problem4-12 - PROBLEM 4.12 KNOWN Electrical heater of...

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PROBLEM 4.12 KNOWN: Electrical heater of cylindrical shape inserted into a hole drilled normal to the urface of a large block of material with prescribed thermal conductivity. s F IND: Temperature reached when heater dissipates 50 W with the block at 25 ° C. SCHEMATIC: ASSUMPTIONS: (1) Steady-state conditions, (2) Block approximates semi-infinite medium with constant properties, (3) Negligible heat loss to surroundings above block surface, (4) eater can be approximated as isothermal at T H 1 . A NALYSIS: The temperature of the heater surface follows from the rate equation written as T 1 = T 2 + q/kS where S can be estimated from the conduction shape factor given in Table 4.1 for a “vertical ylinder in a semi-infinite medium,”
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