A liquid cooling system is often used, for example in lithography such as extreme ultraviolet (EUV) lithography, to control the temperature of an apparatus or its components. Such cooling systems may, for example when used in an lithographic apparatus, be required to not be a source of significant vibrations in order for the apparatus to operate satisfactorily. Known liquid cooling systems comprise a fluid flow in pipes that provide heat transfer to and/or from the relevant components of the lithographic apparatus. A closed control loop with fluid flow may form part of the cooling system. The control loop may feature a sensor that measures the fluid temperature, and a heater which, in dependence on the measured fluid temperature, tunes the temperature of the fluid to a desired level. Accordingly, the performance of the control loop, and in turn the cooling system, is dependent on the accuracy of the temperature measurement. It is therefore important that the temperature measurement is an accurate representation of the cross-sectional mean fluid temperature. The cross-sectional mean fluid temperature may, however, not easily be measured in cases where the flow has thermal radial asymmetry. This asymmetry may be due to an asymmetric source, or an asymmetric heat transfer by the cooling system, e.g. where heat transfer is substantially confined to only one portion of the pipe. In low Reynolds number fluid flow where heat transfer mainly occurs in the thermal boundary layer, the radial asymmetry may be further enhanced due to the low amount of fluid mixing in such a flow. Known cooling systems may also have sensors mounted asymmetrically around the pipe, which causes the temperature measurement to be even less accurate. This is especially true when the sensor is positioned close to and after the heat source in the flow direction, because the flow has not yet had time to mix.
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