The authors construct an analytic solution of a simplified stationary thermohydraulics neutronics model with minimal hypotheses on the absorption and fission cross sections, and on the diffusion coefficient \[ \frac{d}{dz}(\rho u)=0, \] \[ \frac{d}{dz}(\rho u^2+\pi)\rho g, \] \[ \rho u\frac{d}{dz}h=E \sum_f(h)\phi(t,z) \] coupled to the simplified neutronic model based on the diffusion approximation with one energy group \[ -\frac{d}{dz}[D(h)\frac{d}{dz}\phi(z)] +[\Sigma_a(h)-\frac{\nu\Sigma_f(h)}{k_{\mathrm{eff}}}]\phi(z)=0. \] Here, \(z\in[0,L]\) is the spatial variable, \(L>0\) being the length of the nuclear core, \(\rho(z)\), \(u(z)\), \(\pi(z)\) and \( h(z) \) are respectively the density, the velocity, the dynamical pressure and the internal enthalpy of the flow. \(E>0\) is the energy released by a fission, \(\Sigma_f(h)>0\) is the fission cross section, \(\phi(z)\geq 0\) is the scalar neutron flux, \(D(h)>0\) is the diffusion coefficient, \(\Sigma_a(h)>0\) is the absorption cross section, and \(\nu\) is the average number of neutrons produced by a fission. Moreover, the density \(\rho\) and the internal enthalpy \(h\) are linked through the equation of state \(\rho=\varrho(h)\) where \(\varrho(\cdot)\) is a given function. At last, \(k_{\mathrm{eff}}>0\) is the neutron multiplication factor: \(k_{\mathrm{eff}}\in]0,1[\), \(k_{\mathrm{eff}}=1\) and \(k_{\mathrm{eff}}>1\) means that the nuclear core is respectively subcritical, critical and supercritical.