Heat Transfer Project

ME 332 Project 1 Dr. MacCarty, Fall 2020

Due: October 29th 8:00 am on Canvas (10% late penalty per day for up to 5 days)

A shipping container is being converted to serve as a mobile medical clinic for treating covid-19 patients in outbreak hotspots around the world. Double-paned windows will be added to provide daylighting, and insulation will be added to the floor, walls, and roof. An additional layer of durable roofing material will also be added to the roof.

Source: www.clinicinacan.org

As an engineer, you are asked to minimize the heating and cooling requirements for the clinic over a 1-year time period. You will decide on the materials used for insulation and roofing material. You will need to consider all forms of heat transfer including conduction, convection, and radiation through the three house components (walls/floor, roof, and windows). Operational parameters:

● The clinic interior air will need to be maintained at 21°C in both winter and summer, with average outdoor ambient temperatures of 0°C for 6 months (180 days) of winter and 35°C for 6 months (180 days) of summer.

● The shipping container dimensions are 12.2 m long by 2.4 m wide by 2.7 m tall. ● There will be a single 0.5 m wide 1 m tall window on each of the four walls of the container.

Windows have two panes, which are separated by a 1 cm air gap. Window thickness is given in the table below. Neglect radiation and convection within the air gaps, and evaluate air properties at 300K. For the purposes of this project you may assume that any doors are made of the same material as the container walls, and thus are inherently included in your wall calculations.

● The floor, roof, and walls of the shipping container are made of CORTEN-A sheet steel that is 2.1 mm thick on average and has a thermal conductivity of k = 54 W/m-K. Other properties may be approximated as clean stainless steel. You may disregard any beams.

● Insulation is applied to all surfaces that are not windows.

● The floor will receive the same treatment as the walls and undergo the same heat transfer processes since the shipping container is likely elevated slightly above the ground atop bricks or similar.

● The roof of the shipping container will be covered with a layer of insulation covered by an exterior roofing material, as given in the table below.

● Solar irradiation of 550 W/m2 for 12 hours per day in the summer and 175 W/m2 for 12 hours per day in the winter, which acts on the roof only.

● The absorptivity (fraction of incident solar radiation absorbed) of the roof material needs to be accounted for in your analysis. The roof acts as a graybody, meaning absorptivity is equal to emissivity.

● The cost of the insulation is $5 per m3. ● Interior convective heat transfer coefficient, hi=5 W/m2K (for all materials). ● Exterior convective heat transfer coefficient, ho=20 W/m2K (for all materials). ● Surrounding temperature is equal to ambient temperature outside. ● Neglect radiation exchange inside because the temperature difference between walls inside

is negligible. ● The efficiency of cooling is 50%. ● The efficiency of heating is 90%. ● Cost of electricity for cooling is $0.13 per kW-h. ● Cost of gas for heating is $0.03 per kW-h.

Available materials:

Windows

Material Thickness Emissivity k (W/m-K)

Glass 5 mm TBD* TBD*

Insulation

Material Thickness Emissivity k (W/m-K)

Glass fiber blanket insulation (16 kg/m3)

89 mm (default but varied in project)

N/A TBD*

Roofing

Material Thickness Emissivity k (W/m-K)

AISI 304 Stainless steel roofing (cleaned)

2 mm TBD* TBD*

*TBD means this should be determined through your analysis. Values are available in the textbook. Where values are given as a range, e.g. 0.8-0.9, use the mean value of the range, e.g. 0.85. Evaluate all properties at 300 Kelvin.

You will need to determine and fill into the provided template: a) All interior and exterior surface temperatures in summer and winter. Are the temperatures

reasonable? Use your engineering judgement to check your work. b) Energy required for heating on a 24-hr winter day with insulation. c) Energy required for cooling on a 24-hr summer day with insulation. d) Cost of energy for heating and cooling over 1 full year with insulation. e) Energy required for heating on a 24-hr winter day without insulation. f) Energy required for cooling on a 24-hr summer day without insulation. g) Cost of energy for heating and cooling over 1 full year without insulation. h) Payback period for added insulation at given thickness

Also develop a plot of the cost of the added insulation plus the total cost for heating and cooling energy for 10 years as a function of insulation thickness. In other words, Total Cost (insulation + energy cost over 10 years) is on the y-axis while Insulation Thickness is on the x-axis varied from 0 to 0.25 m. Include at least 1 additional plot or table with discussion about how certain input parameter(s) affect the heat transfer in the clinic and how this should influence the design. Encouraged Learning (5% bonus): Consider what would happen if solar panels were added to cover the entire roof. How would the panels affect heating and cooling needs? What is the payback period for the solar panels if they generate electricity used for cooling? Use a relevant resource online to indicate the energy generation capacity and cost of the solar panels to aid in your discussion. You do not need to consider the cost of additional hardware or converter systems. Deliverables: Report. Your report will be graded for professionalism and completeness. It should be no longer than 7 pages. The report should include the following, with the same convention for numbering and section naming as shown in Bold (ie copy and paste the following numbered section into your report and fill it in completely):

1. Problem statement and objective 2. Diagrams including control volumes and any relevant thermal circuits clearly labeled with

all components. 3. Approach, including assumptions. Assumptions given in this document should be included

in this section along with any further assumptions that you have made. 4. Energy balance, energy cost equations, and other relevant analyses. Equations should

be typeset if possible (in Word or LaTeX), but may be legibly handwritten if preferred. Equations should be neat and show clearly what you did for each major calculation (energy balance, thermal circuit, cost, etc.). You don’t need to include every single equation, but all representative equations are needed. You will lose points if it is difficult to understand your work.

5. Results should be transposed into the provided spreadsheet which will be submitted on canvas in addition to the report. Do not change the format because the spreadsheet is autograded using software. You will lose significant points if you do not maintain the format. In your results section of your report, you should also include the required insulation thickness plot and at least 1 additional plot or table with discussion about how input parameters influence the cost of heat transfer in the clinic and how this should influence the design.

6. Conclusions and any thoughts regarding:

a. Discussion of payback period and optimal thickness for the energy-saving features such as insulation.

b. Additional ways energy could be saved in this clinic by using different materials or approaches from those that were included in the problem statement. Include justification/analysis for your claims. For example, based on what you know about the parameters used in the heat flow calculations, how might the widow or the roof be designed to be more energy efficient as well?

c. Consideration of exogenous factors, such as what happens if the price of energy increases or decreases, or the system is moved to a location with significantly different local ambient temperatures.

d. Extended learning discussion of what would happen economically and physically if solar panels were added to the house.

7. Appendix that includes the spreadsheet, code, or EES code that you used for your analysis. Grading Matrix: See rubric on canvas Group Work: You are welcome but not required to work with one partner in completing this assignment. However, you and your partner are to do your work independently (i.e. you cannot copy from other groups or from previous classes). You will submit one set of deliverables for the two of you by self-selecting a group in canvas, but make sure to clearly indicate both names on the cover page. Hints:

1. Start early. 2. Feel free to come by office hours with the TAs or Dr. MacCarty to check your answers and

method to see if you are on the right track. Leave yourself plenty of time to adjust if not. 3. Use engineering judgement. You will need to make assumptions to be able to solve the

problem. These should be listed and justified. 4. Anticipate referencing multiple chapters from the book. 5. The problem can be solved using Excel, a coding package of your choice, or Engineering

Equation Solver (EES). 6. Without knowing the surface temperatures, you will not be able to solve for h_rad explicitly.

So you’ll need to guess and iterate until you converge on the correct surface temperature value via your thermal circuit equations, or solve simultaneously the way it is done in EES.