Chapter 6, Problem 6.34P

Consider the nanofluid of Example 2.2.

1. Calculate the Prandtl numbers of the base fluid and nanofluid, using information provided in the example problem.
2. For a geometry of fixed characteristic dimension L, and a fixed characteristic velocity V, determine the ratio of the Reynolds numbers associated with the two fluids, ${\mathrm{Re}}_{\text{nf}}/R{e}_{bf}.$ Calculate the ratio of the aver- age Nusselt numbers, ${\overline{Nu}}_{\text{L,nf}}/{\overline{Nu}}_{\text{L,bf}},$ that is associated with identical average heat transfer coefficients for the two fluids, ${\bar{h}}_{\text{nf}}={\bar{h}}_{\text{bf}}.$
3. The functional dependence of the average Nusselt number on the Reynolds and Prandtl numbers for a broad array of various geometries may be expressed in the general form
   ${\overline{Nu}}_L=hL/k=C{\mathrm{Re}}^m{\mathrm{Pr}}^{1/3}$
   where C and m are constants whose values depend on the geometry from or to which convection heat transfer occurs. Under most conditions the value of m is positive. For positive m, is it possible for the base fluid to provide greater convection heat transfer rates than the nanofluid, for conditions involving a fixed geometry, the same characteristic velocities, and identical surface and ambient temperatures?