Consider a solid slab of thickness 2L and uniform cross section A. The volumetric rate of heat generation within the slab is ˙g(W m^-3). The slab loses heat by convection at both the ends to air with heat transfer coefficient h. Assuming steady state, one-dimensional heat transfer, the temperature profile within the slab along the thickness is given by:
T(x) = (gL²)/(2k) [1-(x/L)²] + T_s for -L≤x≤L
where k is the thermal conductivity of the slab and T_s is the surface temperature. If T_s=350 K ambient air temperature T_∞=300 K, and Biot number (based on L as the characteristic length) is 0.5, the maximum temperature in the slab is _______ K (round off to nearest integer).