Heating coil
File: heater.doc
Last edition: 2003-03-20/MK
Author: Lars Halling
History: 96-03-01/HN First released version
96-10-04/MK Updated to Menta 1.20
97-09-01/MK Updated to Menta 3.0
2003-03-20/MK Updated to Menta 4.0
Description
This is a simple model of a heating coil controlled by a mixing valve. We assume that the water flow and the air flow through the coil are constant. It can be shown that the temperature rise for the air in this kind of application is mainly determined by the coil efficiency, eps, defined as:
eps = (Twi-Two)/(Twi-Tai)
where
Twi = temperature of water entering the coil, °C.
Two = temperature of return water, °C.
Tai = temperature of air entering the coil, °C.
Note that eps is a constant property for a given heating coil if the water and air flows are kept constant. eps may in theory vary between 0 and 1. The actual value for a given coil can be determined from dimensioning data.
Example
Assume that the return water temperature will be 42°C when the incoming water holds 60°C and the incoming air holds 0°C. In this example we have
eps = (60-42)/(60-0)= 0.3
The dynamics of the return water temperature and of the air leaving the
coil is obtained simply by filtering in a first order filter with nominal
time constant = 30 s.
References
Grindal, A. (1988):"Reguleringsteknikk för ingeniören," Skarland Press A/S, ISBN 82-90033 117, första utgåvan.
Inputs
(Real) Air temperature before heater, °C. (Tai)
(Real) Boiler temperature, °C. (TB)
(Real) Control signal, %. (uc)
Outputs
(Real) Temp. after Heater, °C (Tao)
(Real) Return water temperature, °C. (Two)
Constants
(Real) eps = coil efficiency. Nominal value = 0.3.
(Real) qa = air flow (m3/s). Nominal value = 5.0 m3/s.
(Real) qw = water mass flow (kg/s). Nominal value = 1.0 kg/s.
(Real) ca = air heat capacitivity ( kJ/(kg*K) ) = 1.02 kJ/(kg*K).
(Real) cw = water heat capacitivity ( kJ/(kg*K) ) = 4.18 kJ/(kg*K).
(Real) rho = air density (kg/m3) = 1.2 kg/m3.
(Real) Tc = time constant (s). Nominal value = 20 s.