function dxdt = pke_th_rhs(t, x, plant, Q_sg, u)
% PKE_TH_RHS  ODE right-hand side for coupled PKE + thermal-hydraulics.
%
%  State x = [n; C1..C6; T_f; T_c; T_cold]   (10 x 1)
%
%  Inputs:
%    t      - time [s]
%    x      - continuous state vector (10 x 1)
%    plant  - parameter struct from pke_params()
%    Q_sg   - function handle Q_sg(t) returning SG heat removal [W]
%    u      - external reactivity (rod worth) [dk/k], scalar
%
%  The controller is responsible for computing u; this function treats u
%  as a given input.  Q_sg is the bounded disturbance.

    n      = x(1);
    C      = x(2:7);
    T_f    = x(8);
    T_c    = x(9);
    T_cold = x(10);
    T_hot  = 2 * T_c - T_cold;

    Q_sg_val = Q_sg(t);

    % --- Reactivity with feedback ---
    %   rho = u + alpha_f*(T_f - T_f0) + alpha_c*(T_c - T_c0)
    rho = u ...
        + plant.alpha_f * (T_f - plant.T_f0) ...
        + plant.alpha_c * (T_c - plant.T_c0);

    % --- Neutronics ---
    dndt = (rho - plant.beta) / plant.Lambda * n + plant.lambda_i' * C;
    dCdt = (plant.beta_i / plant.Lambda) * n - plant.lambda_i .* C;

    % --- Thermal-hydraulics ---
    % Fuel node:     fission power in, heat transfer to coolant out
    dTf_dt = (plant.P0 * n - plant.hA * (T_f - T_c)) / (plant.M_f * plant.c_f);

    % Core coolant:  heat from fuel in, bulk enthalpy flow out
    dTc_dt = (plant.hA * (T_f - T_c) - 2*plant.W*plant.c_c*(T_c - T_cold)) ...
             / (plant.M_c * plant.c_c);

    % SG/loop node:  hot leg enthalpy in, SG heat removal out
    dTcold_dt = (plant.W * plant.c_c * (T_hot - T_cold) - Q_sg_val) ...
                / (plant.M_sg * plant.c_c);

    dxdt = [dndt; dCdt; dTf_dt; dTc_dt; dTcold_dt];

end