Consider the nanofluid of Example 2.2.

Example 2.2

(a) Calculate the Prandtl numbers of the base fluid and nanofluid, using information provided in the example problem.

(b) 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, Re_nf /Re_bf. Calculate the ratio of the average Nusselt numbers, Nu_L,nf, / Nu_L,bf, that is associated with identical average heat transfer coefficients for the two fluids, h_nf = h_bf.

(c) 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

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?

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The bulk thermal conductivity of a nanofluid containing uniformly dispersed, noncontacting spherical nanoparticles may be approximated by Knf kp +2kbf +2p(kp- kpt) kp +2kbt9(kp - Kbt)_ Ког where is the volume fraction of the nanoparticles, and kf, kp, and knf are the thermal con- ductivities of the base fluid, particle, and nanofluid, respectively. Likewise, the dynamic viscosity may be approximated as [20] Mnf=Mbf (1+2.5p) Determine the values of Knis Pais Cp.ni Mnfs and anf for a mixture of water and Al₂O3 nanoparticles at a temperature of T = 300 K and a particle volume fraction of p = 0.05. The thermophysical properties of the particle are kp = 36.0 W/m K, pp = 3970 kg/m³, and Cp.p = 0.765 kJ/kg K.