11. The shown 2-D plate is in contact with a heat source at its upper edge, which supplies heat at a constant flux, qo, per unit length. a. Derive a finite-difference relationship to express the steady-state temperature at the shown boundary point Tp, in terms of the temperatures at the surrounding points (TE, Tw, Ts) and the other quantities in the problem (e.g., k, qo, etc.). Follow the methodology outlined in the class notes (i.e., use energy balance). Assume Ax = Ay. y Яo х
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- Heat is generated uniformly in the fuel rod of a nuclear reactor. The rod has a long, hollow cylindrical shape with its inner and outer surfaces at temperatures of TiandTo, respectively. Derive an expression for the temperature distribution.20. The two plates of Problem 11 made of the same material and having constantk are exposed on one side to hot water at Tw and hw and on the other to cold air atTa and ha. Find a) the equation for temperature profile in these plates and b) temperaturesat x = 0 and at x = L if hw = ha = h. [Ans.: a) T1(x) = c1x + c2 where, c1 = hw(Ta – Tw)/c3 and c2 – Ta = – hw(haL +k)(Ta – Tw)/(hac3) where c3 = (k + hwL + hwk/ha)].Solve for this : An engine cover is made from 1 cm thick stainless steel plate (k = 14 W/m K). Air on the inside of the engine cover is heated to 340°C with a heat transfer coefficient of 7 W/m2K. Outside of the engine coverthe ambient air has a temperature of 70°C. If oil was spilled on the outside of the engine cover (ambient side), it could ignite if the surface temperature were to exceed 200°C. In this configuration, would spilled oil ignite? Use calculations to justify your answer. If a 4 mm thermal coating (k = 1.1 W/m K) was applied tothe outside of the engine, what would the outside temperature of the engine cover be reduced to?
- Two inches of urethane foam will reduce heat loss close to 1000% when applied to a 2-inch diameter uninsulated steel pipe. Assume the pipe wall thickness is 0.25-inches, the pipe interior convective heat loss (hi) is 500 BTU/hr-ft2-oF, and the pipe outside convective heat loss ho 20 BTU/hr-ft2-oF, k steel is 25 BTU/hr-ft-oF, and k insulaton is 0.023 BTU/hr-ft-oF. (hint - calculate heat loss with and without insulation.A hollow aluminum sphere, with an electrical heater in the center, is used in tests to determine the thermal conductivity of insulating materials. The inner and outer radii of the sphere are o.18 and o.21 m, respectively, and testing is done under steady-state conditions with the inner surface of the aluminum maintained at 250°C. In a particular test, a spherical shell of insulation is cast on the outer surface of the sphere to a thickness of o.15 m. The system is in a room for which the air temperature is 20°C and the convection coefficient at the outer surface of the insulation is 30 W/m2. K. If 80 W is dissipated by the heater under steady-state conditions, what is the thermal conductivity of the insulation?Question : Studies show that the major energy consumption in Fijian villages is wood which is used for cooking over open fires. Typical consumption of wood is 1 kg person–1day–1. (a) Estimate the heat energy required to boil a 2-liter pot full of water. Assuming this to be the cooking requirement of each person, compare this with the heat content of the wood, and thus estimate the thermal efficiency of the open fire. (b) How much timber has to be felled each year to cook for a village of 200 people?Assuming systematic replanting, what area of crop must the village therefore set aside for fuel use if it is not to make a net deforestation? Hint: refer to Table 10.4. (c) Comment on the realism of the assumptions made, and revise your estimates accordingly. Answer: (a) mcDT ≈ 0.6 MJ (heat losses from pot imply actual requirement is higher). h ≈ 3%. (b) 70 tonnes; 7 ha.
- A closed stirred-tank reactor with two compartmentsis shown in Fig. The basic idea is to feed the reactants continuously into the first compartment, where they will be preheated by energy liberated in the exothermic reaction,which is anticipated to occur primarily in the second com-partment. The wall separating the two compartments is quite thin, thus allowing heat transfer; the outside of thereactor is well insulated; and a cooling coil is built intothe second compartment to remove excess energy liberated inthe reaction. Both tanks are completely full at all times.Tests are to be conducted initially with a single-component feed (i.e., no reaction) to evaluate the reactor’s thermalcharacteristics.(a)Develop a dynamic model for this process under the conditions of no reaction. Assume that q0,Ti,andTc all may vary.(b)Make a degrees of freedom analysis for your model—identifying all parameters, outputs, and inputs that must beknown functions of time in order to obtain a solution.(c)In…. A small dam, which can be idealized by a large slab 1.2-m thick, is to be completely poured in a short period of time. The hydration of the concrete results in the equivalent of a distributed source of constant strength of 100 W/m3. If both dam surfaces are at 16°C, determine the maximum temperature to which the concrete will be subjected, assuming steady-state conditions. The thermal conductivity of the wet concrete can be taken as 0.84 W/m3. Suatu pelat datar dari besi dari seterika listrik berdaya 1200-Question 2: The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, kA 20 W/m K and kC50 W/m K, and known thickness, LA 0.30 m and LC 0.15 m. The third material, B, which is sandwiched between materials A and C, is of known thickness, LB 0.15 m, but unknown thermal conductivity kB. Under steady-state operating conditions, measurements reveal an outer surface temperature of Ts,o 20°C, an inner surface temperature of Ts,i 600°C, and an oven air temperature of T 800°C. The inside convection coefficient h is known to be 25 W/m2 K. What is the value of kB?
- a) Assuming perfect thermal contact between the layers of the composite walls, draw the typical temperature distribution across the layers and determine the heat energy gained per hour through all 4 walls of the room with a total surface area of 20 m2 . What does this heat energy represent in terms of the refrigeration system of the cold room? b) Without any calculations, how would you expect the internal and external air temperatures to be relative to the wall surface temperatures? Explain your answer. c) How do you expect the heat gain calculated in question 1a) above to change if you take into account the floor and the ceiling of the cold room? Explain your answerQ#01: Define the following:a) Steady and Transient state of heat transfer by the help of an example.b) If the area, thickness and temperatures are same across the material. Justify whichmaterial will transfer more heat, either the material with high thermal conductivity valueor the material with low thermal conductivity value?c) If the area and temperatures are same across the material. Explain whether thermalconductivity will have any effect on thickness or not?19) In fabrication process, steel components are formed hot and then quenched in water. Consider 2 m long, 0.2 m diameter steel cylinder (k = 40 W/m.°C, a = 10-5 m² /s), initially at 400 °C, that is suddenly quenched in water at 50 °C. If heat transfer coefficient is 200 W/m². K, calculate the following 20 min min after immersion: a) center temperature, b) surface temperature, c) The heat transferred to the water during the initial 20 min.