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Consider a plane wall of thickness L whose thermal conductivity varies in a specified temperature range as
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HEAT+MASS TRANSFER:FUND...-CONNECTPLUS
- 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_forward2.34 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 , isarrow_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_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_forwardIn a meat processing plant, 2-cm-thick steaks (k =0.45 W/m·K and a = 0.91 * 1027 m2/s) that are initially at25°C are to be cooled by passing them through a refrigerationroom at 211°C. The heat transfer coefficient on both sides ofthe steaks is 9 W/m2·K. If both surfaces of the steaks are to becooled to 2°C, determine how long the steaks should be keptin the refrigeration room. Solve this problem using analyticalone-term approximation method (not the Heisler charts).arrow_forwardA spherical container with an inner radius r1 = 1 m and an outer radius r2 = 1.05 m has its inner surface subjected to a uniform heat flux of q1=7kw/m^2. The outer surface of the container has a temperature T2 = 25°C, and the container wall thermal conductivity is k = 1.5 W/m·K. Show that the variation of temperature in the container wall can be expressed as and determine the temperature of the inner surface of the container at r = r1.arrow_forward
- To defrost ice accumulated on the outer surface of an automobile windshield, warm air is blown over the inner surface of the windshield. Consider an automobile windshield with thickness of 5 mm and thermal conductivity of 1.4 W/m·K. The outside ambient temperature is -10°C and the convection heat transfer coefficient is 200 W/m2·K, while the ambient temperature inside the automobile is 25°C. Determine the value of the convection heat transfer coefficient for the warm air blowing over the inner surface of the windshield necessary to cause the accumulated ice to begin melting.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_forwardA pipe is used to transport refrigerant R-134a with an inner radius of 0.03m, outer radius of 5 cm, and thermal conductivity of k=2.5 W/m-K. The inner and outer surfaces of the pipe are maintained at an average temperature of 20°C and 40°C, respectively. Obtain a general relation for the temperature distribution inside the pipe under steady conditions. Determine the rate of heat gain per unit length by the refrigerant through the pipe.arrow_forward
- Steam 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_forwardA cylindrical fuel rod (k = 30 W/m•K) of 2 cm in diameter is encased in a concentric tube and cooled by water. The fuel rod generates heat uniformly at a rate of 100 MW/m3, and the average temperature of the cooling water is 115°C with a convection heat transfer coefficient of 2500 W/m2.k. The operating pressure of the cooling water is such that the surface temperature of the fuel rod must be kept below 200°C to avoid the cooling water from reaching the critical heat flux (CHF). The critical heat flux is a thermal limit at which a boiling crisis can occur Determine the temperature at the surface of the rod. What can you do to lower the temperature aty the surface?arrow_forward) Consider a solid sphere of radius r=50 cm. The heat is generated steadily inside the sphere at a rate of (15000) W/m3. The conductivity of the sphere is 10 W/m.K. Surface of the sphere is cooled by cooling water whose temperature and convection heat transfer coefficient are 10oC and 125 W/m2.K. Determine the temperatures at the center and surface of the sphere. Find the total heat transfer rate from the surface of the spherearrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning