answer and feedback attached, can show steps more clearly please 4. A bottle of fresh orange juice is taken from a fridge at 4°C and left in a room with anambient temperature of 20°C. The bottle is 70 mm diameter and 125 mm long, andyou may assume that the juice has the same physical properties as water. Theoverall heat transfer coefficient for the can in the room is 15 W m-² K-1.a) Derive a dynamic model (ie a first-order ODE) for the warming of the bottle usingdeviation variables; state clearly any assumptions you make.b) Use separation of variables to solve your model; estimate the temperature of thejuice after 20 minutes. Those who got this far seem to have noticed the similarity to problem 1. After takingthe balance, we obtain an expression in a similar general form. Notice that we aredoing a balance on energy and the energy of the contents of the bottle is mCp(T-Tref).Taking the can out of the fridge is equivalent to a step change in the temperature ofthe surroundings, i.e. Tsurr* = 16 °C.The steady-state gain is 1, since we expect the ultimate change in temperature of thejuice to be equal to Tsurr*.Always start towards a dynamic model by taking the balance:Accum. In - Out + Gen - Cons.We are given an overall heat transfer coefficient (i.e. U). This tells us about the rateof heat loss per unit surface area i.e. it helps us with the "Out" term.You are asked to assume that the orange juice has identical physical properties towater. Density and specific heat capacity are relevant.You can evaluate the surface area and volume of the vessel.By working from there, we obtain,UA61-6 (-Mant)]T* (t) = 16 1 expThus, the juice temperature obeysT(t) = 20 16expMy estimate for the timescale:U = 15Wm ²K-1-UAMCwM≈ 0.48kgA≈ 0.035m²UACwMAfter 20 minutes = 1200s, T = 2016. exp(-0.3)~ 8°C≈ 2.6 × 10-45-1Cw = 4200 Jkg-¹K-¹

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A bottle of fresh orange juice is taken from a fridge at 4°C and left in a room with an ambient temperature of 20°C. The bottle is 70 mm diameter and 125 mm long, and you may assume that the juice has the same physical properties as water. The overall heat transfer coefficient for the can in the room is 15 W m² K-1. a) Derive a dynamic model (ie a first-order ODE) for the warming of the bottle using deviation variables; state clearly any assumptions you make. b) Use separation of variables to solve your model; estimate the temperature of the juice after 20 minutes.

A bottle of fresh orange juice is taken from a fridge at 4°C and left in a room with an ambient temperature of 20°C. The bottle is 70 mm diameter and 125 mm long, and you may assume that the juice has the same physical properties as water. The overall heat transfer coefficient for the can in the room is 15 W m² K-1. a) Derive a dynamic model (ie a first-order ODE) for the warming of the bottle using deviation variables; state clearly any assumptions you make. b) Use separation of variables to solve your model; estimate the temperature of the juice after 20 minutes.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.21P

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