A spherical thermocouple junction 1.0 mm in diameteris

Chapter 7, Problem 7.85

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A spherical thermocouple junction 1.0 mm in diameteris inserted in a combustion chamber to measure thetemperature T?of the products of combustion. The hotgases have a velocity of V?5 m/s.(a) If the thermocouple is at room temperature, Ti, whenit is inserted in the chamber, estimate the timerequired for the temperature difference, T??T, toreach 2% of the initial temperature difference,T??Ti. Neglect radiation and conduction throughthe leads. Properties of the thermocouple junction areapproximated as k?100 W/m?K, c?385 J/kg?K,and ??8920 kg/m3, while those of the combustiongases may be approximated as k?0.05 W/m?K,??5010?6m2/s, and Pr?0.69.(b) If the thermocouple junction has an emissivity of0.5 and the cooled walls of the combustor are atTc?400 K, what is the steady-state temperature ofthe thermocouple junction if the combustion gasesare at 1000 K? Conduction through the lead wiresmay be neglected.(c) To determine the influence of the gas velocity onthe thermocouple measurement error, compute thesteady-state temperature of the thermocouple junc- tion for velocities in the range 1V25 m/s. Theemissivity of the junction can be controlled throughapplication of a thin coating. To reduce the mea-surement error, should the emissivity be increasedor decreased? For V?5 m/s, compute the steady-state junction temperature for emissivities in therange 0.1?1.0.