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

Tc = 424.85 K

Step-by-step 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 \\(As)/(L) = \pi D = \pi \timeS 0.06`

HEAT FLOW Q is

`Q = h_(\infty) As (T_[\infty} - Tw) = 1000 \pi* 0.06 (750-500)`

= 47123.88 w per unit length of rod

volumetric heat rate

`q = (Q)/(LAs)`

`= (47123.88)/((\pi)/(4) D^2 * 1)`

`q = 1.66* 10^(7) w/m^3`

`Tc = (- qR^2)/(4K) + Tw`

`= ( - 1.67* 10^7 * ((0.06)/(2))^2)/(4* 50) + 500`

= 424.85 K