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An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of
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Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
- A cylindrical reactor made of copper with a radius of a= r=5mm has a heat conduction coefficient of k=386 W/moC, and there is heat generation at e ̇= (q ) ̇= 4x10^8 W/m3 inside this reactor. The cylindrical reactor convection heat transfer coefficient is h=2000 W/m0C and 〖T_(ambient= ) T〗_∞= 30 oC by convection, it cools down from the reactor surface to the center. According to the given boundary conditions a)Find the reactor surface temperature and the temperature T(a) at r=a. (VARIABLES: r=1-10mm, T_∞= 0-100oC) b) q(a) =((q ) ̇ * a )/ 2 = (e ̇ * a )/ 2 then find the heat flux amount in kW/m2arrow_forwardA cylindrical electrical heating element is used to heat up a baking oven. The heating element bears a voltage of 120 V/m, and has an electrical resistance of 1000 Ω/m. A ceramic pipe of inside radius rin = 2 mm, and outside radius rout = 5 mm encases the heating element. Thermal conductivity of the ceramic is k = 0.2 W/m-K. Given that the oven air temperature is T∞ = 180oC and convection coefficient h = 10 W/m2-K, find the temperature on the inside of the ceramic pipe.arrow_forwardCalculate the overall heat transfer coefficient of the steel pipe based on the inner surface. The inner diameter of the pipe is 12.7 cm, and the thickness of the pipe is 2.4 cm. The convection heat transfer coefficient in the pipe is 350 W / (m² ° C), the convective heat transfer coefficient outside the pipe is 25 W / (m² ° C), the thermal conductivity of the steel pipe is 15 W / (m ° C). If the pipe is used to deliver steam at 110 ° C and the ambient temperature is 20 ° C, determine the heat transfer rate of the pipe per meter. q = Watt / marrow_forward
- A coil-shaped cooling pipe is made of SS-304 material. This pipe is 1 ft long, 0.4 inch outside diameter, and inch inside diameter. This coil cooling pipe is used to cool the water in the bath. The temperature of the inner coil pipe is 40oF while the outer coil in contact with water is 80oF. The thermal conductivity of SS-304 is a function of temperature where k(T) = 7.75 + (7.78 x 10-3).T where k is in Btu/h.ft.oF and T is in oF. Calculate the rate of heat dissipation in watts! (1287.7)arrow_forwardA small metal building is to be constructed of corrugated steel sheet walls with a total wall overall surface area of about 300 m2. The air conditioner consumes about 1kW of electricity for every 4kW of cooling supplied. Two wall constructions are to be compared on the basis of cooling costs. Assume that electricity costs 10.15 Php/kWh. Determine the electrical energy savings of using 260mm of fiberglass insulation instead of 159 mm of fiberglass insulation in the wall. Assume an overall temperature difference across the wall of 20 ° (Uo (260-mm fiberglass)=0.17W/m2 °C and Uo (159-mm fiberglass)=0.31W/m2 °C)arrow_forwardA steel tube (k = 15 W/m.K) 3 m long carries a refrigerated liquid at 5°C. The inner diameter of the tube is 4 cm and the thickness is 1.5 cm. The convection heat transfer coefficient inside the tube is 80 W/m.K. The fluid receives heat from the external environment, which is at 28°C with a convection heat transfer coefficient of 20 W/m .K. To reduce the gain, it is studied to add a layer of insulating foam to the tube with a thickness of 5 cm and thermal conductivity k = 0.08 W/m.K. The placement of insulation pays off financially if the heat transfer rate is reduced by at least 30% and if the external surface temperature is above 15°C. Ignoring the effects of radiation, verify that these conditions are met.arrow_forward
