Thermodynamics HW Solutions 117

Thermodynamics HW Solutions 117 - 2-77 A 2-kW resistance...

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Chapter 2 Heat Conduction Equation Heat Generation in Solids 2-72C No. Heat generation in a solid is simply the conversion of some form of energy into sensible heat energy. For example resistance heating in wires is conversion of electrical energy to heat. 2-73C Heat generation in a solid is simply conversion of some form of energy into sensible heat energy. Some examples of heat generations are resistance heating in wires, exothermic chemical reactions in a solid, and nuclear reactions in nuclear fuel rods. 2-74C The rate of heat generation inside an iron becomes equal to the rate of heat loss from the iron when steady operating conditions are reached and the temperature of the iron stabilizes. 2-75C No, it is not possible since the highest temperature in the plate will occur at its center, and heat cannot flow “uphill.” 2-76C The cylinder will have a higher center temperature since the cylinder has less surface area to lose heat from per unit volume than the sphere.
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Unformatted text preview: 2-77 A 2-kW resistance heater wire with a specified surface temperature is used to boil water. The center temperature of the wire is to be determined. Assumptions 1 Heat transfer is steady since there is no change with time. 2 Heat transfer is one-dimensional since there is thermal symmetry about the center line and no change in the axial direction. 3 Thermal conductivity is constant. 4 Heat generation in the heater is uniform. 110 C r D Properties The thermal conductivity is given to be k = 20 W/m C. Analysis The resistance heater converts electric energy into heat at a rate of 2 kW. The rate of heat generation per unit volume of the wire is 3 8 2 2 wire W/m 10 455 . 1 m) (0.7 m) 0025 . ( W 2000 = = = = L r Q V Q g o gen gen & & & The center temperature of the wire is then determined from Eq. 2-71 to be C 121.4 = + = + = C) W/m. 20 ( 4 m) 0025 . )( W/m 10 455 . 1 ( C 110 4 2 3 8 2 k r g T T o s o & 2-40...
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This note was uploaded on 01/14/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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