Answer:
Inner surface temperature= 783K.
Outer surface temperature= 873K
Explanation:
Parameters:
Heat,e= 3×10^6 W/m^3
Inner radius = 0.25 m
Outside radius= 0.30 m
Temperature at infinity, T(¶)= 10°c = 273. + 10 = 283K.
Convection coefficient,h = 500 W/m^2 . K
Temperature of the surface= T(s) = ?
Temperature of the inner= T(I) =?
STEP 1: Calculate for heat flux at the outer sphere.
q= r × e/3
This equation satisfy energy balance.
q= 1/3 ×3000000(W/m^3) × 0.30 m
= 3× 10^5 W/m^2.
STEP 2: calculus the temperature for the surface.
T(s) = T(¶) + q/h
T(s) = 283 + 300000( W/m^2)/500(W/m^2.K)
T(s) = 283+600
T(s)= 873K.
TEMPERATURE FOR THE OUTER SURFACE is 873 kelvin.
The same TWO STEPS are use for the calculation of inner temperature, T(I).
STEP 1: calculate for the heat flux.
q= r × e/3
q= 1/3 × 3000000(W/m^3) × 0.25 m
q= 250,000 W/m^2
STEP 2:
calculate the inner temperature
T(I) = T(¶) + q/h
T(I) = 283K + 250,000(W/m^2)/500(W/m^2)
T(I) = 283K + 500
T(I) = 783K
INNER TEMPERATURE IS 783 KELVIN
