---
title: "Condensation of steam on a vertical plate"
subject: "Heat Transfer"
chapter: 5
key: "semester_5/heat_transfer:film-condensation-vertical-plate-numerical"
source: https://www.bctengineer.com/q/semester_5/heat_transfer/film-condensation-vertical-plate-numerical
site: BCT Engineering
---

# Condensation of steam on a vertical plate

Heat Transfer · Chapter 5: Phase Change Heat Transfer

- Asked in: year not given, 6 marks
- Video: [A Problem in Condensation - Vertical Plate - Laminar flow](https://www.youtube.com/watch?v=O4h82fH4mnA) — Engineering Made Simple
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/heat_transfer/film-condensation-vertical-plate-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_5/heat_transfer/chapter-5

## Question

Saturated steam at 100 °C condenses on a vertical plate 0.5 m high and 1 m wide kept at 80 °C. Using Nusselt's theory, calculate (a) the average heat transfer coefficient, (b) the heat transfer rate, (c) the condensate mass flow rate per hour and (d) the film Reynolds number at the bottom. Properties of saturated liquid at film temperature 90 °C: rho_l = 965.3 kg/m^3, k_l = 0.675 W/m K, mu_l = 314.8 x 10^-6 Pa s. At 100 °C: h_fg = 2257 kJ/kg, rho_v = 0.598 kg/m^3.

## Answer

#### (a) Average coefficient (Nusselt)
$\Delta T = 100 - 80 = 20$ K, $L = 0.5$ m, $g = 9.81$ m/s$^2$.

$$
\begin{aligned}
\bar h &= 0.943\left[\frac{\rho_l(\rho_l-\rho_v)\,g\,h_{fg}\,k_l^3}{\mu_l\,L\,\Delta T}\right]^{1/4}\\
&= 0.943\left[\frac{6.34\times10^{12}}{3.148\times10^{-3}}\right]^{1/4}\\
&= 0.943\,[2.014\times10^{15}]^{1/4} = 0.943\times6699\\
&= 6317\ \text{W/m}^2\text{K}
\end{aligned}
$$

#### (b) Heat transfer rate

$$
Q = \bar h A\,\Delta T = 6317\times(0.5\times1)\times20 = 63\,175\ \text{W} = 63.2\ \text{kW}
$$

#### (c) Condensate rate

$$
\dot m = \frac{Q}{h_{fg}} = \frac{63\,175}{2.257\times10^6} = 0.0280\ \text{kg/s} = 100.8\ \text{kg/h}
$$

#### (d) Film Reynolds number

$$
Re_f = \frac{4\dot m}{b\,\mu_l} = \frac{4\times0.0280}{1\times314.8\times10^{-6}} = 356
$$

$Re_f$ lies between 30 and 1800, so the film is **wavy laminar**. Nusselt's equation is then conservative: ripples usually raise $\bar h$ by about 20 percent (Kutateladze correction), so the true value may be near 7500 W/m$^2$K.

**Answer:** $\bar h \approx 6320\ \text{W/m}^2$K; $Q \approx 63.2$ kW; $\dot m \approx 101$ kg/h; $Re_f \approx 356$ (wavy).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. At which temperatures are properties taken in Nusselt's equation?
   A. All at the wall temperature
   B. Liquid properties at film temperature (Tsat + Tw)/2, h_fg at Tsat
   C. All at the saturation temperature
   D. Liquid properties at Tsat and h_fg at film temperature
   Answer: B. Here liquid properties are at 90 C and h_fg is at 100 C. (Key point: Property reference temperatures)

2. How is the condensate flow rate obtained from the heat transfer rate?
   A. m = Q x h_fg
   B. m = Q / (h x A)
   C. m = Q / h_fg
   D. m = Q / (cp x dT)
   Answer: C. All heat transferred is the latent heat released: m = 63 175 / 2.257e6 = 0.028 kg/s (about 101 kg/h). (Key point: Condensate rate from heat)

3. The film Reynolds number is Re_f = 4m/(b mu) with m = 0.028 kg/s, b = 1 m. What flow regime does Re_f = 356 indicate?
   A. Turbulent, because Re_f is above 30
   B. Laminar without ripples, because Re_f is below 1800
   C. Wavy laminar, since it lies between 30 and 1800
   D. Transition between laminar and turbulent at 356
   Answer: C. A wavy laminar film (30 < Re_f < 1800) makes Nusselt's result conservative by about 20 percent. (Key point: Film Reynolds number)

## Related in Heat Transfer

- [Nusselt theory of film condensation](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Anusselt-film-condensation-theory) — Heat Transfer, chapter 5
- [Natural convection from a vertical plate](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Anatural-convection-vertical-plate-heat-loss) — Heat Transfer, chapter 3
- [Heat loss from insulated steam pipe](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Ainsulated-steam-pipe-heat-loss) — Heat Transfer, chapter 2
- [Modes of heat transfer with rate equations](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Amodes-of-heat-transfer) — Heat Transfer, chapter 1
- [Heat loss from a cylinder in cross flow](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Across-flow-air-cylinder-heat-loss) — Heat Transfer, chapter 3
- [Laminar forced convection over a heated flat plate](https://www.bctengineer.com/question.md?key=semester_5%2Fheat_transfer%3Alaminar-flow-over-heated-plate-air) — Heat Transfer, chapter 3

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