Thermocouples attached to a truncated, conical roller bearing in Figure P2.15 show that the temperature profile and heat flow rate are:

\[T(x)=450\left(2-3 x+x^{2}-x^{3}\right) \quad q=7500 W\]

If the cross-sectional area of the bearing is: $A(x)=0.04 \pi(1-x)^{2} \mathrm{~m}^{2}$

a. What is the thermal conductivity as a function of $x$ ?

b. What is the heat flux at $x=0$ ? $x=0.2$ ?

c. Where is the heat flux, highest \(( $0x $0.2)\) ?

Transcribed Image Text:

FIGURE P2.15 q(x) A(x) X