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Consider a spherical shell of inner radius r1 and outer radius r2 whose thermal conductivity varies linearly in a specified temperature range as
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- 1.60 Two electric resistance heaters with a 20 cm length and a 2 cm diameter are inserted into a well-insulated 40-L tank of water that is initially at 300 K. If each heater dissipates 500 W, what is the time required for bringing the water temperature in the tank to 340 K? State your assumption for your analysis.arrow_forwardHeat is transferred at a rate of 0.1 kW through glass wool insulation (density=100kg/m3) with a 5-cm thickness and 2-m2 area. If the hot surface is at 70C, determine the temperature of the cooler surface.arrow_forward2.2 A small dam, which is 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/m K.arrow_forward
- 2.55 A long, 1-cm-diameter electric copper cable is embedded in the center of a 25-cm-square concrete block. If the outside temperature of the concrete is 25oC and the rate of electrical energy dissipation in the cable is 150 W per meter length, determine temperatures at the outer surface and at the center of the cable.arrow_forwardA cooling system is to be designed for a food storage warehouse for keeping perishable foods cool prior to transportation to grocery stores. The warehouse has an effective surface area of 1860 m2 exposed to an ambient air temperature of 32C. The warehouse wall insulation (k=0.17W/(mK)) is 7.5 cm thick. Determine the rate at which heat must be removed (W) from the warehouse to maintain the food at 4C.arrow_forwardA 5 m long section of a steam pipe whose outer diameter is 10 cm passes through an open space at 30°C. The average temperature of the outer surface of the pipe is measured to be 150°C, and the average heat transfer coefficient on that surface is determined to be 180 W/m^2.k. Determine (a) the rate of heat loss through convection from the steam pipe and (b) the annual cost of this energy loss if steam is generated in a natural gas furnace, and the price of natural gas is 0.05 Rs/Kwh, consider a 250 working-day year.arrow_forward
- 1. Steam at 235 °C is flowing inside a steel pipe (k = 61 W/m-°C) whose inner and outer diameters are 10 cm and 12 cm, respectively, in an environment at 20°C. The heat transfer coefficients inside and outside the pipe are 105 W/m²-°C and 14 W/m2-°C, respectively. Determine: (a) the thickness of insulation (k = 0.038 W/m-°C) needed to reduce the heat loss by 95 per cent and, (b) the thickness of the insulation needed to reduce the exposed surface temperature of insulated pipe to 40°C for safety reasons.arrow_forwardSteam at 200ºC flows in a cast iron pipe (k = 80 W/m⋅ºC) whose inner and outer diameters are D1 = 0.20 m and D2 = 0.22 m, respectively. The pipe is covered with 2-cm-thick glass wool insulation (k = 0.05 W/m⋅ºC). The heat transfer coefficient at the inner surface is 75 W/m2⋅ºC. If the temperature at the interface of the iron pipe and the insulation is 194ºC, the temperature at the outer surface of the insulation isarrow_forwardSteam at T∞ 1 = 320°C flows in a cast iron pipe (k = 80 W/m · °C) whose inner and outer diameters are D1 = 5 cm and D2 = 5.5 cm, respectively (Figure Q2b). The pipe is covered with 3-cm-thick glass wool insulation with k = 0.05 W/m · °C. Heat is lost to the surroundings at T2 = 5°C by natural convection and radiation, with a combined heat transfer coefficient of h2 = 18 W/m2 · °C. Taking the heat transfer coefficient inside the pipe to be h1= 60 W/m2 · °C, determine; i) the rate of heat loss from the steam per unit length of the pipe; and ii) the temperature drops across the pipe shell and the insulation.arrow_forward
- In a meat processing plant, 4 cm-diameter spherical meat balls (k=0.45 W/m-K and α=0.91×10-7 m²/s) that are initially at 25 °C are to be cooled by passing them through a refrigeration room at -10 °C. The heat transfer coefficient in the cold room is 22.5 W/m²-K. If surface of the meat balls is to be cooled to 3 °C, determine how long the meat balls should be kept in the refrigeration room. What will be the center temperature of the meat balls at the end of the process?arrow_forwardConsider the rate of conductive heat transfer from the inside of an animal’s body (at 37 ˚C) tothe cooler surroundings (initially at 22 ˚C). Order the following from lowest to highestimpact. Justify your answer. The outside temperature increases to 27 ˚CThe thermal conductivity of the animal’s insulating layer is doubledThe thickness of the animal’s insulating layer is halvedThe volume of the animal is doubledThe surface of the animal becomes coated in an extremely thin layer of black oilarrow_forwardA pipe in a manufacturing plant is transporting superheated vapor at a mass flow rate of 0.3 kg/s. The pipe is 10 m long and has an inner diameter of 5 cm and a wall thickness of 6 mm. The pipe has a thermal conductivity of 17 W/m·K, and the inner pipe surface is at a uniform temperature of 120°C. The temperature drop between the inlet and exit of the pipe is 7°C, and the constant pressure specific heat of vapor is 2190 J/kg·°C. If the air temperature in the manufacturing plant is 25°C, determine the heat transfer coefficient as a result of convection between the outer pipe surface and the surrounding air.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning