Effect of inclination on laminar film condensation
Authors
 Received:
 Revised:
DOI: 10.1007/BF00413072
 Cite this article as:
 Nagendra, H.R. Appl. Sci. Res. (1973) 28: 261. doi:10.1007/BF00413072
Abstract
The effect of inclination on laminar film condensation over and under isothermal flat plates is investigated analytically. The complete set of Navier Stokes equations in two dimensions is considered. Analysed as a perturbation problem, the zeroorder perturbation represents the boundary layer equations. First and second order perturbations are solved to bring about the leading edge effects. Corresponding velocity and temperature profiles are presented. The results show decrease in heat transfer with larger ∥inclinations∥ from the vertical. Comparison with experimental data of Gerstmann and Griffith indicates a closer agreement of the present results than the analytical results of the same authors.
Nomenclature
 C

constant in equation (22)
 C _{p}

specific heat at constant pressure
 F

transformed stream function, eq. (13)
 g

accelaration due to gravity
 Gr _{ x }

a parameter similar to Grashof number used in free convection, (gx ^{3}/ν ^{2})(ρ−ρv/ρ)
 h

local heat transfer coefficient, q/ΔT
 h _{fg}

latent heat of condensation of vapor
 H

temperature variable, eq. (13)
 L

length of the plate
 N

heat transfer parameter, eq. (29)
 Nu _{ x }

local Nusselt number, eq. (28)
 Pr

Prandtl number
 q

rate of heat transfer per unit area eq. (27)
 T

temperature
 u U

velocity components in xdirection
 v V

velocity components in ydirection
 x X y Y

coordinates Fig. 1 and eq. (6)
 α

thermal diffusivity of liquid
 δ

liquid film thickness
 ΔT

temperature difference, eq. (15b)
 ε

Gr _{ L } ^{−1/4}
 η

similarity variable, eq. (13)
 θ

temperature variable
 κ

thermal conductivity of liquid
 ν

kinematic viscosity of liquid
 ρ

density of liquid
 φ

inclination angle from vertical, Fig. 1
 ψ

stream function, eq. (4)
 ▽ ^{2}

Laplacian operator
Subscripts
 0

zeroeth order perturbation
 1

first order perturbation
 2

second order perturbation
 L

quantity based on length of plate
 sat

saturation conditions
 w

value at the wall
 x

value based on ‘x’
Super scripts
 ′

differentiation with respect to η
 

average value