2. Solved Problems

Example 2:Heat Transfer Coefficient 

Hot liquid is flowing at a velocity of 2 m/s through a metallic pipe having an inner diameter of 3.5 cm and length 20 m. The temperature at the inlet of the pipe is 90oC. Following data is given for liquid at 90oC:

Density = 950 kg/m\(^3\)
Specific heat = 4.23 kJ/kg.oC
Viscosity = \(2.55 \times 10^{-4}\) kg/m.s
Thermal conductivity = 0.685 W/m.oC

The heat transfer coefficient (in kW/m\(^2\).oC) inside the tube is (GATE-2008)

(a) 222.22 (b) 111.11 (c) 22.22 (d) 11.11


Solution: From Dittus-Boelter relation, we have \(\text{Nu} = 0.023\, \text{Re}^{0.8}\text{Pr}^{0.33}\).

For the given data, \[\begin{align*} \text{Re} &= \frac{Dv\rho}{\mu} = \frac{0.035\times2\times950}{2.55\times10^{-4}} = 260784 \\ \text{Pr} &= \frac{C_P\mu}{k} = \frac{4.23\times1000\times2.55\times10^{-4}}{0.685} = 1.575 \\ \text{Nu} &= 0.023\times(260784)^{0.8}\times(1.575)^{0.33} = 575.2 \\ \text{i.e.,} \qquad \frac{hD}{k} &= 575.2 \\ \Longrightarrow \quad h &= 575.2 \times \frac{0.675}{0.035} \\ &= 11,257 \text{ W/m$^2$.$^\circ$C} = 11.3 \text{ kW/m$^2$.$^\circ$C} \tag{d} \end{align*}\]