Very thick slurries and pastes sometimes move in channels almost as a solid plug. Thus, one can approximate the velocity by a constant value v, over the conduit cross-section.

1. Develop and Analyze the radial and axial temperature distribution equation for the case as explained above, and convert the equations into dimensionless form.

1. Break down and compare the essential parts of the equation and clearly identify the conductive and convective heat transfer terms in the equation.
2. Illustrate the scheme for the solution for multifunction differential equation as one obtained for this particular case.
3. Evaluate and Illustrate the velocity and temperature profiles from the developed equation

4. Outline the effect of variations in the velocity of the fluid on the temperature distribution in radial as well as axial direction.

5. NOTE: Also include any relevant schematic diagram needed for this question and it must be a detailed step-by-step answer. otherwise you're answer would be disliked.

(,)=2+21241