Hayder,

I think this question can be treated with a multiobjective tool for design optimization.

There are new efficient and powerful tools for multiobjective optimization which considers optimization problems involving more than one objective function to be optimized simultaneously.

Typically, there does not exist a single solution that simultaneously optimizes each objective. Instead, there exists a (possibly infinite) set of optimal solutions.

The CFD code STAR-CCM+ Software has integrated a design exploration and optimization tool called Heeds.

There are also other tools like ModeFRONTIER.

Regards

Looks an interesting problem to analyze. If there is no motion, as you mentioned maximum heat transfer will occur at 90 degree (vertical). But in case of motion, I think it will also depend on the rotation of the inner cylinder. The direction of rotation of the cylinder. Depending upon the direction of rotation, rotation of inner cylinder may promote or oppose the fluid motion due to natural convection, especially when the geometry is inclined.

At present, it seems difficult to imagine which angle will give maximum heat transfer in rotating cylinder case in annular space. Better to conduct numerical simulations for this (If there is no literature available for the same). Simulations for this problems can be done easily.

If you find any appropriate answer, please enlighten us as well.

Thanks

Dear Mounir, Naseem and Uday

I greatly appreciate your comment.

Many thanks

Dear Uday

In case of rotating inner cylinder, mixed convection occurs. I think that the maximum heat transfer will not occur at 90 degree. The numerical solution will be tested for verification.

Many thanks

Dear colleagues

I greatly appreciate your comment.

Many thanks