Other Filmwise Condensation Configurations

From Thermal-FluidsPedia

1 External condensation on a inclined surface
2 Upward-facing horizontal surface
3 Flat plate in parallel stream for saturated vapor
4 References

External condensation on a inclined surface

Nusselt analysis for laminar film condensation for a vertical plate can also be applied to condensation on a plate at an angle (with respect to the vertical) by replacing g with $g cosθ$ :

$\overline{Nu}=\frac{{{\overline{h}}_{L}}L}{{{k}_{\ell }}}=0.943{{\left[ \frac{{{\rho }_{\ell }}\left( {{\rho }_{\ell }}-{{\rho }_{v}} \right)g\cos \theta {{{{h}'}}_{\ell v}}{{L}^{3}}}{{{\mu }_{\ell }}{{k}_{\ell }}({{T}_{sat}}-{{T}_{w}})} \right]}^{1/4}}$	(1)

Upward-facing horizontal surface

For condensation on an upward-facing horizontal surface of a finite size, the condensate in the central region flows toward the edge where it is spilled (Bejan, 1991). For condensation over a long horizontal strip with a width of L, the average heat transfer can be obtained by

$\overline{Nu}=\frac{\overline{h}L}{{{k}_{\ell }}}=1.079{{\left[ \frac{{{\rho }_{\ell }}\left( {{\rho }_{\ell }}-{{\rho }_{v}} \right)g{{{{h}'}}_{\ell v}}{{L}^{3}}}{{{\mu }_{\ell }}{{k}_{\ell }}\left( {{T}_{sat}}-{{T}_{w}} \right)} \right]}^{1/5}}$	(2)

where the exponent on the right-hand side becomes 1/5.

The heat transfer coefficient for film condensation over an upward-facing horizontal circular disk with a diameter of D is

${{\overline{Nu}}_{D}}=\frac{\overline{h}D}{{{k}_{\ell }}}=1.368{{\left[ \frac{{{\rho }_{\ell }}\left( {{\rho }_{\ell }}-{{\rho }_{v}} \right)g{{{{h}'}}_{\ell v}}{{D}^{3}}}{{{\mu }_{\ell }}{{k}_{\ell }}\left( {{T}_{sat}}-{{T}_{w}} \right)} \right]}^{1/5}}$	(3)

Flat plate in parallel stream for saturated vapor

For laminar film condensation on a horizontal flat plate in a parallel stream of saturated vapor, the average heat transfer coefficient is

$\overline{Nu}=\frac{\overline{h}L}{{{k}_{\ell }}}=0.872\operatorname{Re}_{L}^{1/2}{{\left[ \frac{1.508}{{{(1+\text{Ja}/{{\Pr }_{\ell }})}^{3/2}}}+\frac{{{\Pr }_{\ell }}}{\text{Ja}}{{\left( \frac{{{\rho }_{v}}{{\mu }_{v}}}{{{\rho }_{\ell }}{{\mu }_{\ell }}} \right)}^{1/2}} \right]}^{1/3}}$	(4)

where L is the length of the flat plate along the vapor flow direction, ${{\operatorname{Re}}_{L}}={{U}_{\infty }}L/{{\nu }_{\ell }}$ is based on the viscosity of liquid, and $\text{Ja}={{c}_{p\ell }}({{T}_{sat}}-{{T}_{w}})/{{h}_{\ell v}}$ is the Jakob number. Equation (4) is valid for ${{\rho }_{\ell }}{{\mu }_{\ell }}/{{\rho }_{v}}{{\mu }_{v}}=10\sim 500$ and $\text{Ja}/{{\Pr }_{\ell }}=0.01\sim 1$ .