You are a young engineer at an up-and-coming food processing factory founded by chef Richard Blais. His signature at-home cuisine is “Comfort Mac-N-Cheese.” The secret ingredient to this best-selling...

You are a young engineer at an up-and-coming food processing factory founded by chef Richard Blais. His signature at-home cuisine is “Comfort Mac-N-Cheese.” The secret ingredient to this best-selling item is the cheese sauce, whose quality is highly dependent on its processing temperature. The cheese sauce is produced at 45? in a vat at one side of the kitchen, and it is packaged at a location 10 m away. An automated system pumps the cheese sauce to the packaging area through a cylindrical tube when the cheese is at a perfect 45? temperature. However, the elevated temperature of 45? is too high for packaging equipment and packaging materials. Packaging constraints require a maximum cheese sauce temperature of 35?. Currently the cheese sauce is reaching the packaging station (mean outlet temperature) at up to 35?, which is causing concern with reliability engineers. To maintain profitability and speed, Richard has decided to change the diameter of the thinwalled copper tubing that transports the cheese sauce from the production vat to the packaging equipment to increase the rate of cooling. Because of other constraints, he is unable to increase the convection coefficient by adding a fan, etc. He has asked you to size the copper tube diameter to decrease the cheese sauce temperature without altering the mass flow rate of cheese or length of the tube (10 m). Because the flow of cheese is laminar inside the tube, the (internal flow) Nusselt number for the cheese is a constant value (assume a value of XXXXXXXXXXThe external convection coefficient over the cylinder (cylinder in cross flow) is 15 W/m2 -K, and the ambient room air reaches a temperature of 25 ?. Because the cheese sauce is a top secret, you do not know its thermal properties. Apparently this will give away its composition. Luckily you do not need this information. Being a savvy engineer, you look online and find the following article and decide to take the average value of the reported thermal conductivity. http://www.foodeng.wisc.edu/images/publications/2001-6.pdf The current tube is 1 cm in diameter with a length of 10 m. You are to select the appropriate thinwalled tube diameter to ensure an outlet cheese sauce temperature of 32 ? if the inlet temperature is 45?. Your report should be less than one page in length (including data/figures), although your analysis and calculations can be attached. Please include a problem description and describe your approach with relevant equations. The first draft will be graded, and a revised report will be submitted at a later date. Your final grade on this short project will be the average grade between the first and second (revised) submissions.