MSOLVER: "Invalid function" probably due to the integration in "Black Body Radiation"

[Wiljea]

The solution of MSOLVER takes a very long time and finally gives "Invalid function". This is probably due to the integration in the following equations: "Black Body Radiation", "{ " // In eqn 2, change the calls for F0λ to explicit integral where the integration limits are from x1 to x2 with xi,j=Ⓒh·Ⓒc/((λi,j_nm)·Ⓒk·(TK)) "'(eb(W/m^2))=Ⓒσ·(T_K)^4' " //"'f=F0λ((λ2nm);(T°C))-F0λ((λ1nm);(T°C))' " "'f=15/Ⓒπ^4·∫(Ⓒh·Ⓒc/((λ2_nm)·Ⓒk·(T_K));Ⓒh·Ⓒc/((λ1_nm)·Ⓒk·(TK));x^3/expm1(x);X)' " "'(eb12(W/m^2))=f·(eb_(W/m^2))' " "'(λmaxnm)·(Tmax°C)=Ⓒc3' " "'(qW)=(eb(W/m^2))·(A_(cm^2))' " "}",

[Wiljea]

But I discover that it is truly related to ISSUE #1314. Moreover in the present case the integration limits are pure numbers with: T=1273,15_K λ1=1000_nm λ2=600_nm 'ⒸhⒸc/((λ2_nm)Ⓒk(T_K))'=1.88347 62339 3⁳⁻⁸ m/nm and if I apply BASE I obtain 18.83476 23393 'ⒸhⒸc/((λ1_nm)Ⓒk(T_K))'=1.13008 57403 6⁳⁻⁸ m/nm and if I apply BASE I obtain 11.30085 74036

Then the integral computes 'f='15/Ⓒπ^4*∫(11.30085 74036;18.83476 23393;X^3/expm1(X);X)'=3.60929 06376 4e-3

Therefore in this case EITHER we need an algebraic expression of BASE to apply it to the limits OR the integration algorithm needs to apply BASE to the limits X1 & X2

[Wiljea]

I just write to c3d, because I was able to rule out the problem, not by deleting units using VALUE for instance but by imposing the required simplification. Because, indeed, the limit of integration is a complicate algebraic expression: 'ⒸhⒸc/((λ2_nm)Ⓒk(T_K))' which simplifies to a pure number that I can recover by doing: with T=1273,15_K λ1=1000_nm λ2=600_nm '→NUM(UBASE(ⒸhⒸc/((λ2_nm)Ⓒk(T_K))))'=18.83476 23393 '→NUM(UBASE(ⒸhⒸc/((λ1_nm)Ⓒk(T_K))))'=11.30085 74036

Then we can compute the integral without problem. A similar technique may also apply to ISSUE #1314. I will do a commit of equations.cc including these corrections and I hope that a special version will be available soon. This concerns 13 different simulations !