Answer:
A) q'_free = 3146.41 W/m²
B) q'_forced = 7521.41 W/m²
Explanation:
We are given;
Free convection coefficient; h_fr = 5 W/m²K
Force convection coefficient; h_forced = 30 W/m²K
Emissivity; ε = 0.95
Temperature of surrounding which is equal to temperature of air; T_s = T_air = 200°C = 473K
Initial temperature; T_i = 25°C = 298K
A) Now, since the convection feature is disabled, the mode of heat transfer associated with this condition is through free convection and radiation.
Thus, the formula for the heat flux under this condition is given as;
q'_free = q'_free convection + q'_radiation
q'_free convection = h_free(T_∞ - T_i) where T_∞ is equivalent to the value of T_air
Also, q'_radiation = ε•σ((T_air)⁴ - (T_i)⁴)
Where, σ is stephan boltzmann constant and has a constant value of 5.67 × 10^(−8) W/m²K⁴
Thus, rewriting;
q'_free = q'_free convection + q'_radiation
We have;
q'_free = [h_free(T_∞ - T_i)] + [ε•σ((T_air)⁴ - (T_i)⁴)]
Plugging in the relevant values to obtain;
q'_free = [5(473 - 298)] + [0.95•5.67 × 10^(−8)((473)⁴ - (298)⁴)]
q'_free = 875 + 2271.41
q'_free = 3146.41 W/m²
B) Now, in this case, since the convection feature is disabled, the mode of heat transfer associated with this condition is through forced convection and radiation.
Thus, the formula for the heat flux under this condition is given as;
q'_forced = q'_forced convection + q'_radiation
Where;
q'_forced convection = h_forced(T_∞ - T_i) where T_∞ is equivalent to the value of T_air
Also, q'_radiation = ε•σ((T_air)⁴ - (T_i)⁴)
Thus, rewriting;
q'_forced = q'_free convection + q'_radiation
We have;
q'_forced = [h_forced(T_∞ - T_i)] + [ε•σ((T_air)⁴ - (T_i)⁴)]
Plugging in the relevant values to obtain;
q'_forced = [30(473 - 298)] + [0.95•5.67 × 10^(−8)((473)⁴ - (298)⁴)]
q'_forced = 5250 + 2271.41
q'_forced = 7521.41 W/m²
