A small hemispherical oven is built of an inner layer of insulating firebrick (110 mathrm{~mm}) thick, and

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A small hemispherical oven is built of an inner layer of insulating firebrick \(110 \mathrm{~mm}\) thick, and an outer covering \(80 \%\) magnesia \(45 \mathrm{~mm}\) thick. The inner surface of the oven is \(850^{\circ} \mathrm{C}\) and the heat transfer coefficient for the outside surface is \(12 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\); the room temperature is \(26^{\circ} \mathrm{C}\). Calculate the heat loss through the hemisphere, if the inside radius is \(1.0 \mathrm{~m}\). Take the thermal conductivities of firebrick and \(80 \%\) magnesia as 0.32 and \(0.06 \mathrm{~W} / \mathrm{mK}\).

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