A 1 m x 1.25 m hot surface at 300°C is to be cooled by attaching a rectangular fins (k = 200 W/m-K) with 30 mm length, 75 mm width and 5 mm base thickness. Fins are exposed to an ambient air condition of 25°C and heat transfer coefficient is 30 W/m K. If there are 2250 fins, calculate; a. The heat transfer rate from a single fin. b. The increase in the rate of heat transfer. c. Determine the overall effectiveness of the fins. с.
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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.One hundred circumferential aluminum fins of rectangular profile are mounted on a 1.0-m tube having a diameter of 2.5 cm. The fins are 1 cm long and 2.0 mm thick. The base temperature is 180°C, and the convection environment is at 20°C with h=50 W/m2· °C. Calculate the total heat lost from the finned-tube arrangement over the 1.0-m length.Finned heat sinks are used to keep computer chips in an acceptable temperature range. The heat sink base is 53 mm x 57 mm, and the maximum allowable chip temperature is 75 C. An array of 54 aluminum fins (k = 237 W/m*K) which have a square cross-section (3 mm x 3 mm) are attached to the heat sink. The length of each fin is 30 mm. The cooling air supplied to the heat sink is 25 C. If the convection heat transfer coefficient is 125 W/m2*K, what is the heat transfer rate (in W) from the heat sink, assuming adiabatic fin tips? (Hint: heat transfer does not solely occur from the fins.)
- J 5 A cylindrical steel tank with a diameter of 1.8m and a height of 2m, is insulated with polyurethane on its lateral faces and its lid. The insulation is 40 mm thick and covered with a thin layer of metal. The tank contains water that is kept warm by an electric heater in such a way as to maintain the inner surface of the tank at a temperature of 55C. The ambient air temperature is 10C and the external skin coefficient is 10 w/m2K. If the energy cost is $0.15/kwh. What is the monthly energy cost for water storage?Chips of width L _ 15 mm on a side are mounted to a substrate that is installed in an enclosure whose walls and air are maintained at a temperature of Tsur=T∞=25oC. The chips have an emissivity of ε=0.60 and a maximum allowable temperature of Ts=85oC. (a) If heat is rejected from the chips by radiation and natural convection, what is the maximum operating power of each chip? The convection coefficient may be approximated as h=11.7 W/m2K. (b) If a fan is used to maintain airflow through the enclosure and heat transfer is by only forced convection, with h=250 W/m2K, what is the maximum operating power400 circumferential fins of rectangular profile (k = 386 W/m °C) are installed on a tube having a diameter of 3 cm and 1 m length that is maintained at a temperature of 200°C. The single fin has a length of 2 cm and a thickness of 0.7 mm. The heat is transferred to the surrounding air at 100°C with a convection heat-transfer coefficient of 524 W/m2 °C. How many times is the heat transfer rate enhanced when the fins are installed on the tube?
- A hot surface at 350°C is to be cooled by attaching straight aluminum rectangular fins (k-250 W/m K) with 35 mm length, 70 mm width and 5 mm base thickness. Fins are exposed to an ambient air condition of 28°C and heat transfer coefficient is 35 W/m² K. If there are 1750 fins per m² surface area, calculate; a. The heat transfer rate from a single fin. b. The increase in the rate of heat transfer per m² surface area as a result of attaching 1750 fins. c. Determine the overall effectiveness of the fins.a) A 50 mm diameter carbon steel tube (ρ = 7833 kg/m3; Cp = 465 J/kg.K, k = 54 W/mK) at an initial uniform temperature of 18°C is heated in an oven with air circulation that is at a temperature of 250°C and has a convection heat transfer coefficient of 45 W/m2.K. How long must the tube be in the oven for the surface temperature to reach 100°C? b) The figure below illustrates the temperature distribution inside a flat solid at two instants for two different situations (A and B). In both situations is there heat transfer? What causes them to behave differently?a) A 50 mm diameter carbon steel tube (ρ=7833 kg/m³; Cp = 465 J/kg.K, k = 54 W/mK) at an initial uniform temperature of 18°C is heated in an oven with air circulation that is at a temperature of 250°C and has a convection heat transfer coefficient of 45 W/m².K. How long must the tube be in the oven for the surface temperature to reach 100°C? b) The figure below illustrates the temperature distribution inside a flat solid at two instants for two different situations (A and B). In both situations is there heat transfer? What causes them to behave differently?
- 400 circumferential fins of rectangular profile (k = 386 W/m oC) are installed on a tube having a diameter of 3 cm and 1 m length that is maintained at a temperature of 200oC. Thesingle fin has a length of 2 cm and a thickness of 0.7 mm. The heat is transferred to the surrounding air at 100oC with a convection heat-transfer coefficient of 524 W/m2 oC. Howmany times is the heat transfer rate enhanced when the fins are installed on the tube?A 1 m long, 5 cm diameter, cylinder placed in an atmosphere of 40°C is provided with 12 longitudinal straight fins (k = 75 W/m.K), 0.75 mm thick. The fins protrudes 2.5 cm from the cylinder surface. The heat transfer coefficient is 23.3 W/m^2.K.W/m2.K. Calculate the rate of heat transfer and fin efficiency, if the surface temperature of cylinder is at 150°C.Circular cooling fins of diameter D = 1 mm andlength L = 25.4 mm, made of copper (k = 400 W/m·K), areused to enhance heat transfer from a surface that is maintainedat temperature Ts1 = 132°C. Each rod has one end attached tothis surface (x = 0), while the opposite end (x = L) is joinedto a second surface, which is maintained at Ts2 = 0°C. Theair flowing between the surfaces and the rods is also at T` =0°C, and the convection coefficient is h = 100 W/m2·K.(a) Express the function u(x) = T(x) - T` along a fin, andcalculate the temperature at x = L/2. (b) Determine the rate of heat transferred from the hot surface through each fin and the fin effectiveness. Is the use of fins justified? Why? (c) What is the total rate of heat transfer from a 10-cm by 10-cm section of the wall, which has 625 uniformly distributed fins? Assume the same convection coefficient for the fin and for the unfinned wall surface.