Q. Sometimes (surprisingly!) it is easier to do mass transfer measurements than heat transfer ones. As part of a study you have been asked to determine the heat transfer coefficient, h, as a function of wind speed, for flow around a complex object, GT (you are working for an Italian car manufacturer).
To do this, you have painstakingly constructed a 1/10 scale model of GT, [all model lengths are 0.1 times the full scale length] made of pure naphthalene. The surface area of the model 0.12 m^{2} . Air at 1 atm and at a constant temperature of 25^{o}C was blown over the model at a free stream velocity of 120 m/s. It was observed that 70 g of naphthalene sublimated in 15 minutes of flow.
(i) Finding and referencing suitable data for the equilibrium and diffusivity of naphthalene in air, determine the values of the relevant dimensionless groups for the forced convection mass transfer over your model.
(ii) Assuming that heat and mass transfer are analogous, (ie, that if Sherwood Number is a certain function of Reynolds and Schmidt Numbers, then Nusselt Number will be exactly the same function of Reynolds and Prandtl Numbers) explain what this can tell us about heat transfer from the full scale object? [Hint: assume that your unknown function shows the same scaling of heat/mass transfer with the fluid dimensionless group ( Pr or Sc ) as common turbulent flow correlations - there are good theoretical grounds why this should be the case].
(iii) Finally, use common scalings of Nu with Re to give an estimate of how h will vary with windspeed. Comment on possible limitations of this approach.
Q. The author of Q1 above has been very lazy and guessed the amount of naphthalene sublimated above. Assuming GT is a sphere (with area 12 m^{2} ), using and referencing correlations for mass transfer around a sphere, determine how much sublimation would be expected from the model (sphere).
Q.(based on a problem in Heat and Mass Transfer by Cengel and Ghajar). A "Stefan tube" is commonly used to determine diffusivity in air. The diffusivity of ethanol in air was checked in a Stefan tube, in which the liquid is placed in an open vertical cylinder and a gas stream of known vapour content is blown across the top. (In our case the vapour contains no ethanol) The tube has a uniform cross-sectional area of 0.8 cm2. Initially, the ethanol surface was 10 cm from the top of the tube, and after 10 hours have elapsed, the surface was 25 cm from the tube top. If T = 24^{o}C and P = 1 atm, determine the diffusivity of ethanol in air.