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Calculate time needed for thermocouple read the temperature

A thermocouple of K type is suddenly exposed to air with temperature of 1273K, Initial temperature was 293 K. Calculate the time needed for the thermocouple read the temperature with accuracy of better that 99%. Ignore radiation and conduction. The measuring element has a ball shape of diameter of 0.5 mm. The surrounding air flow at velocity of 100 m/s Use the Heat transfer convection of air around a sphere Please use the following terminology: Tm = temperature of the surrounding medium =1273K T=probe temperature q=rate of heat transfer by convection h=convection heat transfer coefficient A= surface area of the sensor through which the heat is transferred m=mass of sensor C= specific heat capacity of the sensor 

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