Crew Parker Lab 2 Report

MAE 107 Lab Report 2 Fall 2023 Crew Parker ID: 14186406 Instructor: Dr. Y. Wang TA: Cody Lab 2 Report Summary To perform this lab, a pot of water is brought to a boil using a heating plate, as appropriate safety personnel watch over the area. An aluminum sphere with an embedded thermocouple is hung from a lab stand, and submerged in the boiling water. The thermocouple allows us to monitor and graph the sphere’s temperature as it increases. This data is later imported into google sheets to calculate and plot specific values. The sphere is removed once it reaches 100 degrees Celsius, and hung back on its lab stand to cool naturally in the ambient air. The sphere is then submerged in boiling water again, removed, and placed into a wind tunnel with the flow set to a maximum to cool. This causes a forced convection cooling process of the sphere. The whole process is then repeated with a brass sphere cooled naturally and through forced convection. All data is recorded and plotted. Cooling the spheres through different methods shows that forced convection cools faster than natural convection. Additionally, using two different materials for the spheres shows that thermal conductivity affects the rate at which materials gain or lose heat through heat transfer processes. Our results ended up matching quite closely with those from the textbook, which gave us confidence in our methods and instruments. The Solidworks simulations of the same heating and cooling of the sphere actually produced a very similar graph to that made up of the data we collected during the forced convection cooling process in lab. Crew Parker 1

MAE 107 Lab Report 2 Fall 2023 Questions Q2.) Plot T s versus t and ln θ versus t for each run. Find a way to use the curve of ln θ versus t to calculate h. a. See Graphs b. In order to use the curve of ln θ versus t to calculate h, we can select any two points on the graph, find the slope between the points, and multiply that slope by -((m*C v )/A s ). Q3.) From the development of Equation 7 and the experimental design, what do you think may contribute to the errors (not related to the exp. equipment) in calculating h? How to minimize the errors? Eq. 7 After rearranging the equation given in the textbook, it can be seen that errors, without considering faulty lab equipment, can be made if one incorrectly measures the weight of the ball, the size of the ball, or the amount of time it took for the ball to reach a certain temperature. It can also come from one recording the data from the graph at incorrect times. The errors can be minimized by making sure each of the measurements are correct as well as starting the recording of data prior to allowing the ball to heat/removing the ball from the heated medium. Q4.) Compute the Biot number for each run. Are the Biot numbers small enough to justify the lumped capacity system assumption? (Biot # Equation) Crew Parker 2

MAE 107 Lab Report 2 Fall 2023 the analytical result (Equation 8) and simulation result (using the center temperature). For simulation, reduce the thermal conductivity by 100, please replot T(r,t) and comment on the result. The temperature vs time graph produced by the cooling simulation in Solidworks very closely matched our graphed data of experimental cooling. In terms of shape and values, it most closely matched with the forced cooling graphs. See Graphs Q1.) In the sample of experimental data, estimate the uncertainties in the measurements of time and temperature. The approximate uncertainty is calculated by dividing the most precise decimal place of the measurement instrument by 2. Therefore, for the stopwatch, the uncertainty of the time measurement is 0.0005 seconds, and, for the thermocouple, the temperature uncertainty would be 5 degrees C. Q9.) The TES tank at the central plan of UC IRVINE is a large cylinder 105 feet high and 88 feet in diameter to store the excess chilled water. Estimate the heat loss from the tank for winds of 0 and 20 m s−1. Take the surface of the tank to be 40 °F and the air temperature to be 120 °F. For a 12 hour period, compare energy loss to “that” stored in the tank. Would more insulation be worth it? Use the heat transfer coefficients from the experiments. h = 105 ft D = 88 ft V = 0 (Natural), 20 m/s (Forced Conv.) T s = 40 ℉ = 277.594 K T ∞ = 120 ℉ = 322.039 K t = 12 hr Crew Parker 4

MAE 107 Lab Report 2 Fall 2023 More insulation would be worth adding, as this would decrease the amount of heat lost in the process and increase the efficiency of the cycle. Q10.) Use ~30 data points around the time constant in your measurement of forced convection for the brass sphere cooling to calculate h (~30). Plot the frequency distribution of h (please choose a proper bin size). Make a comment on the Histogram This histogram represents the heat transfer coefficients for forced convection with the Brass sphere. Our calculated heat transfer coefficients are fairly spread out but most of our values lie between 183 and 253. Q11.) If the cooling starts at t=10 s, instead of 0 s, please rederive the solution to Equation 1. → → → 𝛳 = 𝑇 ? −𝑇 ∞ 𝑇 𝑖 −𝑇 ∞ ?θ θ = ?(??𝜃) =− ℎ𝐴 ? ?𝐶 𝑣 ?? 𝛳 = 𝐶 1 ? − ℎ𝐴 ? ? ?𝐶 𝑣 (With 𝜃 =1 and t=10) → → 1 = 𝐶 1 ? − 10𝐴 ? ℎ ?𝐶 𝑣 𝐶 1 = ? − 10𝐴 ? ℎ ?𝐶 𝑣 = 𝛳 = 𝑇 ? −𝑇 ∞ 𝑇 𝑖 −𝑇 ∞ ? − 10𝐴 ? ℎ ?𝐶 𝑣 * ? − ℎ𝐴 ? ? ?𝐶 𝑣 Crew Parker 5

MAE 107 Lab Report 2 Fall 2023 d. Aluminum, Forced Convection: Q8.) Solidworks Generated Graphs Crew Parker 7

MAE 107 Lab Report 2 Fall 2023 k = 234 k = 134 Sample Calculations Q7.) δℎ = −?𝐶 𝑣 ?𝐴 ? δ𝑇 + ?𝐶 𝑣 ??(θ) 𝐴 ? ? 2 δ? Set dT=.05 and dt=.005 = 1.958936 δℎ = −.586(385) (295)(.00202) (. 005) + (>586)(385)(−1.16) (.002)(295 2 ) (. 05) References “Practical Handbook of Thermal Fluid Science”. Yun Wang. Crew Parker 8