# Steam Heating Processes - Load Calculating

## Calculating the amount of steam in non-flow batch and continuous flow heating processes

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In general steam heating is used to

**change**a product or fluid temperature**maintain**a product or fluid temperature

### Changing the Product Temperature - Heating up with Steam

The amount of heat required to raise the temperature of a substance can be expressed as:

Q = m c_{p}dT(1)

where

Q= quantity of energy or heat (kJ)

m= mass of the substance (kg)

c_{p}= specific heat capacity of the substance (kJ/kg^{o}C ) - Material Properties and Heat Capacities for several materials

dT= temperature rise of the substance (^{o}C)

Preferring Imperial Units - Use the Units Converter!

This equation can be used to determine a **total amount of heat energy** for the whole process, but it does not take into account the **rate of heat transfer** which is:

- amount of heat energy per unit time

In non-flow type applications a fixed mass or a single batch of product is heated. In flow type applications the product or fluid is heated when it constantly flows over a heat transfer surface.

### Non-flow or Batch Heating

In non-flow type applications the process fluid is kept as a single batch within a tank or vessel. A steam coil or a steam jacket heats the fluid from a low to a high temperature.

The mean rate of heat transfer for such applications can be expressed as:

q = m c_{p}dT / t(2)

where

q= mean heat transfer rate (kW (kJ/s))

m= mass of the product (kg)

c_{p}= specific heat capacity of the product (kJ/kg.^{o}C) - Material Properties and Heat Capacities for several materials

dT= Change in temperature of the fluid (^{o}C)

t= total time over which the heating process occurs (seconds)

#### Example - Time required to Heat up Water with direct Injection of Steam

The time required to heat *75 kg* of water *(c _{p} = 4.2 kJ/kg^{o}C)* from temperature

*20*to

^{o}C*75*with steam produced from a boiler with capacity

^{o}C*200 kW (kJ/s)*can be calculated by transforming eq. 2 to

*t = m c _{p} dT / q*

* = (75 kg) (4.2 kJ/kg^{o}C) ((75 ^{o}C) - (20 ^{o}C)) / (200 kJ/s) *

* = 86 s*

**Note!** - when steam is injected directly to the water all the energy from the steam is transferred instantly.

When heating through a heat exchanger - the heat transfer coefficient and temperature difference between the steam and the heated fluid matters. Increasing steam pressure increases temperature - and increases heat transfer. Heat up time is decreased.

Overall steam consumption may increase - due to higher heat loss, or decrease - due to to shorter heat up time, depending on the configuration of the actual system.

### Flow or Continuous Heating Processes

In heat exchangers the product or fluid flow is continuously heated.

The mean heat transfer can be expressed as

q = c_{p}dT m / t(3)

where

q= mean heat transfer rate (kW (kJ/s))

m / t= mass flow rate of the product (kg/s)

c_{p}= specific heat capacity of the product (kJ/kg.^{o}C) - Material Properties and Heat Capacities for several materials

dT= change in temperature of the fluid (^{o}C)

### Calculating the Amount of Steam

If we know the heat transfer rate - the amount of steam can be calculated:

m_{s}= q / h_{e}(4)

where

m_{s}= mass of steam (kg/s)

q= calculated heat transfer (kW)

h_{e}= evaporation energy of the steam (kJ/kg)

The evaporation energy at different steam pressures can be found in the Steam Table with SI Units or in the Steam Table with Imperial Units.

### Example - Batch Heating by Steam

A quantity of water is heated with steam of* 5 bar (6 bar abs)* from a temperature of *35 ^{ o}C to 100^{ o}C* over a period of

*20 minutes (1200 seconds)*. The mass of water is

*50 kg*and the specific heat capacity of water is

*4.19 kJ/kg.*.

^{o}CHeat transfer rate:

q= (50 kg) (4.19 kJ/kg^{o}C) ((100^{ o}C) - (35^{ o}C)) / (1200 s)

= 11.35 kW

Amount of steam:

m_{s}= (11.35 kW) / (2085 kJ/kg)

= 0.0055 kg/s

= 19.6 kg/h

### Example - Continuously Heating by Steam

Water flowing at a constant rate of *3 l/s* is heated from *10 ^{ o}C to 60^{ o}C* with steam at

*8 bar (9 bar abs)*.

The heat flow rate can be expressed as:

q = (4.19 kJ/kg.^{o}C) ((60^{ o}C) - (10^{ o}C)) (3 l/s) (1 kg/l)

= 628.5 kW

The steam flow rate can be expressed as:

m_{s}= (628.5 kW) / (2030 kJ/kg)

= 0.31 kg/s

= 1115 kg/h

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