Heat Loss From An Insulated Pipe

This Excel spreadsheet models heat loss from an insulated pipe. This is a very common system in the process industries - insulated pipes are everywhere, and engineers need a sound grasp of heat transfer principles to model their effects. Although the model in the spreadsheet is simplified to aid understanding, complexity can be easily added.

Liquid flows through the pipe, with heat exchanged with the insulation. Heat is lost from the insulation to the environment via convection (no radiation losses are considered). The thermal effects of the pipe wall are ignored (although this can be easily implemented).

These equations are used in the spreadsheet to define the heat transfer process.

• q is the heat flowrate through the pipe and insulation (W m^-1)
• T_s is the temperature at the surface of the insulation (K)
• T_a is the ambient air temperature (K)
• T_f is the fluid temperature inside the pipe (K)
• D_O is the pipe diameter (m)
• D_S is the outside diameter of the insulated pipe (i.e. the pipe diameter plus two times the insulation thickness) (m)
• k is the insulation thermal conductivity (W m^-1 K^-1)
• ΔT is the temperature difference between the insulation surface and ambient air T_s-T_a (K)
• h_s is the insulation-to-air heat surface heat transfer coefficient (W m² K^-1)

The equation for the surface heat transfer h_s coefficient is a correlation; any other valid relationship can be substituted.

The equations are implicit - the heat transfer coefficient is a function of the surface temperature T_s, but the surface temperature is a function of the heat transfer coefficient. 

Hence the equations need to be solved iteratively with Goal Seek in Excel. Simply 

• break the loop by estimating a value of T_s, 
• use this to calculate all other properties (including the heat transfer rate)
• use the heat transfer rate to backcalculate T_s
• use Goal Seek to make the two values of T_s equal by varying the estimated value of T_s (or any other parameter

You can easily modify the heat transfer equations to include more complex effects, such as effect of fouling on the pipe surface, multiple layers of different insulation, radiative losses, thick large pipe walls (which act as a heat sink) etc.

Download Excel Spreadsheet to Model Heat Loss from Insulated Pipe