Air Temperature

Return

Supply

Temperature

Temperature

(3-1)

where *q *= heat output from the radiator (W)

and the subscripts denote the following operating conditions

0 = "design" condition for the radiators, usually the maximum load condition

at maximum supply temperature

1 = condition of actual supply temperature with the flow rate as determined

under the design condition

2 = any actual operating condition.

Equation 3-1 uses the logarithmic mean temperature difference *T*ml and exper-

imentally determined constants to predict heat exchanger performance. The log-

arithmic mean temperature difference is defined as

(Ts - *T*a ) - (Tr - *T*a ) =

.

(3-2)

l n(Ts - *T*a ) - ln(Tr - *T*a ) l n[ (Ts - *T*a )/(Tr - *T*a ) ]

One problem that results from using the logarithmic mean temperature differ-

temperature. This limits the extent of closed form analysis and ultimately, when

calculations are required, it forces solution by iterative numerical methods. As a

solution to these problems, the use of the arithmetic mean as an approximation for

the logarithmic mean was proposed by Soumerai (1987). The arithmetic mean

temperature difference for this case is defined as

(3-3)

The arithmetic mean temperature difference has the advantage that it can be used

return temperature *T*r given the value of the arithmetic mean temperature differ-

ence. The disadvantage of using the arithmetic mean temperature difference as an

approximation for the logarithmic mean temperature difference is the error induced

by this approximation. As Soumerai (1987) points out, within certain ranges of the

temperatures involved, the resultant errors are usually acceptable, given the other

uncertainties in heat transfer engineering. Soumerai (1987) recommends the use of

the arithmetic mean as an approximation for the logarithmic mean in cases where

the approach factor *AF *is equal to or greater than 0.5. The approach factor for this

type of heat exchanger is given by

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