Derive three-dimensional heat equation in cylindrical polar coordinate system.
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Q: Derive the general 3D heat conduction equation for a cylindrical coordinate.
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Q: Derive the one-dimensional heat conduction equation for a sphere.
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Q: Derive the combined one-dimensional heat conduction equation.
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- 2.29 In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation where = local rate of heat generation per unit volume at r = outside radius = rate of heat generation per unit volume at the centerline Calculate the temperature drop from the centerline to the surface for a 2.5-cm-diameter rod having a thermal conductivity of if the rate of heat removal from its surface is 1.6 .The heat transfer coefficient for a gas flowing over a thin float plate 3-m long and 0.3-m wide varies with distance from the leading edge according to hc(x)=10x1/4Wm2K If the plate temperature is 170C and the gas temperature is 30C, calculate (a) the average heat transfer coefficient, (b) the rate of heat transfer between the plate and the gas, and (c) the local heat flux 2 m from the leading edge. Problem 1.183.10 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.
- A square silicon chip 7mm7mm in size and 0.5-mm thick is mounted on a plastic substrate as shown in the sketch below. The top surface of the chip is cooled by a synthetic liquid flowing over it. Electronic circuits on the bottom of the chip generate heat at a rate of 5 W that must be transferred through the chip. Estimate the steady-state temperature difference between the front and back surfaces of the chip. The thermal conductivity of silicon is 150 W/m K. Problem 1.6Derive the general 3D-general heat conduction equation for a spherical coordinate.How important the forced and free convection know as a mechanical engineer?
- Create two problem solving about steady-state heat flow (Heat convection in fluids) and show your solutions. Thank you!Provide the answers with clear explantion and images. Coolant flowing through a radiator at the rate of 3 kg/s are cooled from 105 0C to 81 0 The specific heat capacity of coolant and air are 4.19 kJ/kg K and 1.13 kJ/kJ/K respectively. Th overall heat transfer coefficient from gas to water is 140 W/m2 K. Calculate the surface area required for the radiation if the vehicle speed is 100 km/h. Consider the density of air as 1.225 kg/m3.Derive from the first principles the general heat conduction equation for the 3-dimensional system with cylinderical and spherical coordinates respectively.
- Derive the combined one-dimensional heat conduction equation.Derive the general 3D heat conduction equation for a cylindrical coordinate.Hi, can you help me with the following problem? A thermally insulated tank of water 2 m x 2 m, depth 1 m is stirred with a paddle for threehours. If the paddle is driven by a motor whose shaft power is 8 kW determine the rate ofchange of temperature in degrees C per hr and the increase in temperature of the water.The specific heat of water is 4200 J/kgC. Identify a system and start your analysis from anappropriate form of the Fist Law of Thermodynamics