Heat Loss Calculator for
a Stainless Steel
Complex Pipe System
By: Thomas Morris
& Jacob Hannon
The Problem Background
• We work at a Research and Development
company that designs various hot fluid systems.
• Systems are on machines that are subject to wind
and cold weather.
• The systems have heat exchangers with known
temperature inputs, and then long complex
arrangements of stainless steel pipe to deliver the
hot water.
• Each prototype is costly to build and test.
• We need a way of estimating the temperature and
pressure loss in a system before building a
prototype.
Objective
• Determine the final temperature and
pressure loss.
• Determine if the losses are significant if
the wind is blowing and for different
outside temperatures.
Setup of Heat Transfer Problem
Combined entry length
use Eq. 8.57 to obtain
Nusselt’s #
Obtain internal heat
transfer coefficient h
Choose appropriate
Nusselt’s # based upon
previous calculations
and conclusions
Thermal entry length
use Eq. 8.56 to get
Nusselt’s #
Fully developed Eq.
8.55 for Ts=constant to
obtain Nusselt’s #
Use Gnielinsti Eq. 8.62
to determine Nusselt’s
#
Obtain overall
convective coefficient
Thermal analysis to
obtain output fluid
temperature using
Eq.(8.45)
Use free convection
Eq. 9.34 to determine
Nusselt’s #
Obtain external heat
transfer coefficient h
Choose appropriate
Nusselt’s # based upon
previous calculations
and conclusions
Use combined free and
forced convection
equations to determine
Nusselt’s #
Obtain thermal
coefficient K for pipe
material at Ave. pipe
temperature
Property calculations
Use forced convection
Eq 7.54 Churchhill to
determine Nusselt’s #
Obtain properties mass
flow rate, Cp of fluid,
and perimeter and
length of pipe
Property calculations
Partial Continuation 1
Combined entry
length use Eq. 8.57
to obtain Nusselt’s #
Thermal entry length
use Eq. 8.56 to get
Nusselt’s #
Determining region
by comparing critical
lengths to pipe
length
Decide if laminar
determine xfd,h xfd,t
Fully developed Eq.
8.55 for Ts=constant
to obtain Nusselt’s #
Use Gnielinsti Eq.
8.62 to determine
Nusselt’s #
Calculate reynold’s #
Determine friction
factor
Decide if turbulent
determine xfd,h xfd,t
Calculate needed
property values
Partial Continuation 2
Use free convection
Eq. 9.34 to determine
Nusselt’s #
Calculate Rayleigh #
Property calculations
and lookup
Use combined free and
forced convection
equations to determine
Nusselt’s #
If combined calculate
free and forced
Nusselt’s #’s first
Property calculations
and lookup
Use forced convection
Eq 7.54 Churchhill to
determine Nusselt’s #
Calculate Reynold’s #
for flow over a cylinder
Property calculations
and lookup
Determine Grashof #
and Reynold’s # and
use to determine type
of convection
Calculate needed
property values
Initial Conditions
Excel Spread Sheet Solution
• All calculations including property
interpolations are self contained
• Perform iterations without switching
between a property tables calculator
• Could easily be adaptable for other fluids
than water or other pipe materials.
Excel Spread Sheet
Link
Summary of results pertaining to
initial conditions
• Only required one
iteration to decrease
error
• Change in temperature
lower than expected
• Pressure loss seems
appropriate
• Internal flow was
turbulent
• Changing wind speed
had little effect
• Radiation had a small
to negligible effect
Conclusions
•
Small temperature change due to these factors
–
–
–
•
•
•
•
•
•
•
Large internal heat transfer coefficient (116449.3 W/m^2*K) is 1047.4 times bigger than the small
external heat transfer coefficient (111.179 W/m^2*K)
Small diameter pipe (13.7 mm)=small surface area thus the heat rate between the pipe and the air
was very small
The pipe actually stored most of the energy. During an experiment the pipe changed color
validating this result.
Changing Wind Speed only changed output temperature a few degrees because the
external heat transfer coefficient did not change enough to have significant effect.
The Pressure Drop seemed appropriate for the length, diameter, and relative roughness.
Experiment was performed using very cold outside temperatures and a high temperature
loss was expected. The results do not support this hypothesis and in fact show that on a
hot day the losses could be even smaller/negligable.
We anticipated the need to insulate the pipe but according to the results this is not
necessary.
Under 140 mph hurricane winds there was only a 11.8 degree change (Due again to
previously stated conlusions)
Significantly increasing the length adds surface area and can make a huge difference in
the temperature loss. For example with a 105.4 m pipe the delta T was 76.6 degrees.
A lot of factors not investigated here can also affect the result (ie mass flow rate, pipe
diameter, thickness, etc.) and using this spreadsheet will help determine the optimal
configuration for any future fluid system.
Appendix
• Property tables were entered into the
spreadsheet from Fundamentals of Heat
and Mass Transfer 6th edition by
Incropera, Dewitt, Bergmann, and Lavine
Copywright 2007 John Wiley and Sons
• Equations used also from the same source