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Heat flow rate calculation

How to calculate the heat exchange required ?

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Section summary
1. General calculation formula
2. Calculation without change of state

1. General calculation formula

How to calculate the heat that must be exchanged to bring a substance from condition 1 to condition 2 ?

The heat required to bring a substance from a condition 1 to a condition 2 can be calculated thanks to enthalpies. The substance at condition 1 has a given enthalpy H1 (which you can assimilate to a quantity of energy) and the same substance in condition 2 has another enthalpy H2. The difference in between condition 1 and condition 2 can be only a matter of temperature but can also include a change of phase (vaporization for example).

The heat required to bring a mass m from condition 1 to condition 2 is then, with enthalpies referring to mass :

Q = m*(H2-H1)

Q = heat flow rate in kW
m = mass flowrate in kg/s
H1 = mass enthalpy at condition 1 in kJ/kg
H2 = mass enthalpy at condition 2 in kJ/kg

Note that Q can be positive or negative.

This method allows to cover change of states if it happens in between conditions 1 and 2. It however requires that the engineer has a table or a graph allowing to determine the enthalpies. It is also very important that the reference state for both enthalpies H1 and H2 is the same.

2. Calculation without change of state

Enthalpy values are not always available, the specific heat c is more often known. It can be at constant pressure, Cp, or constant volume Cv. It can be used the following way when measuring the heat required to go from conditions 1 to conditions 2, again, without change of state.

Q = m*c*(T2-T1)

Q = heat flow rate in kW
m = mass flowrate in kg/s
c = specific heat in kJ/kg/K
T1 = temperature at condition 1 in K
T2 = temperature at condition 2 in K

Note that Q can be positive or negative.

c is the general expression for the specific heat of a substance, in practice, values at constant pressure Cp and sometimes at constant volume Cv are available.