function out = h_nat_dT(T,Tamb,L)
% Derivative with respect of T of the function h_nat.

% Air properties.
k = 2e-2; % Thermal condunctivity [W/(m*K)].
rho = 1; % Density [kg/m^3].
cp = 1e3; % Heat capacity [J/(kg*K)].
mu = 1e-6; % Dynamic viscosity [Pa*s].
g = 9.81; % Gravity [m/s^2].

Pr = cp*mu/k;
Ra = 2*g*rho^2*cp/(mu*k)*abs((T-Tamb)./(T+Tamb)+eps).*L.^3;
Ra_dT = 2*g*rho^2*cp/(mu*k)*L.^3*2.*Tamb./(T+Tamb).^2;
num = 387e-3*Ra.^(1/6);
num_dT = 387e-3/6*Ra.^(-5/6).*Ra_dT;
denom = (1+(492e-3/Pr)^(9/16))^(8/27);
Nu_dT = num_dT.*(2*825e-3+2*num/denom)/denom;
out = k.*Nu_dT./L;