Question

An air heater may be fabricated by coiling Nichrome wire and passing air in cross flow over the wire. Consider a heater fabricated from wire of diameter D 1 mm, electrical resistivity P, conductivity 10 - 25 W/m - K, and emissivity .m. thermal The heater is designed to deliver air at a temperature of = 0.20 T. -50°C under flow conditions that provide a con- vection coefficient of 250 W/m The temperature of the housing that encloses the wire -K for the wire. and through which the air flows is T -50 C. Wire D. LP ,, Housing. Tu 0000 00000 If the maximum allowable temperature of the wire is To 1200C, what is the maximum allowable elec- tric current ? Ir the maximum available voltage is AE TIO V. what is the corresponding length of wire that may be used in the heater and the power rating of the heater? Hint: In your solution, assume 4. For the hair dryer shown above assume the filament resistance is: - Write out, but do not solve, the full equation to solve for Loire including the assumptions you are making

Answer 1

Assumptions : TO Uniform loire tera beratuse 2) Steady State 3) constant properties 14) Radiation exchange with large surrounding Solution : her - Tmas - T(&=-) To E Eo (Ts + Toure) ( Ts? + Tsure A total = htheo Esmer = 2ht (Ts - To) - ro à: I It Re LAC I'o Pe LlAJE LA 1992 2 - © TD 312 Iman = limon) D2 - ©

DE = Ire I PL AC LE DE AC Tman Pe L = DEAC 12h (Т. –To 72 А. Pe 112(h the) (Ts-To) Pellas 1 role 1 12 Anse Pele = DE: Iman =DE/21h the ) CTS-To) ) Eo Pe