Superheated steam at an average temperature 200𝑜𝑜𝐶𝐶 is transported through a steel pipe

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Superheated steam at an average temperature 200𝑜𝑜𝐶𝐶 is
transported through a steel pipe �𝑘𝑘 = 50 𝑊𝑊 𝑚𝑚 ∙ 𝐾𝐾, 𝐷𝐷𝑜𝑜 = 8
𝑐𝑐𝑐𝑐,𝐷𝐷𝑖𝑖 = 6 𝑐𝑐𝑐𝑐, 𝑎𝑎𝑎𝑎𝑎𝑎 𝐿𝐿 = 20 𝑚𝑚�. The pipe is insulated with
a 4-cm thick layer of gypsum plaster (𝑘𝑘 = 0.5 𝑊𝑊/𝑚𝑚 ∙ 𝐾𝐾). The
insulated pipe is placed horizontally inside a warehouse where the
average air temperature is 10𝑜𝑜𝐶𝐶. The steam and air heat transfer
coefficients are estimated to be 800 𝑎𝑎𝑎𝑎𝑎𝑎 200 𝑊𝑊/𝑚𝑚2 ∙ 𝐾𝐾,
respectively. Calculate: (a) The daily rate of heat transfer from
the superheated steam, and (b) The temperature on the outside
surface of the gypsum plaster insulation.