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A cylindrical stone mix concrete beam of diameter D - 0.5 m initially at T_{i} = 20°C is exposed to hot gases at T_{∞} = 500°C. The convection coefficient is h - 10 W/m^{2} ∙ K.
(a) Determine the centerline temperature of the beam after an exposure time of t - 6 h.
(b) Determine the centerline temperature of a second beam that is of the same size and exposed to the same conditions as in part (a) but fabricated of lightweight aggregate concrete with density 1495 kg/m^{3}, thermal conductivity k 0.789 W/m ∙ K, and specific heat c_{p} = 880 J/kg ∙ K.
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