A 3.2mm stainless steel wire, 30cm long has a voltage of 10 volt impressed on it. The outer surface temperature of the wire is maintained at $93^0C$. Calculate the center temperature of the wire. Take resistivity ($\rho$) of the wire as $70×10^{-8}$ ohm-m and the thermal conductivity as 22.5W/m-K.

Given,

d = 3.2mm = 0.0032m (Diameter of wire)

l = 30cm = 0.3m (Length of wire)

V = 10V (Voltage)

ts = 93℃ = 366K (Surface temperature of wire)

$ρ = 70×10^{-8}Ωm$ (Specific resistance of wire)

K = 22.5W/mK (Thermal conductivity of wire material)

Find: (1) tc (center temperature …