In a pipe, laminar flow in a fully developed region with constant heat flux from the pipe wall, bulk mean temperature of fluid

Explanation:

Bulk mean temperature:

Bulk mean temperature of the fluid at a given cross-section of the pipe is defined as temperature which takes into account the variation of the temperature of the fluid with respect to the radius r at that cross-section of the pipe by averaging it.

Q = ṁ × C_p × T_b

Q is the heat transported by the fluid at that cross-section and ṁ is the mass flow rate and T_b is the bulk mean temperature at that cross-section.

There are two distinct conditions that occurs in the forced convection flow

Constant Heat flux conditions:

In the case of laminar flow condition at a fully developed region with constant heat flux from the pipe wall, bulk means the temperature of fluid and wall temperature both increases in the flow direction. This is explained in the figure below,

Constant wall temperature conditions:

In the case of laminar flow condition at a fully developed region with constant wall temperature, only bulk mean temperature is increasing in the direction of flow. 

Note:

For Constant Heat flux condition, Nusselt number = 4.36

For constant wall temperature condition Nusselt number = 3.66