q v = volume flow air (m 3 /s)
t o = temperature out of heater ( o C)
t i = air temperature in to heater ( o C)
The heat transfer through a heat exchanger surface can be expressed as
H = A dt m U (2)
A = heating surface (m 2 )
dt m = logarithmic mean temperature difference ( o C)
U = heat transmission coefficient (W/m 2 K)
The heat transmission coefficient - U - depends on the air speed and the water (fluid) speed through the heater.
The heating process on the water (fluid) side of the heat exchanger can be expressed as
H = ρ w c pw q w (t wi - t wo ) (3)
ρ w = density water (1000 kg/m 3 )
c pw = specific heat of water (4.2 J/kg o C)
q w = water volume flow (m 3 /s)
t wi = temperature water in to the heater ( o C)
t wo = temperature water out of the heater ( o C)
If saturated steam is used to heat air the heating process can be expressed as
H = q s h e (4)
q s = steam flow (kg/s)
h e = evaporating enthalpy of water (J/kg)
The evaporating enthalpy of water depends on the steam pressure. At one bar absolute pressure (100 o C) the evaporating enthalpy is 2258 kJ/kg (539 kcal/kg) . At ten bar absolute pressure (180 o C) the evaporating enthalpy is 2014 kJ/kg (481 kcal/kg) .
Important design criteria when selecting heaters:
When coolers are calculated, it is important to know if the surfaces are dry or wet.
For a cooler with a dry surface the same equation used for the heating process (1) may be modified and used:
H c = ρ c p q v (t i - t o ) (5)
H c = heat removed from air (W)
ρ = air density (kg/m 3 )
c p = specific heat of air (J/kg o C)
q v = volume flow air (m 3 /s)
t o = temperature out of the cooler ( o C)
t i = air temperature in to the cooler ( o C)
For coolers with wet surfaces, the water vapor in the air is condensed and the enthalpy of air - the sensible and latent heat - must be used in the calculations:
H c = ρ q v (h i - h o ) (6)
h o = enthalpy in moist air out from the cooler (kJ/kg)
h i = enthalpy in moist air into the cooler (kJ/kg)
The water flow cooling process can be calculated with a modified formula similar as for the heating process.
Important design criteria when selecting coolers:
Systems for ventilation and air handling - air change rates, ducts and pressure drops, charts and diagrams and more.
Arithmetic Mean Temperature Difference in Heat Exchangers - AMTD - and Logarithmic Mean Temperature Difference - LMTD - formulas with examples - Online Mean Temperature Calculator.
Design procedure for ventilation systems - air flow rates, heat and cooling loads, air shifts according occupants, air supply principles.
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