# Other Filmwise Condensation Configurations

## 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 gcosθ:

 $\overline{Nu}=\frac{{{\overline{h}}_{L}}L}{{{k}_{\ell }}}=0.943{{\left[ \frac{{{\rho }_{\ell }}\left( {{\rho }_{\ell }}-{{\rho }_{v}} \right)g\cos \theta {{{{h}'}}_{\ell v}}{{L}^{3}}}{{{\mu }_{\ell }}{{k}_{\ell }}({{T}_{sat}}-{{T}_{w}})} \right]}^{1/4}}$ (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 $\text{Ja}/{{\Pr }_{\ell }}=0.01\sim 1$.

## References

Bejan, A., 1991, “Film Condensation on a Upward Facing Plate with Free Edges,” International Journal of Heat and Mass Transfer, Vol. 34, pp. 578-582.

Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA

Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.