1D Heat Equation Explicit Scheme (fixed)

Question

Gabriel Quattromani 2022-4-19

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1699740-1d-heat-equation-explicit-scheme-fixed

编辑： Gabriel Quattromani 2022-4-30

clear all
p=2050;     % density(kg/m^3)
k=0.52;     % conductivity(W/m-K)
c=1840;     % specific heat capacity(J/kg-K)
T_ini=20;       % initial temperature(K)
T_inf=-15;      % external temperature(K)
alpha=k/(p*c);       % Let thermal diffusivity be alpha
t=60*60*60*24;      %time in seconds
DELTA_t=100;        % change in time per timestep
M=t/DELTA_t;        % number of timesteps
N=300;      % number of steps of depth
L=3;        % maximum depth being analyzed
DELTA_x=L/(N);      % change in depth per step
t_diff=t/M;
time=0:t_diff:t;
%explicit scheme
% Boundary Conditions
T(1:N,1:M+1)=T_ini;
T(1,1:M+1)=T_inf;
CFL=(alpha*DELTA_t)/(DELTA_x^2);        % Courant number, which should be less than 0.5
% Finding temperature for next timestep for each depth 
for j=1:M
    for i=2:N-1
        T(i,j+1)=T(i,j)+((alpha*DELTA_t)/((DELTA_x)^2))*(T(i+1,j)-2*T(i,j)+T(i-1,j));
    end
end
Z=N*(0.1/L); % t=0.1 seconds in terms of the time step
xm=(69/300)*L;
plot(time,T(Z,:), 'b',time,T(69,:), 'r')
xlabel('Time')
ylabel('Temperature')
grid on
set(gca,'fontsize',16)
legend('0.1','xm')