Question

4) Consider the schematic diagram of a thermowell/thermocouple which is used to measure temperature (T) of a fluid. The measured temperature Tm is recorded via thermocouple leads. The energy balance equation is given below. T. mc = UAT-T...) dt Here, m is the mass of the fluid in the thermowell, C is the specific heat, U is the heat transfer coefficient and A is the area of the thermowell wall. Page 2 of 2 (a) Derive the transfer function between the output Tm(s) and the input T" (s) (b) What are the ways in which we can decrease the measurement lag 7 for this system?

Answer 1

Solution » (a) Deriving transfer function between the Output Timils) and the input I'(s). energy balance equation is :- mc dlm UA (T- Tm) dt For steady state condition cq o may Written as a 10 = UA (Tg- Tras) , t <0 -2 Above equation states that Ts = Tms, or the thermocouple measures the true Mature equation Im C alim-Tms) at VA [(T-Ts) - (Tm-Toms)] Note that del Tm-Tms) d Tm at as Toms is constant. dt between Now let us define deviation variables to be difference variables and their steady State values. = Tm-Tms T'=T- To .. equation becomes Im C d Tim dt VA (T' - Tm) Pare No

T en 4 becomes T & Tm at T-Im Taking laplace transform of equation ③ T'(s) - I'm(s) as I'm(s) on Rearranging equation ③ © ESTI Parameter t is called time constant of system. 6 measurement lag can be decreased by using primary element of sufficiently small size and better heat Conductivity.