Answer to Question #183122 in Mechanical Engineering for luke

Question

A bakelite coating is to be used with a 10mm diameter conducting rod whose surface is maintained at 200C by passage of an electrical current. The rod is in a fluid at 25C and the convection coefficient is 140W/m2-K. Considering a coating used with thickness corresponding to the critical radius, determine the rate of heat transfer per meter of the rod (watts) 

Answer 1

Obtain the value of thermal conductivity of Bakelite

$k_b=1.4 W/m.K$

$r_c=\frac{k}{h}=\frac{1.4}{140}=0.01 m$

$q=\frac{T_1-T_{\infin}}{\frac{1}{2 \pi r_c Lh}+ \frac{\ln(r_c/r_1)}{2 \pi Lk}}$

$q=\frac{200-25}{\frac{1}{2 \pi \times 0.01 \times 140 }+ \frac{\ln(0.01/0.005)}{2 \pi \times 1.4}}=909.232 W/m$