where
is the tank's temperature (expressed in kelvin),
is the initial temperature as well as the temperature of the stream flowing into the tank,
is the heating rate (through steam heating) expressed in watts,
is the process time constant (in seconds),
liters is the tank volume,
is the fluid density (
), and
is the heat capacity of the fluid expressed in
. We take the following assumption concerning the fluid's characteristics:
.
The steady-state temperature of the tank is higher if either
or
is increased. By choosing small process time constants, for any specified value of
the response to added heat is faster (i.e., the time needed to reach the steady-state temperature is shorter). This type of dynamic response is typical of a first-order system.
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