I'd like to solve the following equation in wxMaxima:
k*A*((T_2-T_1)/L)=ε*σ*A*(T_1^4-T_a^4)
for T_1. The problem is that with regular Solve and Solve_to_poly I get extremely long outputs but not what I would expect. I need a real and positive solution since T_1 is a temperature in Kelvins. I can substitute the values but I'd prefer to get a symbolic formula as output. Is there a way to get such a solution in wxMaxima?
Apparently, it's not possible to solve this equation in such a way that a symbolic solution in form of a formula for T1 is obtained. Thus, I had to substitute the values and then solve for unknown T1. Either using float(solve([...],[T1])) which gives 4 solutions (with only one being real and positive - the one of interest) or using find_root(...,T1,0,1000). Lower and upper bounds for T1 (0 K - 1000 K) can be selected based on the physics of the problem.