Chapter 9, Problem 9.4P

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 of the form, Nusselt number is governed by an expression of the form, $N{u}_L~R{a}^n$ , obtain the corresponding relationship between $F_N$ , and the fluid properties. For a representative value of $n=0.33$ , calculate values of $F_N$ for air $\left(k=0.026\text{W/m}\cdot \text{K,}\beta =0.0035{\text{K}}^{-1},v=1.5\times {10}^{-5}{\text{m}}^2/\text{s,}Pr=0.70\right)$ , water $\left(k=0.600\text{W/m}\cdot \text{K,}\beta =2.7\times {10}^{-4}{\text{K}}^{-1},v={10}^{-6}{\text{m}}^2/\text{s,}Pr=5.0\right)$ , and a dielectric liquid $\left(k=0.064\text{W/m}\cdot \text{K,}\beta =0.0014{\text{K}}^{-1},v={10}^{-6}{\text{m}}^2/\text{s,}Pr=25\right)$ . What fluid is the most effective cooling agent?