Heat transfer project | Mechanical Engineering homework help

 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.  

 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.