Although Matlab is much easier than other languages, it takes a big memeory. For example, Matlab takes momory 5 times more than Fortran. So, it depends on your problem, if your case is not big you can go with Matlab.
How complex is the problem you are trying to solve? 1D, 2D, 3D? The complexity of your problem is going to dictate the type of software you use to analyse it. OpenFOAM, or CFX or Fluent are better suited to more complex 2D or 3D problems. I use CFX primarily for my research, which is 3D transient CHT. I'd probably use MATLAB for 1D heat transfer if I was going to try to tackle a problem like that, but mostly because I'm more familiar with the code.
If you need to build your solver from scratch, you should use the programming language you are comfortable with, as long as your simulation is not critical in terms of memory and CPU time. Otherwise I would recommend (and I would use myself) a mix of C with some operators from C++.
For development from scratch -- C++ . Easy to parallelize(MPI and GPU) and manage.
I will advice against FORTRAN and MATLAB. MATLAB is OK for small codes like 2d lid driven cavity, etc. For complex codes, MATLAB requires far more memory.
FEniCS is a popular open-source computing platform for solving partial differential equations (PDEs). FEniCS enables users to quickly translate scientific models into efficient finite element code. With the high-level Python and C++ interfaces to FEniCS, it is easy to get started, but FEniCS offers also powerful capabilities for more experienced programmers. FEniCS runs on a multitude of platforms ranging from laptops to high-performance clusters. (https://fenicsproject.org)
I recommend C++ and C# for CFD simulation. You can use object oriented concept to improve the code performance. Matlab is not recommended for 2D or 3D problems because of high memory and computational costs. Fortran is also good but I think debugging in C# or C++ environment is easier than Fortran.
Most of the times, when I see people recommending Matlab or C/C++ for serious scientific work I just let it go. Some other times (like this one) I am commenting that Matlab is good for nothing, other than somewhat faster development at the cost of very poor performance. Just don't do it.
Now, C, C++ (someone even recommended C#) is out of question, unless you want trouble without any reason. C doesn't support matrices at all - they are just pointers with literally zero array support. C++ tried to solve that issue, adding the worst matrix features ever. What you want to do can be done in C or C++, but those languages aren't designed with Mathematics in mind.
Fortran is the way to go. You don't really need an object-oriented programming language to do simulations but even if you want to do that, Fortran 2003/2008 has excellent support for both module and object-oriented programming. If you need ready-made algorithm implementations for solving the differential equations describing heat flow, www.netlib.org has plenty of them, well-tested and with excellent performance. Most of them are written in Fortran. There is also gams.nist.gov, a website that facilitates searching for the proper ready-made code for the problem at hand.
Please note that systems like Matlab actually use ready-made Fortran code in the background (mostly taken by Netlib.) Scilab and Octave openly admit that but Matlab doesn't, for obvious reasons.
so i think it depends on what do u want programing for ; for example if you want to perfume a huge amount of mathematical equations and if the time important for you fortran is the best soloution for you and i have a code i think it could help your in fortran i can give it to you if you want😊
When writing a program in Fortran, C++ etc. you know what and how you count. You can also make intermediate prints, which makes it easier to start the code. However, you must know the numerical methods and there may be problems with physicochemical data. There are also so-called black boxes like Aspen with powerful physicochemical databases - and where you do not need to know the numerical methods. Regards,
For the system modelling and simulation it is more suitable to use matlab as it has many math tools for the different branches of the science such as signal processing, communications, filters etc. It has also the simulink when you use it to build the mathematical model of the system or the subsystem you can convert it into other forms of codes such as C -code and VHDL code.