characteristics, which strongly affect heat transfer rate, has received much attention from early researchers, particularly through experimental studies. Due to experimental difficulties, the estimation of in-situ film properties was however tackled by introducing a steady-state analytical model in the late 90s. Over the past two decades, the modifications based on this framework have primarily focused on constant temperature and heat flux boundary conditions. 
This paper proposes a new analytical formulation describing the relationship between shear stress and film thickness to be added to the existing system of equations to model falling film over a convective non-isothermal pipe wall. The remarkable feature of this study is considering the combined effect of friction force and mass transfer shear stress at the liquid-vapor interface, the subcooling effect, and the influence of the convective boundary on film heat transfer. Vapor phase condensation in heat pipes with relatively longer condenser lengths, where temperature variation is inevitable, is covered by this model. 
The novel formulation is solved numerically in combination with the analytical solution of conservation equations and Linehan's (1968) expression for shear stress. The following well-justified assumptions for modeling thin film and counter-current two-phase flow system are considered: (1) neglecting fluid inertia in the momentum equation, (2) neglecting the convection in the energy equation, (3) incompressible vapor flow, (4) linear temperature profile inside the liquid element, (5) insignificant curvature effect, and (6) the mean vapor velocity is assumed to be equal to its value at the film edge. 
Two iterative loops are used in the solution algorithm: first, film thickness and shear stress are calculated through the inner iterative loop, assuming a value for heat flux. Second, the assumed heat flux toward the wall is corrected in the outer iterative loop as a function of ambient air temperature and Nusselt number by employing a thermal resistance analogy connecting the inner wall temperature to the ambient cooling air. Optimized relaxation factors are used, and when all convergence criteria are met, the model marches over the condenser section. The high accuracy of the model in regenerating literature data allowed the implementation of a parametric study analysis on the variation of ambient air temperature, wind velocity, and changing geometrical parameters, including the pipe diameter and indicating the influence of finned outer pipe surface on the film features. Nusselt theory calculations are also carried out, and its underestimation in film thickness prediction and, consequently, overestimation of local heat transfer coefficient is discussed. The introduced model indicated the promising potential for laminar to wavy-laminar film regimes and could be applied to similar cases, e.g., co-current flows and evaporating thin films. 

Presenting Author: Mohammad Zolfagharroshan Mcgill University

Presenting Author Biography: PhD student in mining engineering working on phase change and heat transfer enhancement in heat pipes with a background in petroleum and geothermal engineering.

Authors:

Mohammad Zolfagharroshan Mcgill University
Minghan Xu McGill University
Ahmad Zueter Dalhousie University
Agus Sasmito McGill University