Steam Economical Insulation Thickness Payback

Steam Economical Insulation Thickness Payback formula

\(\large{  C_i1 = 1000 \frac {\pi} {4}    \left( \left( d +2L \right)^2  - d{^2}  \right) C_i2  \; \cdot \; N  + 0.001 C_e  h  Q_r     }\)

\(\large{  N = \frac { i  \left( 1 + i \right)^m } { \left( 1 + i \right)^m -1 }  }\)

\(\large{  Q_r =  \frac{ 2 \pi \: \left( T_s + T a m  \right)  }          {  \frac{ l }{ \lambda }  \; \cdot \; i \pi \: \left( \frac{ d + 24L }{ d } \right)  \; + \;  \frac{24 }{ \pi \left( d + 24L\right)  }    }  }\)

Where:

\(\large{  C_i1  }\) = annual average insulation cost

\(\large{  N  }\) = rate of payback

\(\large{  Q_r  }\) = radiant heat

\(\large{  T_a  }\) = ambient temperature

\(\large{  i  }\) = annual interest rate

\(\large{  C_e  }\) = energy unit cost

\(\large{  h  }\) = heat transfer coefficient

\(\large{  C_i2  }\) = insulation and labor cost

\(\large{  L  }\) = insulation thickness

\(\large{  d  }\) = outside diameter of pipe

\(\large{  m  }\) = payback period

\(\large{  \pi  }\) = Pi

\(\large{  l  }\) = pipe length

\(\large{  T_s  }\) = steam temperature

\(\large{  \lambda  }\)  (Greek symbol lambda) = thermal conductivity coefficient