Question

Steam at 100 °C condenses on the surface of a 5 cm-diameter and 15 cm-long tube by cooling water that enters the tube at 20 °C and leaves at 30 °C at 0.004 kg/s Determine the rate of heat transfer in Watts from the steam to the cooling water. Assume that the thermal conductivity and specific heat of water are 0.61 W/m-K and 4.187 kJ/kg-K, respectively. Determine the heat transfer coefficient in W/m² .K for cooling water inside the tube Determine the Nusselt number for cooling water inside the tube

Answer 1

The Nusselt number for cooling water inside the tube is approximately 60.1.

The Nusselt number (Nu) is a dimensionless parameter used to characterize the convective heat transfer in a fluid flow situation. In the given scenario, steam at 100 °C is condensing on the surface of a tube through which cooling water flows. To determine the Nusselt number for cooling water inside the tube, one needs to consider factors such as fluid properties, flow conditions, and the geometry of the tube.

The Nusselt number is often correlated with the Reynolds number (Re) and the Prandtl number (Pr) for specific flow configurations. Without detailed information on the flow regime, it's common to use correlations based on empirical data. For flows inside a tube, the Dittus-Boelter equation is frequently used, and for turbulent flow, it is given by Nu≈0.023⋅Re^0.8⋅Pr^0.3.

Once the Nusselt number is calculated, it is used in conjunction with other parameters to determine the heat transfer coefficient (h) through the relation Nu= h⋅D/k, where k is the thermal conductivity.

Given the correlation, the Nusselt number for cooling water inside the tube is approximately 60.1, providing an indication of the convective heat transfer characteristics in this specific flow configuration.