Dear Mr.Raam,

As per your query "2. As per the above formula insulated pipe has no change in temperature. So will it expand or contract during operating case. If it does kindly explain me how?"

Yes.

There will be an expansion and contraction if the operating temperatures are above and below 21 deg C or 70 deg F. Since, universally it is assumed that @ 21 deg C or 70 deg F, the material will have a zero expansion or contraction. If the material is exposed above or below the 21 deg C or 70 deg F, there will be an expansion or contraction.

As in your case, since the operating temperatures are 5 deg C to 100 deg C. so there will be a contraction and expansion in your pipe irrespective of insulation.

When we talk about the insulated pipe, the ambient temperature has no effect, provided the all the parts of piping system are fully insulated.
There are some cases, particular in the gulf part, where the operating temperature is (for example) 50 deg C below the black body temperature, then the design temperature shall be 84 deg C (Black body temperature). If the piping system is insulated for the process requirement, then the piping system shall be stress analyzed for the operating temperature of 50 deg C only. Since the design temperature is selected based on the atmospheric condition, it is no effect on insulated piping system.

Hope so this may clarify your doubt. Also I request the other members to provide a solution if my suggestion seems to be not accepted.