How to eliminate variables in a system of equations that contains exponential equations

I tried to eleminate variables from a system of equations. The four equations are bellow. My variables are m'', Pv,eq, Psat, Tlv, Pv, Pd, Pc. Others are just constants. I want to eliminate Pv,eq, Psat, Tlv, and write m'' as a equation of Pv, Pd, Pc. I try to use "eliminate" to do that, but got this error

Error using mupadengine/feval_internal

List must consist of polynomial expressions.

Error in sym/eliminate (line 30)

V = feval_internal(symengine, 'groebner::eliminate', polylist, vars);

I think that may be because my equation (9) is not polynomial. Then how to eliminate the variables I want to eliminate?

[Walter Roberson]

please post your code

[Zhihan Wu]

sigbar = 1
Mbar = 0.1142
Rbar = 55.91
rhol = 660.7
Tv = 343
kl = 0.1164
hfg = 337945


syms m Pveq Psat Tlv Pv Pd Pc
eqns = [m == 2*sigbar/(2-sigbar)*sqrt(Mbar/(2*pi*Rbar))*(Pveq/sqrt(Tlv)-Pv/sqrt(Tv)), Pveq == Psat*exp((Pveq-Psat-(Pd+Pc))/(rhol*Tlv*Rbar/Mbar)),Psat == Pv*exp(hfg*Mbar/Rbar*(1/Tv-1/Tlv)),m == kl/hfg*(Tlv)];
eliminate(eqns,[Pveq Psat Tlv])

Error using mupadengine/feval_internal
List must consist of polynomial expressions.

Error in sym/eliminate (line 30)
V = feval_internal(symengine, 'groebner::eliminate', polylist, vars);

Here is it

Answer 1

[Walter Roberson]

Q = @(v) sym(v);
sigbar = Q(1);
Mbar = Q(0.1142);
Rbar = Q(55.91);
rhol = Q(660.7);
Tv = Q(343);
kl = Q(0.1164);
hfg = Q(337945);
syms m Pveq Psat Tlv Pv Pd Pc
Psat = Pv*exp(hfg*Mbar/Rbar*(1/Tv-1/Tlv))

Psat = 

eqn1 = Pveq == Psat*exp((Pveq-Psat-(Pd+Pc))/(rhol*Tlv*Rbar/Mbar));
solPveq = solve(eqn1, Pveq, 'returnconditions', true)

solPveq = struct with fields:
          Pveq: -(184698685*Tlv*lambertw(k, -(571*Pv*exp(38593319/19177130)*exp(-38593319/(55910*Tlv))*exp(-(571*Pv*exp(38593319/19177130)*exp(-38593319/(55910*Tlv)))/(184698685*Tlv))*exp(-(571*Pc)/(184698685*Tlv))*exp(-(571*Pd)/(184698685*Tlv)))/(184…
    parameters: k
    conditions: in(k, 'integer') & Pv ~= 0 & Tlv ~= 0

Pveq = solPveq.Pveq

Pveq = 

eqn2 = m == kl/hfg*(Tlv);
solTlv = solve(eqn2, Tlv)

solTlv = 

eqn3 = subs(m == 2*sigbar/(2-sigbar)*sqrt(Mbar/(2*pi*Rbar))*(Pveq/sqrt(Tlv)-Pv/sqrt(Tv)), Tlv, solTlv)

eqn3 = 

solm = solve(eqn3, m)

Warning: Unable to find explicit solution. For options, see help.

 
solm =
 
Empty sym: 0-by-1
 

That is, you can isolate down to a single equation for m, but m is involved on both sides, and MATLAB is not able to solve for m.

When I look at the equation, complete with the LambertW call that itself involves m, it does not surprise me that there might not be a closed form solution.