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Vsevolod [243]
3 years ago
9

A long rod of 60-mm diameter and thermophysical properties rho= 8000 kg/m3, c= 500 J/kg·K, and k= 50 W/m·K is initially at a uni

form temperature and is heated in a forced convection furnace maintained at 750 K. The convection coefficient is estimated to be 1000 W/m2· K. What is the centerline temperature of the rod when the surface temperature is 550 K?
Engineering
1 answer:
Dvinal [7]3 years ago
7 0

Answer:

Tc =    = 424.85 K

Explanation:

Data given:

D = 60 mm = 0.06 m

\rho = 8000 kg/m^3

k = 50 w/m . k

c = 500 j/kg.k

h_{\infty} = 1000 w/m^2

t_{\infity} = 750 k

t_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 56} +  500

   = 424.85 K

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