A airplane layer of coal of thickness together = 1 m experiences uniform volumetric generation at a price of q = 20 W/m3 due to slow oxidation that the charcoal particles. Averaged over a everyday period, the optimal surface of the layer transfers heat by convection come ambient air because that which h = 5 W/m2 ∙ K and also T∞ = 25°C, while receiving solar irradiation in the quantity Gs = 400 W/m2. Irradiation native the setting may it is in neglected. The solar absorptivity and also emissivity that the surface space each together = ε = 0.95.

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(a) create the steady-state kind of the heat diffusion equation because that the layer of coal. Verify that this equation is satisfied through a temperature circulation of the form T(x) = Ts + qL2/2k (1-x2/L2) native this distribution, what deserve to you say about conditions in ~ the bottom surface ar (x = O)? map out the temperature distribution and also label an essential features.

(b) achieve an expression because that the rate of warmth transfer by conduction per unit area at x = L. Applying an energy balance to a control surface around the peak surface the the layer, attain an expression for Ts. Evaluate Ts and T(0) for the prescribed conditions.

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(c) everyday average values of G s and h count on a variety of factors such together time the year, cloud cover, and wind conditions. Because that h = 5 W/m2 ∙ K, compute and also plot Ts and also T (0) as a duty of Gs for 50 ≤ Gs ≤ 500 W/m2. Because that Gs = 400 W/m2, compute and plot Ts and T (0) as a role of h for 5 ≤ h ≤ 50 W/m2 ∙ K.

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