Staring with an energy balance on a cylindirical shell volume element, derive the steady one dimensional heat conduction equation for a long cylinder with constant thermal conductivity in which heat is generated at a rate of egen.
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Staring with an energy balance on a cylindirical shell volume element, derive the steady one dimensional heat conduction equation for a long cylinder with constant thermal conductivity in which heat is generated at a rate of egen.
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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 .2.43 A turbine blade 6.3 cm long, with cross-sectional area and perimeter , is made of stainless steel . The temperature of the root, , is . The blade is exposed to a hot gas at , and the heat transfer coefficient is K. Determine the temperature of the blade tip and the rate of heat flow at the root of the blade. Assume that the tip is insulated.The handle of a ladle used for pouring molten lead is 30 cm long. Originally the handle was made of 1.9cm1.25cm mild steel bar stock. To reduce the grip temperature, it is proposed to form the handle of tubing 0.15 cm thick to the same rectangular shape. If the average heat transfer coefficient over the handle surface is 14 W/m K, estimate the reduction of the temperature at the grip in air at 21C.
- 3.17 A 1.4-kg aluminum household iron has a 500-W heating element. The surface area is . The ambient temperature is 21°C, and the surface heat transfer coefficient is . How long after the iron is plugged in does its temperature reach 104°C?A 0.6-cm diameter mild steel rod at 38C is suddenly immersed in a liquid at 93C with hc=110W/m2K. Determine the time required for the rod to warm to 88C.Show that the rate of heat conduction per unit length through a long, hollow cylinder of inner radius ri and outer radius ro, made of a material whose thermal conductivity varies linearly with temperature, is given by qkL=TiTo(rori)/kmA where Ti = temperature at the inner surface To = temperature at the outer surface A=2(rori)/ln(ro/ri)km=ko[1+k(Ti+To)/2]L=lenthofcyclinder
- One end of a 0.3-m-long steel rod is connected to a wall at 204C. The other end is connected to a wall that is maintained at 93C. Air is blown across the rod so that a heat transfer coefficient of 17W/m2 K is maintained over the entire surface. If the diameter of the rod is 5 cm and the temperature of the air is 38C, what is the net rate of heat loss to the air?3.38 An egg, which for the purposes of this problem is assumed to be a 5-cm-diameter sphere having the thermal properties of water, is initially at a temperature of . It is immersed in boiling water at for 15 min. The heat transfer coefficient from the water to the egg is assumed to be . What is the temperature of the egg center at the end of the cooking period?2.5 Derive an expression for the temperature distribution in a plane wall in which there are uniformly distributed heat sources that vary according to the linear relation where is a constant equal to the heat generation per unit volume at the wall temperature . Both sides of the plate are maintained at and the plate thickness is 2L.
- Suppose that the 10 cm thick concrete wall of a commercial building measures 30 mby 4 m. The energy impinging on the surface is 700 Wm-2. Under these conditionsthe external air temperature is 25ºC, and the internal and external surfacetemperatures of the concrete wall are 17ºC and 40ºC, respectively.(a) State and briefly describe the three heat transfer mechanisms.[30%](b) Calculate the net amount of thermal energy radiated by the wall.[40%](c) State your assumptions and briefly discuss their effect on the relativesizes of the heat transfer mechanisms.[30%]Data for Question A3.Heat transfer coefficient of air at 25ºC = 5 Wm-2K-1Thermal conductivity of concrete = 1.2 Wm-1K-1Emissivity of concrete = 0.85Stefan’s constant = 5.7 x 10-8 Wm-2K-4Derive an expression for the thermal resistance for one-dimensional heat conduction through a spherical shell assuming steady state.D e