To assess the efficacy of different liquids for cooling by natural convection it is convenient to introduce a figure of merit. F N, which combines the influence of all pertinent fluid properties on the convection coefficient. If the Nusselt number is governed by an expression of the form, NuL - Ran, obtain the corresponding relationship between F N and the fluid properties. For a representative value of n = 0.33, calculate values of FN for air (k = 0.026 W/m ∙ K, β = 0.0035 K-1, v = 1.5 x 10-5 m2/s, Pr = 0.70), water (k = 0.600 W/m ∙ K, (3 = 2.7 x 10-4 K-1, V = 10-6 m2 /s, Pr = 5.0), and a dielectric liquid (k = 0.064 W/m ∙ K, β = 0.0014 K-1, v = 10-6 m2/s, Pr = 25) what fluid is the most effective cooling agent?