Question

Suppose a thermocouple is to be used to measure the temperature of a hot gas flowing through a duct. The thermocouple junction is initially at ambient temperature Ti-25°C before it is inserted into the gas stream. Hot duct wall Tsur 400°C Gas stream Junction, Tt) 1,-25°C, D p 8500 kg/m3 T 200°C 0.7 mm 400 Jkg.K Approximating the thermocouple junction as a sphere and using the lumped capacitance model, an energy balance on the thermocouple junction will result in a governing differential equation for the temperature of the thermocouple junction T as a function of time t Accounting only for the convection heat transfer between the thermocouple junction and the gas stream, e governing equation is 6h dT α (To-T), where α pcD

Solve the differential equation analytically

Answer 1

dt (T-T) 七 0