Athermocouple, with a spherical junction diameterof 0.5 mm, is used for measuring the temperature of hot airflow in a circular duct. the convection heat transfer coefficient of the air flow can be related with the diameter (d) ofthe spherical junction and the average air flow velocity (v)as h 5 2.2(v/d)0.5, where d, h, and v are in m, w/m2? kand m/s, respectively. the properties of the thermocouple junction are k 5 35 w/m? k, r 5 8500 kg/m3, and cp 5320 j/kg? k. determine the minimum air flow velocity thatthe thermocouple can be used, if the maximum responsetime of the thermocouple to register 99 percent of the initial temperature difference is 5 s.

Newton's law of cooling states that the rate of change in the temperature t(t) of a body is proportional to the difference between the temperature of the medium m(t) and the temperature of the body. that is, startfraction dt over dt endfraction equals upper k left bracket upper m left parenthesis t right parenthesis minus upper t left parenthesis t right parenthesis right bracket , where k is a constant. let kequals0.04 left parenthesis min right parenthesis superscript negative 1 and the temperature of the medium be constant, m(t) font size decreased by 3 equivalent font size decreased by 3 294 kelvins. if the body is initially at 369 kelvins, use euler's method with hequals0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes.