Question

A long rod of 60-mm diameter and thermophysical properties rho=8000 kg/m^3, c=500J/kgK, and k=50 W/mK is initally at a uniform temperature in a forced convection furnace maintained at 750K. The convection coeffiecent is estimated to be 1000 W/m^2K.
What is the centerline temperature of the rod when the surface temperature is 550K?

Answer 1

Answer:

Tc = 424.85 K

Explanation:

Given that,

$D = 60 mm = 0.06 m$

$\rho = 8000 kg/m^3$

$k = 50 w/m . kc = 500 j/kg.k$

$h_{\infty} = 1000 w/m^2t_{\infity} = 750 kt_w = 500 K$

$surface area = As = \pi dL \\\frac{As}{L} = \pi D = \pi \timeS 0.06$

HEAT FLOW Q  is

$Q = h_{\infty} As (T_[\infty} - Tw) = 1000 \pi\times 0.06 (750-500)$

 = 47123.88 w per unit length of rod

volumetric heat rate

$q = \frac{Q}{LAs}$

$= \frac{47123.88}{\frac{\pi}{4} D^2 \times 1}$

$q = 1.66\times 10^{7} w/m^3$

$Tc = \frac{- qR^2}{4K} + Tw$

$= \frac{ - 1.67\times 10^7 \times (\frac{0.06}{2})^2}{4\times 50} + 500$

  = 424.85 K