1. Heat Loss Calculator for a Stainless Steel Complex Pipe System By: Thomas Morris & Jacob Hannon

2. 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.

3. Objective Determine the final temperature and pressure loss. Determine if the losses are significant if the wind is blowing and for different outside temperatures.

4. Setup of Heat Transfer Problem Thermal analysis to obtain output fluid temperature using Eq.(8.45) Obtain overall convective coefficient Obtain internal heat transfer coefficient h Choose appropriate Nusselts # based upon previous calculations and conclusions Combined entry length use Eq. 8.57 to obtain Nusselts # Thermal entry length use Eq. 8.56 to get Nusselts # Fully developed Eq. 8.55 for Ts=constant to obtain Nusselts # Use Gnielinsti Eq. 8.62 to determine Nusselts # Obtain external heat transfer coefficient h Choose appropriate Nusselts # based upon previous calculations and conclusions Use free convection Eq. 9.34 to determine Nusselts # Use combined free and forced convection equations to determine Nusselts # Use forced convection Eq 7.54 Churchhill to determine Nusselts # Obtain thermal coefficient K for pipe material at Ave. pipe temperature Property calculations Obtain properties mass flow rate, Cp of fluid, and perimeter and length of pipe Property calculations

5. Partial Continuation 1 Calculate needed property values Calculate reynolds # Decide if laminar determine xfd,h xfd,t Determining region by comparing critical lengths to pipe length Combined entry length use Eq. 8.57 to obtain Nusselts # Thermal entry length use Eq. 8.56 to get Nusselts # Fully developed Eq. 8.55 for Ts=constant to obtain Nusselts # Decide if turbulent determine xfd,h xfd,t Determine friction factor Use Gnielinsti Eq. 8.62 to determine Nusselts #

6. Partial Continuation 2 Calculate needed property values Determine Grashof # and Reynolds # and use to determine type of convection Property calculations and lookup Calculate Rayleigh # Use free convection Eq. 9.34 to determine Nusselts # Property calculations and lookup If combined calculate free and forced Nusselts #s first Use combined free and forced convection equations to determine Nusselts # Property calculations and lookup Calculate Reynolds # for flow over a cylinder Use forced convection Eq 7.54 Churchhill to determine Nusselts #

7. Initial Conditions

8. 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.

9. Excel Spread Sheet Link

10. 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

11. 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.

12. Appendix Property tables were entered into the spreadsheet from Fundamentals of Heat and Mass Transfer 6 th edition by Incropera, Dewitt, Bergmann, and Lavine Copywright 2007 John Wiley and Sons Equations used also from the same source