simultaneous non linear excel

I haven't had enough time to really analyze your problem. How much help do you need? Is there a specific part you are having trouble with? Are you familiar with using Solver in Excel to solve these kind of problems (or simpler problems)?

I would start a problem like this by first identifying A) the "input variables" to the problem, B) any "intermediate values" that are calculated along the way, and C) the final values that need to be calculated. In performing this analysis, I would keep in the back of my mind that I am going to use Solver, so I will be looking to arrange these quantities in the spreadsheet in a way that makes it easy to set up a Solver model.

In a quick look over the problem, it appears that Thm and Tma are example of "input variables". Recognizing that I am likely to use Solver for this, I would put all of my input variables into a range/block of cells that I will use in the "by changing" field in Solver.

After putting some initial guesses in for the input variables, then you can calculate any intermediate values (A, C, and Jv look like examples of intermediate values) from the input variables.

From there, it appears that you have several different expressions for q based on those input variables and intermediate values. I would set up a block of cells that will calculate the different values for q.

At this point, the problem appears to be "find the values for the input variables that will make all the q's equal. You will need to come up with an "objective function" that you can put into the "set target cell" to a "min/max/value of" fields in Solver.

At this point, it should be as simple as calling Solver and telling it to set your objective function to the desired value/max/min by changing your input variables.