A thermocouple indicates a temperature of $800^0C$ when placed in a pipeline where a hot gas is flowing at $870^0C$. If the convective heat transfer coefficient between the thermocouple and gas is $60 W/m^2K$, find the duct wall temperature. $ \epsilon(thermocouple) = 0.5$.

Given,

$ttc = 800℃=1073K (Temperature \ indicated \ by \ thermocouple) \\ tg = 870℃=1143K (Temperature \ of \ gas) \\ hgas = 60 W/m^2K (Convective \ heat \ transfer \ coefficient \ of \ gas) \\ \epsilon = 0.5 (Emissivity \ of \ thermocouple)$

Find: tw (Duct wall temperature) …