The temperature is very interesting phenomena in the well system. Due to the geo-thermal gradient induced by the core of the earth, deeper well means higher temperature. The wellbore temperature during drilling depends on many factors such as wellbore geometry, wellbore depth, flow rate, the properties of the formation, the properties of the fluid, the geothermal gradients etc. Analytical modeling is very helpful to understand the heat phenomena in the well system and how the thermal effects are working in the well system. In this paper, two analytical modelings are investigate to discover how the temperature distributes in the wellbore. Some sensitivity analyses are calculated.

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