Lesson 5 - Convection SAQ

* Calculate the heat transfer rate due to convection in a pipe between water flowing within it at 90°C and the inside of the pipe wall at 10°C.  The length of the pipe is 6.5 m with an inner diameter of 0.5 m. The film heat transfer coefficient is 1,020 W m^-2 K^-1.

Response: 

To calculate the heat transfer rate due to convection, we will use Fourier’s law:

Where

q is the rate of heat flow, measured in J s^-1 (W)

A is the surface area, measured in m²

h is the film heat transfer coefficient in Wm^-2 K^-1

T_w is the temperature of wall or pipe, measured in K

T_∞  is the bulk temperature of the fluid past the thermal boundary layer, measured in K

We first need to calculate the surface area for heat transfer via convection. The surface area of a pipe is as follows:

The rest are given in the problem statement, and therefore we can simply enter them and calculate.

Note: although we have defined T_w and T_∞ in Kelvin, as any temperature in centigrade is the temperature in Kelvin minus 273, (T_{w -} T_∞) has the same value in both units. We therefore don’t need to convert centigrade into Kelvin for this calculation.

Note that the value calculated here is a negative number. This is because the heat is being removed from the hot water.