I fully support Bhaskar's opinion. Since heat transfer for simply geometries was investigated for long time, the industrial applications of (C)FD including heat transfer are very challenging especially for complex geometries and fluid properties (multi phase- / component). Thus, If you would focus on heat transfer (industrial or academic) you cannot bypass fluid dynamics. Both topics are very interesting and challenging regarding modeling issues and are worth further research.

In this way , what is the field in computional field which is not that complex?

What you suggest ? if I want solid career mathematics behind CFD is useless and focusing only on commerical softwares? or I must be good at those stuff ?

this is very hard to answer. I am doing a PHD in CFD and as Bhaskar already said, code developement in CFD makes you understanding the mathemtics behind it BUT you will not have the same "turn around time" for validation as done with commercial codes. If you want to focus on model developement in heat transfer for example, you dont need necessarly a self made CFD code. Developing CFD and heat transfer codes (laminar & turbulent flows...meshing...modeling...compressible... etc. ) would be too much.

Both fields are very complex from a mathemtical and code point of view. So if you focus on heat transfer problems you would maybe use a commercial code for instance to solve fluid dynamics. If you work with CFD and only need a little heat transfer you will implement small heat transfer module in your CFD code.

best patrick

Ahmed, I guess you are talking about the career that using computational skill. So, I'll comment solely from computation point of view.

CFD and HT are the same from the mathematical point of view unless you are dealing with the compressible flow that normally seen in aeronautical/aerospace industry. So, some ppl like me will think CFD includes HT. Mastering both is a plus for your career. My undergraduate majored in FD. My master extended to CFD & HT. In my Ph.D., I can easily built lubrication and mass transfer upon this foundation.

To use CFD, mathematics and coding experience can help you learn and use commercial code. It is very often to ppl got stuck in the convergent problem. If you have coding experience, you can quickly find a way to fix the iteration problem. That saves you tremendous time on trail and error. I understand nowadays many students don't have too much experience in coding. I feel at least should have knowledge of algorithm and scheme. Don't just run a commercial code without knowing how it works.

Nowadays, many multiphysics commercial codes are available. You cannot separate fluid dynamics and heat transfer in the real problem. So, you probably also need to understand the physics of both fluid dynamics and heat transfer. When you have the base of CFD, Fluid dynamics and heat transfer, it is not difficult use your multiphysics software to real problem, or even to the field you are not familiar with like EM. All you need to add then is the physics knowledge of the new field and be acquainted with more governing equations.

I was not too much experience using CFD, but I try to comment. I think it depends on the complexity of geometry. About taking Fluid Dynamic and heat transfer, I think your idea is very good. It can be more useful. If you have difficulty, you can model the simplest heat transfer with some assumptions.