# Overall Heat Transfer Coefficient

#### Contents:

**The overall heat transfer coefficient, or U-value, refers to how well heat is conducted over a series of mediums. Its units are the W/(m ^{2}°C) [Btu/(hr-ft^{2}°F)].**

In the following article, we will discuss how to calculate the U value to evaluate the heat transfer of steam and hot water through different types of mediums.

### Steam vs. Hot Water

The overall heat transfer coefficient is influenced by the thickness and thermal conductivity of the mediums through which heat is transferred. The larger the coefficient, the easier heat is transferred from its source to the product being heated. In a heat exchanger, the relationship between the overall heat transfer coefficient (U) and the heat transfer rate (Q) can be demonstrated by the following equation:

where

Q = heat transfer rate, W=J/s [btu/hr]

A = heat transfer surface area, m^{2} [ft^{2}]

U = overall heat transfer coefficient, W/(m^{2}°C) [Btu/(hr-ft^{2}°F)]

ΔT_{LM} = logarithmic mean temperature difference, °C [°F]

From this equation we can see that the U value is directly proportional to Q, the heat transfer rate. Assuming the heat transfer surface and temperature difference remain unchanged, the greater the U value, the greater the heat transfer rate. In other words, this means that for a same kettle and product, a higher U value could lead to shorter batch times.

Several equations can be used to determine the U value, one of which is:

where

h = convective heat transfer coefficient, W/(m^{2}°C) [Btu/(hr-ft^{2}°F)]

L = thickness of the wall, m [ft]

λ = thermal conductivity, W/(m°C) [Btu/(hr-ft°F)]

### Heat transfer through a metal wall

The convective heat transfer coefficient (h), sometimes referred to as the film coefficient, is often used when calculating heat transfer between a fluid and a solid. In the case of a heat exchanger, heat transfer basically occurs from fluid 1 (source of heat) to solid (metal wall) to fluid 2 (product being heated). In the event that heat transfer occurs through several solids, the above equation can be adapted by supplementing the solid's thickness (L) divided by its thermal conductivity (λ).

To simplify the calculation, the following values may be used as a reference for the convective heat transfer coefficients:

Fluid | Convective heat transfer coefficient (h) |

Water | about 1000 W/(m^{2}°C) [176 Btu/(hr-ft^{2}°F)] |

Hot Water | 1000 – 6000 W/(m^{2})°C [176 - 1057 Btu/(hr-ft^{2}°F)] |

Steam | 6000 – 15000 W/(m^{2}°C) [1057 - 2641 Btu/(hr-ft^{2}°F)] |

### Example

Two jacketed kettles made of carbon steel (λ = 50 W/(m°C) [28.9 Btu/(hr-ft°F)] ) with an inner wall thickness of 15mm [0.049 ft] are used to heat water. One uses hot water as the heat source, while the other uses steam. Assuming heat transfer coefficients of 1000 W/m^{2}°C [176 Btu/(hr-ft^{2}°F)] for the water being heated, 3000 W/m^{2}°C [528 Btu/(hr-ft^{2}°F)] for hot water, and 10000 W/m^{2}°C [1761 Btu/(hr-ft^{2}°F)] for steam, let's calculate the U values for both heating processes.

**Carbon Steel Jacketed Kettle**

**Hot water: **

**U = 681.8 W/(m ^{2}°C)**

**Steam:**

**U = 731.7 W/(m ^{2}°C)**

In this case, steam could theoretically improve the U-value by 17%. Let's now imagine the same kettle is lined with glass 1mm [0.0033 ft] thick (λ = 0.9 W/(m°C) [0.52 Btu/(hr-ft°F)]). Including these values into the above U-value equation gives the following:

**Glass-lined Jacketed Kettle**

**Hot water: **

**U = 387.9 W/(m ^{2}°C) **

**Steam:**

**U = 403.6 W/(m ^{2}°C)**

In this case, the U-value is only improved by 9%, which shows how a poor thermal conductor such as glass can greatly interfere with heat transfer. So in a carbon steel kettle, for example, changing the heat source from hot water to steam can potentially improve the U-value by several 10’s of percent. However, the same effect would not be expected in a glass-lined kettle.

Nevertheless, certain circumstances require that a kettle remain unchanged. For example, some processes require kettles made of a certain material to prevent reactivity with the product. If such is the case and the heat transfer rate needs to be improved, changing the heat source from hot water to steam may provide the needed solution.

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