Question 14.7: Air at free stream temperature of T∞ = 90 °C flows past a ba...

Step 1 Since properties of air are not very sensitive to temperature, the factor involving the ratio of Prandtl numbers may be taken as unity. The fluid properties, as usual, are evaluated at the mean temperature given by T_{m}=\frac{T_{\infty}+T_{w}}{2}=\frac{90+30}{2}=60^{\circ} C.

Density: \rho_{m}=1.0496 kg / m ^{3}

Kinematic viscosity: \nu_{m}=19.08 \times 10^{-6} m ^{2} / s

Thermal conductivity: k_{m}=0.029 W / m ^{\circ} C

Prandtl number: P r_{m}=0.7

Step 2 The Reynolds number may be determined as

Staggered tube arrangement

Step 3 The ratio of transverse to longitudinal pitch is given by

The constants in the Nusselt number correlation are chosen fromTable 14.2 as C = 0.35, m = 0.6. The Nusselt number is obtained using Eq. 14.55 as

Table 14.2 Constants for use with correlating Eq. 14.55

\overline{N u}_{D}=C R e_{D}^{m} \operatorname{Pr}^{0.36}\left(\frac{P r_{\infty}}{P r_{w}}\right)^{\frac{1}{4}}  (14.55)

Step 4 The mean heat transfer coefficient may then be obtained as

Aligned tube arrangement

Step 5 The constants in the Nusselt number correlation are chosen fromTable 14.2 as C = 0.27, m = 0.63. The Nusselt number is obtained using Eq. 14.55 as

Step 6 The mean heat transfer coefficient may then be obtained as