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

Preliminary Heat Exchanger Design

Introduction
This article will help you understand how you can estimate the initial design characteristics of a heat exchanger.  An Excel spreadsheet using the equations developed in this article is also provided. The equations are derived from a simple heat balance, and a few other elementary relationships.

These equations act as initial estimates, and the results will need to be refined by more sophisticated calculations.  If you just want the spreadsheet then click here, but read the rest of the article if you want to understand the theory.

Theory
Consider a heat exchanger operating in countercurrent flow.

Assume that we know the

• desired input and output temperatures of all streams, 
• specific heat capacities, 
• the overall heat transfer coefficient, 
• and the mass flowrate of the cold stream.  

We will now calculate

• the flowrate of the hot stream, 
• the heat transfer rate 
• and the heat transfer area.

A heat balance on the cold and hot streams gives

Qc gives the overall heat transfer rate.

But Qh = Qc.  Equating both equations and rearranging for the mass flowrate of the hot liquid stream gives

The log mean temperature difference is

The overall heat transfer rate Qc can be defined in terms of the log mean temperature difference

The final two equations can be easily rearranged to give the overall heat transfer area A in terms of the heat transfer rate Qc, the heat transfer area A and the log mean temperature difference.

Excel Implementation
Implementing these basic heat transfer equations in Excel is easy, and no special explanation is required.

Download Excel Spreadsheet for Preliminary Heat Exchanger Design

Related article: Modeling the Temperature Dynamics of a Cross-Flow Heat Exchanger