A large plane wall has a thickness L = 50 cm and thermal conductivity k = 25 W/m ∙ K. On the left surface (x = 0), it is subjected to a uniform heat flux q̇₀ while the surface temperature T₀ is constant. On the right surface, it experiences convection and radiation heat transfer while the surface temperature is T_L = 225°C and the surrounding temperature is 25°C. The emissivity and the convection heat transfer coefficient on the right surface are 0.7 and 15 W/m² ∙ K, respectively. Show that the variation of temperature in the wall can be expressed as T(x) = (q̇₀/k)(L - x) + T_L, where q̇₀ = 5130 W/m², and determine the temperature of the left surface of the wall at x = 0.

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90 Plane wall k = 25 W/m-K 0 ε = 0.7 L Tsurr = 25°C T%= 25°C h = 15 W/m².K TL = 225°C X