- A steel tube (k = 15 W/m.K) 3 m long carries a refrigerated liquid at 5°C. The inner diameter of the tube is 4 cm and the thickness is 1.5 cm. The convection heat transfer coefficient inside the tube is 80 W/m².K. The fluid receives heat from the external environment, which is at 28°C with a convection heat transfer coefficient of 20 W/m².K. To reduce the gain, it is studied to add a layer of insulating foam to the tube with a thickness of 5 cm and thermal conductivity k = 0.08 W/m².K. The placement of insulation pays off financially if the heat transfer rate is reduced by at least 30% and if the outside surface temperature is above 15°C. Ignoring the effects of radiation, verify that these conditions are met.arrow_forwardQUESTION 41 A domestic refrigerator with inner dimensions of 0.7 m by 0.7 m at the base and height 1 m was designed to maintain a set temperature of 6 °C. The bodies consist of two 10-mm-thick layers of Aluminium (k = 225 W/mK) separated by a 30 mm polyurethane insulation (k=0.028 W/mK). If the average convection heat transfer coefficient at the inner and outer surfaces are 11.6 W/m2K and 14.5 W/m2K respectively, calculate: the resistance(R) for the Aluminium near the outer thermal layer in K/W to 8 decimal places.arrow_forwardQuestion 1 A large stainless-steel plate (k = 10 W/m. °C) has a thickness of 2 cm. Due to the electricity flowing through the plate, it generates heat which was dissipated form the sides of the plate. If the surface temperature of the plate was 50°C while the heat generated was 1 x 106 W/m3, calculate the maximum temperature inside the plate.arrow_forward
- The inside wall of a furnace is at 2100oF and the outside wall is at 300oF. The wall of a furnace must be designed to transmit no more than 220 Btu/hr-ft2. Two types of bricks are available for construction:TYPE A: k = 0.38 Btu/ hr-ft-R with an allowable maximum temperature of 1400oFTYPE B: k = 0.98 Btu/ hr-ft-R with an allowable maximum temperature of 2300oF Both types of bricks have the same dimensions (9” x 4.5” x 3”) but the cost for Type B brick is twice the cost of Type A brick. What is the rate of heat conduction through wall A? If a 15 ft2 wall is to be constructed, how many bricks will be used? how many brick A and how many brick B?arrow_forwardThe inside wall of a furnace is at 2100oF and the outside wall is at 300oF. The wall of a furnace must be designed to transmit no more than 220 Btu/hr-ft2. Two types of bricks are available for construction:TYPE A: k = 0.38 Btu/ hr-ft-R with an allowable maximum temperature of 1400oFTYPE B: k = 0.98 Btu/ hr-ft-R with an allowable maximum temperature of 2300oF Both types of bricks have the same dimensions (9” x 4.5” x 3”) but the cost for Type B brick is twice the cost of Type A brick. Model the wall as one-dimensional and determine the most economical arrangement of the bricks. Include:a drawing labeled with all given informationthe variables used in the appropriate places on the drawing (along with values and units, if provided)a thermal circuit showing the paths for heat transmissionequations and calculationsCalculations that show that the maximum temperature for Type A brick does not exceed 1400oFA recommendation for the number and orientation of the bricks. The inside temp is 2100f…arrow_forward(2.23) A finned heat exchanger tube is made of aluminum alloy (k = 186 W/m · K) and contains 125 annular fins per meter of tube length. The bare tube between fins has an OD of 50 mm. The fins are 4 mm thick and extend 15 mm beyond the external surface of the tube. The outer surface of the tube will be at 200°C and the tube will be exposed to a fluid at 20°C with a heat-transfer coefficient of 40 W/m2 · K. Calculate: (a) The rate of heat transfer per meter of tube length for a plain (un-finned) tube. (b) The fin efficiency. (c) The fin and prime surface areas per meter of tube length. (d) The weighted efficiency of the finned surface. (e) The rate of heat transfer per meter of tube length for a finned tube. (f) If the cost per unit length of finned tubing is 25% greater than for plain tubing, determine whether plain or finned tubing is more economical for this service. %3D Ans. (a) 1130 W. (b) 98.6%. (c) 0.8946 m? and 0.07854 m². (d) 98.7%. (e) 6920 W.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning