GATE Mechanical Engineering (ME) 2022 Shift 1 Solved Paper

Consider a solid slab (thermal conductivity, k = 10 W∙m^-1∙K^-1) with thickness 0.2 m and of infinite extent in the other two directions as shown in the figure. Surface 2, at 300 K, is exposed to a fluid flow at a free stream temperature (T_∞) of 293 K, with a convective heat transfer coefficient (h) of 100 W∙m^-2∙K^-1. Surface 2 is opaque, diffuse and gray with an emissivity (ε) of 0.5 and exchanges heat by radiation with very large surroundings at 0 K. Radiative heat transfer inside the solid slab is neglected. The Stefan-Boltzmann constant is 5.67 × 10^-8 W∙m^-2∙K^-4. The temperature T₁ of Surface 1 of the slab, under steady-state conditions, is _________ K (round off to the nearest integer).