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1. It turns out that being able to calculate the net energy exchange due to radiation between two parallel wallsis very important for variety of engineering applications. In many cases, the space between the walls is either evacuated or filled with gas that does not have significant emissivity or absorptivity and thus can be ignored in terms of its participation in radiation heat transfer (note though if gas exists in the space between the plates that consideration of convective heat transfer may be very important still). 21 Q, Answer the following questions: a. If the two walls are black bodies and held at temperatures T2 and T2 by exchanging heat with other bodies in the amounts of Q2 and Q2 and the space between the walls is vacuum, what is the net flux of energy exchanged between them(< Q2/A? You canleave your answer in terms of symbols b. Now if the two walls are grey bodies with emissivities & and 82, show that the net flux of energy between them can be calculated as: 21-2 0(T1-T5) A 8,82 2. It very popular today to buy the equivalent of "thermos" bottle to store warm or cold beverages. In cross section, the basic design of a thermos bottle simply double walled container. Real Thermos brand vessels had metal outer wall and a glass inner wall and were evacuated between the walls, but there are many different varieties of such containers on the market now, ones in which the gas between the two walls has been evacuated ones which contain air between the walls, ones in which the walls are made of shiny metal, ones in which the walls are made of dull plastic, etc. An example of cut-away view of such a thermos bottle you can buy today that has double metal wall construction with the cavity between the walls being evacuated is shown below: BO In this problem, we will look at these cases to see which ones are good insulators and if just using Styrofoam cupis as good. a. The picture shown above is for commercial double walled evacuated metal bottle like those sold by Hydro Flask and Klean Kanteen and others. If we assume that the walls of the thermos bottle are separated by very thin gap compared to overall size of the thermos, we can approximate the geometry locally as transfer between parallel walls and we can ignore the end cap/spout roughly since is small compared to the rest of the vessel. Analyze the case where the walls are made of highly polished silvered metal with &wail 0.02 and you want to store boiling hot coffee at 100 °C from the environment at 20 °C. What is thenetrate of heat transfer to the surroundings in this case? b. Tervis also makes such double walled containers such as their "tumblers' but most of their product line is made of plastic. If we analyze the same case as in Part A with the space between the walls being evacuated, but now make the walls from polycarbonate plastic (Ewall= 0.94) what net rate of heat transfer to the surroundings for your coffee? c. In reality, Tervis generally just leaves the cavity between the walls filled with air that can conduct heat due to natura convection inside the walls. If we assume that we can approximate the cavity between the walls as being a vertical rectangular cavity with large aspect ratio (i.e. the height of the vessel divided by gap between walls 10) and ignore end effects, what is the net rate of heat transfer to the surroundings for the case like in Part but where we assume the gas filling the cavity between the walls has the properties of nitrogen. Does leaving the air in between the walls make significant difference in the rate of heat transfer? d. Finally the double wall evacuated bottle from Part A seems like pretty good insulator maybe, but to get better feel lets figure out how it compares to a traditional Styrofoam cup. What thickness of Styrofoam cup would you need to get the same rate of heat loss from your coffee as in Part A? So is the thermos stylebottle much better choice? 3. You have a cylindrical vessel whose walls have an effective emissivity of 0.8 and which are maintained at temperature of 540 °F Assume that the floor of the vessel sits on a good insulator and thus can be considered a reradiating (i.e. perfectly reflective) surface. The top of the vessel is open to the surroundings which are maintained at a constant 40 °F Answer the following questions: a. What will the temperature of the floor of the vessel be in this case? b. What is the net rate of radiant heat transfer to the surroundings in thiscase? 4. A fresh coat of paint in the form of thin film, 1.0 mm thick, has been sprayed over a 1.5 m 1.5 m steel plate. The solvent for the paint is benzene and the paint surface exerts partial pressure of 0.137 atm at the drying chamber temperature of 27 °C. Sixty cubic meters of air per minute is blown into the rectangular drying chamber which measures 1.5 m in length, .0m in height above the plate, and 1.5m in width. The air pressure in the drying chamber is atm and is maintained at 27°C. Drying chamber 60 m³/min air =1.0m 27°C, atm (W-1.5m) Painted steel plate L=1.5m Assume that at the air flow rate specified that the concentration of solvent in the bulk flowing air is negligible and that any latent heat affects are small such that the temperatures involved do not change. Answer the following questions: a. What is an appropriate convective mass transfer coefficient for this case? b. What is the solvent evaporation rate at the beginning of the drying process in [g/min] units under these conditions?

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