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Unsteady Heat Transfer

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The overall heat transfer coefficient, U for an unsteady heat processing in a universal food processor was determined. Additionally, the effect of various circulating heating medium temperatures on the overall heat transfer coefficient was investigated. In this experiment, there are 3 forms of heat transfers between the water in the vessel and the heating water within the heating jacket: (1) heat convection between the water an inside surface of the vessel, (2) heat conduction through the jacket wall of the vessel and (3) heat convection between the jacket wall surface and the heating water. My report is free for all because I need good karma to be reborn as a thin woman in my next life and it's because I love you that's why. :)
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  Sonia Gawade 1 | Page  Experiment 2: Unsteady Heat Transfer Objectives: The overall heat transfer coefficient, U for an unsteady heat processing in a universal food  processer was determined. Additionally, the effect of various circulating heating medium temperatures on the overall heat transfer coefficient was investigated. Notations: A Lateral surface area of a truncated cone c y-intercept of a straight line C  p Specific heat capacity of water h Convective heat transfer coefficient m Gradient of a straight line equation t Time t 1  Time at an earlier interval t 2  Time at the later interval T Temperature at a specified time interval T 0 Initial temperature of the cold water T 1  Temperature at the earlier time interval T 2  Temperature at the later time interval T ∞   Temperature of the heating medium TR Temperature ratio U Overall heat transfer coefficient V   Volume of water in vessel x Horizontal coordinate of a straight line graph y Vertical coordinate of a straight line graph ρ  Density of water in vessel  Sonia Gawade 2 | Page  ∆ T Change in temperature ∆ t Change in time π  Mathematical constant that is the ratio of a circle's circumference to its diameter Introduction:   Transient or unsteady heat transfer is a function of both time and location. On the other hand, steady heat transfer varies solely as a function of location (Singh and Heldman, 2001). Knowledge on unsteady heat transfer is important especially for food processes such as sterilisation or pasteurisation as unsteady heat transfer is the dominant form of heat transfer in these processes (Singh and Heldman, 2001). In this experiment, there are 3 forms of heat transfers between the water in the vessel and the heating water within the heating jacket: (1) heat convection between the water an inside surface of the vessel, (2) heat conduction through the jacket wall of the vessel and (3) heat convection between the jacket wall surface and the heating water. The heat transfer coefficient for these 3 heat transfers is termed as the overall heat transfer coefficient or U. The thermal conductivity coefficient, k; was ignored as the vessel wall was very thin. Water has low thermal conductivity. At 2°C, thermal conductivity of water is 0.5606 a  W/ (m.K) and at 97°C, thermal conductivity of water is 0.6723 a  W/ (m.K). Hence temperatures  between 2°C and 97°C have thermal conductivities ranging between 0.5606 W/ (m.K) to 0.6723 W/ (m.K). The temperature of the heating medium used was at 35°C, 50°C and 65°C for this experiment. Thus it is imperative to note that internal resistance to heat transfer is negligible as water was being used as the heating medium. a   Standard Reference Data for the Thermal Conductivity of Water. (1995). American Institute of Physics and American Chemical Society. IUPAC.  Sonia Gawade 3 | Page  Materials and Method: The circulator bath was switched on. Temperature of the circulating medium was set to 35°C using the temperature control dial. Heating control lamp flashed when temperature of 35°C was reached. Seven litres of water was collected and its initial temperature (T o ), was measured using a digital food thermometer. The vessel was filled with 7 L of water and  processor was switched on. Agitation was initiated by adjusting the motor control knob. Initial temperature shown on the display panel of the food processor was recorded. Initial temperatures of the cool water were recorded using different thermometers for comparison  purposes. Temperature of the water (T), in the vessel was recorded at 30 seconds intervals for 5 minutes, then at 1 minute intervals for 10 minutes and finally at 3 minute intervals for 15 minutes. Temperature at frequent time intervals would be recorded initially as the initial temperature gradients would be large. Hence having the temperature recorded at frequent time intervals, would allow for better tracking of temperature changes. After recording was done, the upper and lower circumferences of water in the vessel were measured using a string. Height of the water was measured using a 30 cm ruler. Area and volume were calculated using the dimensions obtained. The vessel was then emptied. The steps above were repeated for circulating medium temperatures of 50°C and 65°C excluding the measurement of dimensions of water in the vessel.  Sonia Gawade 4 | Page  Results:  [Table 1]: Dimensions of the water in the vessel. Processing Vessel Processing Conditions Upper diameter = Upper circumference / π   Where π was taken as 3.14159265359.  Upper circumference was 0.983 m. Therefore, upper diameter was: 0.983 m / π  = 0.313 m Initial product temperature (T 0 ): 26 26 28 Heating medium temperature (T ∞ ): 35 50 65 Bottom diameter = Bottom circumference / π   Where π was taken as 3.14159265359.  Bottom circumference was 0.67 m. Therefore, bottom diameter was: 0.67 m / π  = 0.21 m Height: 0.118 m Volume: 0.00662 m Area: 0.1058 m Area was calculated assuming the vessel took on truncated cone geometry. Detailed calculations available in the Appendix, Section 1. [Table 2]: Temperature profile when T ∞  was 35°C. Time (s)   T (°C)   T ∞  - T (°C)   ΔT  (°C)   Δt  (s)   ΔT/Δt (°C/s)   TR    ln TR   30 26 9 1 180 0.00556 1 0 210 27 8 1 330 0.00303 0.88889 -0.1178 540 28 7 1 120 0.00833 0.77778 -0.2513 660 29 6 1 600 0.00167 0.66667 -0.4055 1260 30 5 1 180 0.00556 0.55556 -0.5878
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