A hot wire/film anemometer is an instrument used to measure velocities of fluids

Question

A hot wire/film anemometer is an instrument used to measure velocities of fluids. In one version of the instrument, a resistance wire is maintained at a constant temperature. The heat transfer rate is a function of the velocity of the fluid. By calibrating the voltage across the element (which is related to the power dissipation, i.e., the heat transfer rate from the element) as a function of the fluid velocity, the instrument can be used to measure the velocity of fluids. In one such instrument, the resistance wire is made of a platinum wire, 0.2 -mm diameter and 0.5-cm long. The wire is maintained at 50 degree C when it is used in water (at 20 degree C) flowing perpendicular to the axis of the element. Estimate the heat transfer rate from the surface to the water if the velocity of the water is 3.0 m/s.

Explanation / Answer

For a wire element innersed in fluid flow, electrical power input is equal to
power lost during thermal equilibrium so, I^2*R = h*A*(Tw - Tf) here, I is
input current,R is resistance of wire, Tw is temperature of wire, Tf is temperature of fluid and h is heat trransfer coefficient of wire

but R = Ro(1 + alpha*(Tw - Tf))
alpha -> Thermal coefficient of wire

now from kings' law
h = a + b*v^c [ where a, b and c are coefficients obtaied from callibration and v is velocity of fluid]

combiongin the three

v = [[{I^2*Ro{1 + alpha(Tw - Tref)}}/{A(Tw - Tf)} - a]/b]^1/c
given, r = 0.1 mm
l = 0.5 cm
Tw = 50 C
Tw = 20
v = 3 m/s

so heat trtansfer rtate = h*2*pi*r*l(Tw - Tf) = 2*h*pi*0.1*10^-3*0.5*10^-2(50 - 20) = 9.424*10^-5 h
but h = a + bv^c = a + bsqroot(3) [ taking c = 0.5]

so, heat transfer rate = 9.424*10^-5 [ a + bsqroot(3)] W
where a and b are calibration constants

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