36. Heat Exchanger
Heat exchange is a natural phenomenon occurring throughout our environment. It drives the weather cycles and energy exchange between ecosystems. Harnessing its utility through accurate control of heat exchange has been a focus of our industry for over a century.
Heat exchangers allow control over the dynamics of heat transfer between fluids. They are used in widespread applications, such as solar heating, pool heating, domestic water heating, radiant floor heating, food processing, marine applications, general industrial process control, and more
Below are parametric thermodynamic equations that define the nature of heat exchange and performance of a heat exchanger for any given application. Once these thermal parameters are determined they can be used to calculate heat exchanger performance in order to select the most suitable product based on the specific application.
Theoretical Heat of a Fluid
The heat transfer principal in heat exchangers is based on a colder fluid gaining heat from a relatively hotter fluid separated by, and flowing over, a heat conductive material.
This is expressed by the following formula:
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(eqn 1)
Q = Total heat load
m = Mass flow rate of fluid.
cp = Specific heat of fluid at constant pressure.
D
T = Change in temperature of the fluid.
This formula provides the Theoretical Heat Yield to or from a given fluid undergoing a temperature change, D
T at a mass flow rate,
m with the fluid’s specific heat property,
cp.
Practical Heat Transfer Control
The
theoretical heat yield of a fluid gives the amount of heat that needs to be transferred into or from a fluid. The
practical heat transfer is a function of the physical geometry of the heat exchanger, its material composition, and the fluid condition.
The general form of the equation defining the maximum potential heat transfer through a heat exchanger is expressed by the formula:
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(eqn 2)
U = Overall heat transfer coefficient
A = Surface area
LMTD = Logarithmic mean temperature difference
The Practical Heat Transfer Control is determined by the molecular thermodynamic interactions between the fluids flowing through the heat exchanger and the geometry of the heat exchanger itself.
The overall
U value is calculated by an equation specific to the geometric configuration of a Heat Exchanger. It is a function derived using dimensionless numbers such as
Reynolds Number (Re),
Prandlt Number (Pr), along with fluid flow parameters. The overall U value is calculated over the total surface area
A of the heat exchanger, across which the fluids exchange heat.
The log mean difference of the inlet and outlet temperatures (
LMTD) of the hot and cold fluids for a
counter flow exchanger is expressed by the formula:
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(eqn 3)
Thi = Inlet temperature of hot fluid
Tco = Outlet temperature of cold fluid
Tho = Outlet temperature of hot fluid
Tci = Inlet temperature of cold fluid
Practical heat exchange value,
Qp, can be compared to the
theoretical, Qt, value to determine if the heat Exchanger has enough capacity to fulfill the application requirements.
