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Unformatted text preview: Chapter 15 Steady Heat Conduction Heat Conduction in Cylinders and Spheres 364C When the diameter of cylinder is very small compared to its length, it can be treated as an indefinitely long cylinder. Cylindrical rods can also be treated as being infinitely long when dealing with heat transfer at locations far from the top or bottom surfaces. However, it is not proper to use this model when finding temperatures near the bottom and the top of the cylinder. 365C Heat transfer in this short cylinder is onedimensional since there will be no heat transfer in the axial and tangential directions. 366C No. In steadyoperation the temperature of a solid cylinder or sphere does not change in radial direction (unless there is heat generation). 342 Chapter 15 Steady Heat Conduction 367 A spherical container filled with iced water is subjected to convection and radiation heat transfer at its outer surface. The rate of heat transfer and the amount of ice that melts per day are to be determined. Assumptions 1 Heat transfer is steady since the specified thermal conditions at the boundaries do not change with time. 2 Heat transfer is onedimensional since there is thermal symmetry about the midpoint. 3 Thermal conductivity is constant. Properties The thermal conductivity of steel is given to be k = 15 W/m C. The heat of fusion of water at 1 atm is h if = 333 7 . kJ / kg . The outer surface of the tank is black and thus its emissivity is = 1. Analysis ( a ) The inner and the outer surface areas of sphere are 2 2 2 2 2 2 m 49 . 79 m) 03 . 5 ( m 54 . 78 m) 5 ( = = = = = = o o i i D A D A We assume the outer surface temperature T 2 to be 5C after comparing convection heat transfer coefficients at the inner and the outer surfaces of the tank. With this assumption, the radiation heat transfer coefficient can be determined from .K W/m 570 . 5 )] K 5 273 ( K) 30 273 ]( ) K 30 273 ( ) K 5 273 )[( .K W/m 10 67 . 5 ( 1 ) )( ( 2 2 2 4 2 8 2 2 2 2 = + + + + + = + + = surr surr rad T T T T h The individual thermal resistances are Then the steady rate of heat transfer to the iced water becomes ( b ) The total amount of heat transfer during a 24hour period and the amount of ice that will melt during this period are Check: The outer surface temperature of the tank is which is very close to the assumed temperature of 5 C for the outer surface temperature used in the evaluation of the radiation heat transfer coefficient. Therefore, there is no need to repeat the calculations. 343 4 Chapter 15 Steady Heat Conduction 368 A steam pipe covered with 3cm thick glass wool insulation is subjected to convection on its surfaces. The rate of heat transfer per unit length and the temperature drops across the pipe and the insulation are to be determined....
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 Spring '11
 ENgel
 Heat Transfer, Insulation

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