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 m^{2}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.

## 2 comments:

Hi Samir,

Thank you for your spreadsheets, they are very useful.

I am trying to produce a spreadsheet which calculates the rate at which a cylinder of water can be heated from a coil heat exchanger.

I am heating a fluid in a pipe at a rate of 10kW, this fluid travels through a copper coil 22mm diameter inside a cylinder of cold water (300 litres).

I've tried adapting your spreadsheet for cross flow heat exchanger, but it only deals with static temperatures into the copper coil and an air temperature.

Is this something you could help with?

Many thanks!

Craig

Hi Samir,

I have heated waste water left over from a processing plant that currently runs to waste. I want to use this heated waste water to increase the air temperature in a warehouse office area. I am thinking of installing a copper pipe a low level around the wall to act as the radiator and then the water will still run to waste. What I want to know is how many watts of heat energy I will recover for space heating and what would the waste water temp drop too before going to waste.

waste water temp 38C

water flow 6 lts/sec

proposed pipe size 80mm copper

length of pipe 45 metres

ambient air temp 15C

## Post a Comment