Question

Where does the maximum value of the temperature occurs in a Couette flow?

(a) Top plate

(b) Bottom plate

(c) Midpoint between the two plates

(d) No maximum temperature occurs

I have been asked this question during a job interview.

Question is from Couette Flow topic in division Numerical Techniques for Nonlinear Supersonic Flow, Elements of Hypersonic Flow, Couette and Poiseuille Flow of Aerodynamics

Answer 1

The correct answer is (c) Midpoint between the two plates

To elaborate: The temperature variation in the Couette flow is given by:

T = Tw + \(\frac {Pru_e^2}{2c_p} \big [\frac {y}{D} – \big ( \frac {y}{D} \big )^2 \big ] \)

Where, Tw is the temperature at y = 0 that is at the lower plate

ue is the velocity at y = D that is at the upper plate.

Pr is Prandtl number

cp is coefficient of pressure

D is the distance between the two plates

According to this, the temperature in Couette flow varies parabolically in y – direction. The maximum temperature occurs at y = D/2 which is the midpoint between the two parallel plates.

Tmax = Tw + \(\frac {Pru_e^2}{8c_p}\)