Chapter 6, Problem 6.30P

To assess the efficacy of different liquids for cooling an object of given size and shape by forced convection, it is convenient to introduce a figure of merit, $F_F,$ 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, ${\overline{Nu}}_L\sim {\mathrm{Re}}_L^m{\mathrm{Pr}}^n,$ obtain the corresponding relationship between $F_F$ and the fluid properties. For representative values of $m=0.80$ and $n=0.33,$ calculate values of $F_F$ for air $\left(k=0.026\text{W/m}\cdot \text{K,}v=1.6\times {10}^{-5}{\text{m}}^{\text{2}}\text{/s,}\mathrm{Pr}=0.71\right),$ water $\left(k=0.600\text{W/m}\cdot \text{K,}v={10}^{-6}{\text{m}}^{\text{2}}\text{/s,}\mathrm{Pr}=5.0\right),$ and a dielectric liquid $\left(k=0.0064\text{W/m}\cdot \text{K,}v={10}^{-6}{\text{m}}^{\text{2}}\text{/s,}\mathrm{Pr}=25\right).$ Which fluid is the most effective cooling agent?