fan constantly running on hp elitebook 8460p ubuntu 18.04.3 LTS

Are you sure that the fan is OK? Noisy worn out fans usually have a much slower fan speed than usual due to friction, for example 600 RPM instead of 2000 RPM. Some computer fans run at up to 4000 RPM. Install Psensor. Psensor is an application for monitoring hardware sensors, including temperatures and fan speeds. Psensor displays itself on the desktop as a little thermometer icon in the notification area in the upper right corner of the desktop. You can right-click the thermometer icon at any time to display the hardware temperatures and fan speeds.

To install Psensor open the terminal and type:

sudo apt install psensor lm-sensors

Psensor uses lm-sensors to monitor the rotation speed of the fans.

The temperatures are within the normal range, but the temperature range is a little bit broader than normal (38°-60° C). This indicates that the fan is dragging (probably due to friction) and starting up more slowly than usual when the computer heats up. If this problem keeps on getting worse you should replace the fan.