Q3:A- a cylindrical fuel rod consist of a fuel region of diameter (10mm). If the temperature at the center line of the fuel is (1800°C) and the heat generation rate is (q//=4x10 W/m'). 1- Find the temperature distribution along the radial direction of the fuel meat. Assume steady state one dimensional heat flow d?Tr 1 d + = 0 dr? r dr 2- Calculate the temperature at the surface of the fuel. Take the average thermal conductivity of the oxide fuel to be (1.9 W/m °C). 3- Calculate the temperature distribution along the radius of the fuel meat 4- Draw the temperature distribution along the radius of the fuel meat
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Q: Subject:heat
A: Solution: 1. d2(T(r)dr2+1rddr(krddr)+q'''kf=01rddrr.dTdr=-q'''kfddrr.dTdr=-rq'''kf
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Given data as
1.
The conduction equation for steady-state one-directional heat conduction in the cylinder is as
2. Given
For finding the temperature at the surface (Ts) put the values in the above equation
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- 3.10 A spherical shell satellite (3-m-OD, 1.25-cm-thick stainless steel walls) re-enters the atmosphere from outer space. If its original temperature is 38°C, the effective average temperature of the atmosphere is 1093°C, and the effective heat transfer coefficient is , estimate the temperature of the shell after reentry, assuming the time of reentry is 10 min and the interior of the shell is evacuated.Hot water at 160 ⁰C is passing through a pipe, and it is lagged with a plastic covering. The coefficient of thermal conduction of the plastic is 0.2 Wm-1K-1 and the heat transfer coefficient is 16 Wm-2K-1. The ambient temperature surrounding the pipe is 25 ⁰C. Determine the critical radius and hence the maximum heat loss. Calculate the heat loss for varying thicknesses of lagging and plot this against the thickness. From the graph, estimate an optimal thickness of lagging and explain your reasons. You can use Excel for the calculations and plotting.Through a stainless steel wire (k=19W/m°C) of 3mm in diameter and 1m in length passes certain electrical current generating a power of 3960W. The yarn is immersed in a fluid a 110°C and the convection heat transfer coefficient is 4kW/m2°C. calculate the temperature from the center of the wire.
- Task 3Superheated steam at 575ºC is routed from a boiler to the turbine of an electric power plant through steel tubes (k = 35 W/m K) of 300 mm inner diameter and 30 mm wall thickness. To reduce heat loss to the surroundings and to maintain a safe-to-touch outer surface temperature, a layer of calcium silicate insulation (k = 0.10 W/m K) is applied to the tubes, while degradation of the insulation is reduced by degradation of the insulation is reduced by wrapping it in a thin sheet of aluminium having an emissivity of ε= 0.20. The air and wall temperatures of the power plant are 27ºC. Assume that the inner surface temperature of a steel tube corresponds to that of the steam and the convection coefficient outside the aluminium sheet is 6 W/m2 K, (a) What is the minimum insulation thickness needed to ensure that the temperature of the aluminium does not exceed 50ºC? (b) What is the corresponding heat loss per unit meter?(c) What is the difference between lagged and unlagged pipes in…A non-thermally insulated industrial water vapor pipe is 25 m long and 100 mm in diameter. This line crosses a building whose walls and ambient air are at 25oC. Pressurized steam holds the tube surface at 150oC and the convective coefficient is 10 W/(m.K). The surface emissivity is ε=0.8. (a) the heat loss on this line; (b) if the steam is generated in a boiler that operates at 90% efficiency and uses natural gas priced at $0.20/MJ, what is the annual cost of this heat loss? Answer: (a) 18.41 W; (b) $129,000When can the conductive thermal resistance of the tube in a heat exchanger be neglected in overall heat transfer coefficient calculation? Never When the tube is thin or the material is highly conductive When the tube is thin. When the tube material is highly conductive. Which of the following sentence(s) is/are true? We cannot calculate thermal resistance of a solid slab. Thermal resistance concept is applicable only in Cartesian or Cylindrical coordinate. We cannot calculate thermal resistance of a solid cylinder. To apply thermal resistance concept, a problem only needs to be one dimensional and steady.
- T0 2-Water is heated as it flows through a square duct with side a=2 cm and the mean velocity through each is U = 3.2 cm/s. Duct is heated electrically by 2000 W/m2 into the water. Assuming that the water properties can be evaluated at 50◦C and that the flow is thermally fully developed: (a) Verify that the flow is laminar. (b) Calculate heat transfer coefficient (c) the mean temperature difference between the wall and the water stream. (d) Calculate the rate of temperature increase along the channel, (e) calculate pressure drop per unit lengthA square isothermal chip is of width 5mm on a side mounted in a substrate such that its side and back surfaces are well insulated, while the front surface is exposed to the flow of coolant at 15C. From reliability considerations, the chip temperature must not exceed 85C. If air is used as a coolant, h = 200W/m2. If a dielectric liquid is used as coolant, h = 3000W/m2. What is the difference in maximum allowable power through the chip between the two coolants? (answer in W) *plz answer this,ASAP,thx At high temperatures a nuclear reactor consists of a cylindrical wall composite as the fuel element thorium (k = 57 W/mK) wrapped in graphite (k = 3 W/mK) and helium gas flows through a circular cooling channel. Cylinder length 200 mm. Taking into account the helium temperature = 600°C and the convection coefficient, h= 200 W/m²K. When measured, the outside temperature is 100°C, and h = 5 W/m².K. Draw the electrical analogy, and calculate the overall heat transfer rate!
- Most automobiles have a coolant reservoir to catch radiator fluid that may overflow when the engine is hot. Such a radiator, made of copper, is filled to its 12-L capacity when at 10.0°C. -What volume of radiator fluid, in liters, will overflow when the radiator and fluid reach their 99.5°C operating temperature, given that the fluid’s thermal coefficient of volume expansion is 400.0 × 10-6 / °C? The coefficient of volume expansion for copper is 5.1 × 10-5 /°C.A refrigerant 22 condenser has four water passes and a total of 60 copper tubes that are 14 mm ID and have 2 mm wall thickness. The conductivity of copper is 3 90 W/m • K. The outside of the tubes is finned so that the ratio of outside to inside area is 1.7. The cooling-water flow through the condenser tubes is 3.8 L/s (a) Calculate the water-side coefficient if the water is at an average temperature of 30°C, at which temperature k = 0.614 W/m • K, p = 996 kg/m3 , andµ= 0.000803 Pa• s (b) Using a mean condensing coefficient of 1420 W/m2 • K, calculate the overall heat-transfer coefficient based on the condensing area.The liquid food is heated in a tubular heat exchanger. The inside pipe wall temperature is 110 °C. The internal diameter of the pipe is 50 mm. The product flows at 0.7 kg/s. If the initial temperature of the product is 7 °C, calculate the convective heat transfer coefficient. The thermal properties of the product are as follows: specific heat = 3.7 kJ / (kg °C), thermal conductivity = 0.6 W / (m °C), product viscosity = 500 x 10-6 Pa s, density = 1000 kg / m³ , product viscosity at 110 °C = 410 x 10-6 Pa s. a. Determine Reynolds number = Answer35668.7898. b. Determine the number Prantl = Answer3.083. c. Determine Nuselt number = Answer d. Convection coefficient = Answer W/m² °C.