function out = h_nat(T, Tamb, L)
% h_nat returns the value of the heat transfer coefficient corresponding to
% the cooling of a vertical plate by air in natural convection. The heat
% transfer coefficient is depends on the surface temperature T, the
% temperature of the surrounding air Tamb and the length of the of the
% wall.

% 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].

% Definition of Prandt number.
Pr = cp*mu/k;
% Definition of Rayleigh number.
Ra = 2*g*rho^2*cp/(mu*k).*abs((T-Tamb)./(T+Tamb)).*L.^3;
% Defifinition of Nusselt number.
num = 387e-3*Ra.^(1/6);
denom = (1+(492e-3/Pr)^(9/16))^(8/27);
Nu = (825e-3+num/denom).^2;
% Return heat transfer coefficeint.
out = k.*Nu./L;