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What is the time required for the center of a thermocouple junction, made of a material with thermal conductivity ( k ) of 3 0

What is the time required for the center of a thermocouple junction, made of a material with thermal conductivity (k) of 30 W m-1K-1 and density (\rho ) of 8000 kg m-3, to reach 0.981 of its initial temperature difference in a turbulent water flow? The heat transfer coefficient (h) between the junction and water is 1000 W m-2 K-1, and the heat capacity (Cp) of the junction is 300 J kg-1 K-1. The junction has a diameter of 15 mm to withstand water impact, and the analysis employs an exact solution with a one-term approximation using solution coefficients A1=0.03 and \alpha =0.6. The characteristic length of the junction is given by the junction radius Lc =7.5 mm.

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