Is there a special relation which Fluent uses to calculate Nusselt number and convection coeffecient? Is there a safe temperature zone within which the experiments should be conducted in order to obtain sensible values of both?

Check the discussion below concerning a Nusselt number of 35000. Due to Fluents somewhat unusual definition of the Nusselt number, I'd avoid temperatures near the reference temperature, Tref. By default this temperature is 288.16K. Thus, the Nusselt number is infinite when the cell temperature reaches 288.16K. Luckily you can change this default value.