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- 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=lenthofcyclinder2.34 Show that the temperature distribution in a sphere of radius . made of a homogeneous material in which energy is released at a uniform rate per unit volume , is3.17 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?
- The heat transfer coefficient between a surface and a liquid is 57 W/(m2K). How many watts per square meter will be transferred in this system if the temperature difference is 10C?2.46 The wall of a liquid-to-gas heat exchanger has a surface area on the liquid side of with a heat transfer coefficient of . On the other side of the heat exchanger wall flows a gas, and the wall has 96 thin rectangular steel fins 0.5 cm thick and 1.25 cm high as shown in the accompanying sketch. The fins are 3 m long and the heat transfer coefficient on the gas side is . Assuming that the thermal resistance of the wall is negligible, determine the rate of heat transfer if the overall temperature difference is .A plane wall, 7.5 cm thick, generates heat internally at the rate of 105 W/m3. One side of the wall is insulated, and the other side is exposed to an environment at 90C. The convection heat transfer coefficient between the wall and the environment is 500 W/m2 K. If the thermal conductivity of the wall is 12 W/m K, calculate the maximum temperature in the wall.
- 3.16 A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on one side is and on the other side is . If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how long it takes for the copper plate to reach a temperature of 82°C.: A spherical container ( k= 30 W/moC ) with inner radius r1 = 2 m and outer radius ro=2.1 m is is filled with ice water T= 0 oC subjected to the convection on the outer surface T∞2 = 25 oC , h∞2= 18 W/m2 oC .For steady one-dimensional heat transfercalculate a) The mathematical formulation b) the variation of temperature, and c) therate of heat transfer are to be determined foq1 The inner and outer surfaces of a 5-m x 6-m brick wall of thickness 30 cm and thermal conductivity 0.69 W/m · °C aremaintained at temperatures of 20°C and 5°C, respectively. Determine the rate of heat transfer through the wall, in W.
- A:Find the amount of heat transferred through an iron fin of thickness 5 mm, length 10 cm and width 100 cm. Also determine the temperature difference e at the tip of the fin at: 1- adiabatic tip, 2-heat convection at the tip. Assuming the atmospheric temperature of 28°C K=50 w/mK, h=10 w/m’K, O,=80°C. B-Why is the dimensional heat flow assumption important in the analysis of fins problems? C- Why are the annular fins more efficiency than others?.saturated steam at 110°C flows inside a steel pipe ( thermal conductivity 50W/mK) having an internal diameter of 10cm and external diameter of 12 cm . The surface heat transfer coefficient on steam side is 12 kW/m^2K and that onthe outside surface of pipe is 18W/m^2K . Determine the heat loss from the pipe if it is located in a space at 25 °C.A cylindrical vessel (D=98,4 cm) is filled with water (ρ=1000 kg/m3, c=4.187 kJ/kg.K) to a depth of 113,64 cm. The initial temperature of the water is 15°C. Determine the time [min] required to increase the water temperature to 50°C when it is immersed into tank, filled with oil at 105°C. (NOTE: The overall heat transfer coefficient between the oil and the water is 284 W/m2.K. The surface area is 4.2 m2.)