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Main [.m]

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Lisa Pizzo 2026-01-28 13:13:13 +01:00
commit 571d318235
1 changed files with 50 additions and 28 deletions
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Project/Main.m
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@ -4,20 +4,20 @@ clear; clc; close all;
%% General values that we use in the entire script
%Task 3) Thermal conductivity
lambda_wall = 30; % ceramic
lambda_fluid = 0.6089; % water
lambda_wall = 1.5; % ceramic
lambda_fluid = 0.6; % water
lambda_air = 0.026; % air
%Task 4)
alpha = 10; % heat transfer coefficient
u_out = 18; % ambient air temperature (°C)
%Task 4) heat transfer coefficient
alpha=10;
u_out = 18; % ambient air temperature (°C)
%Task 6) Volumetric heat capacities: rho * c_p
% Densities [kg/m^3]
rho_wall = 2400; % ceramic
rho_fluid = 1000; % water
rho_air = 1.2; % air
% Specific heats [J/(kg*K)]
cp_wall = 900;
cp_fluid = 4184;
cp_wall = 1085;
cp_fluid = 4186;
cp_air = 1005;
% Volumetric heat capacities [J/(m^3*K)]
c_wall = rho_wall * cp_wall;
@ -44,7 +44,7 @@ g5 = [2; B(1); C(1); B(2); C(2); 1; 0]; % Outer ceramic
g6 = [2; C(1); H(1); C(2); H(2); 1; 3]; % Top rim: (C-H) ceramic-air
g7 = [2; H(1); F(1); H(2); F(2); 1; 3]; % Inner ceramic wall (H-F) ceramic-air
g8 = [2; F(1); E(1); F(2); E(2); 1; 2]; % Inner ceramic bottom (F-E) ceramic-fluid
g9 = [2; F(1); G(1); F(2); G(2); 2; 3]; % Fluid surface (F-G) fluid-air
g9 = [2; F(1); G(1); F(2); G(2); 2; 3]; % Fluid surface (F-G) fluid - ceramic
g10 = [2; G(1); I(1); G(2); I(2); 2; 3]; % Fluid surface (G-I) fluid-air
g11 = [2; D(1); H(1); D(2); H(2); 3; 0]; % Air top boundary: (D-H) air-outside
@ -55,7 +55,19 @@ geometryFromEdges(model, g);
% figure(1);
% pdegplot(model, 'EdgeLabels','on', 'FaceLabels','on');
% axis equal;
% title('Geometry with edge and face labels');
% hold on;
%
% % Plot points
% Pts = [A; B; C; D; E; F; G; H; I];
% plot(Pts(:,1), Pts(:,2), 'ro', 'MarkerFaceColor','r');
% % Label points
% labels = {'A','B','C','D','E','F','G','H','I'};
% for k = 1:length(labels)
% text(Pts(k,1), Pts(k,2), [' ' labels{k}], ...
% 'FontSize',10, 'Color','r', 'FontWeight','bold');
% end
% title('Geometry with edge, face, and point labels');
% hold off;
% Generate mesh, linear and 3 nodes per element
mesh = generateMesh(model, 'Hmax', 0.002, 'GeometricOrder','linear');
@ -159,7 +171,7 @@ u = K \ F;
%% Task 5: Axisymmetric Laplace + Robin BC
[K, F] = CalculateLaplace_mult_rot(model, lambda_wall, lambda_fluid, lambda_air);
[K, F] = ApplyRobinBC_mult_rot(model, K, F, alpha, u_out);
[K,F] = ApplyRobinBC_mult_rot(model, K, F, alpha, u_out);
% Direct solve
u = K \ F;
@ -178,6 +190,7 @@ M = AddMass_mult_rot(model, M, c_wall, c_fluid, c_air);
%% Task 7: Initial solution
u0 = Init_Solution_mult(model, 18, 80, 18);
% TRY WITH HOTTER LIQUID
% figure(7)
% pdeplot(model, 'XYData', u0, 'Mesh','on');
@ -186,8 +199,8 @@ u0 = Init_Solution_mult(model, 18, 80, 18);
% colorbar
%% Task 8: Time-dependent simulation (explicit scheme)
tau = 0.5; % time step in seconds
T_end = 400; % total simulation time (seconds)
tau = 1; % time step in seconds
T_end = 1000; % total simulation time (seconds)
Nt = ceil(T_end/tau); % number of time steps
A = (1/tau)*M+K; % Left-hand side matrix
@ -209,15 +222,25 @@ for k = 1:Nt
end
%To see the 9 snapshots paste here the codes in "AdditionalPlotCodes.txt"
M = sparse(Nnodes, Nnodes);
M = AddMass_mult_rot(model, M, c_wall, c_fluid, c_air);
%% Task 9 (i): Heating time using inner ceramic wall temperature
T_target = 67; % [°C]
[K, F] = CalculateLaplace_mult_rot(model, lambda_wall, lambda_fluid, lambda_air);
[K, F] = ApplyRobinBC_mult_rot(model, K, F, alpha, u_out);
tau = 0.1; % time step in seconds
T_end = 1000; % total simulation time (seconds)
Nt = ceil(T_end/tau); % number of time steps
[K,F] = CalculateLaplace_mult_rot(model, lambda_wall, lambda_fluid, lambda_air);
[K,F] = ApplyRobinBC_mult_rot(model, K, F, alpha, u_out);
A = (1/tau)*M+K; % Left-hand side matrix
innerWallNodes = findNodes(model.Mesh,'region','Edge',8); % Edge 8 = ceramic–fluid interface
u = u0;
innerWallNodes = unique([findNodes(model.Mesh,'region','Edge',8), findNodes(model.Mesh,'region','Edge',9)]);
%innerWallNodes = findNodes(model.Mesh,'region','Edge',9);
u= u0;
% Storage
timeVec = (0:Nt-1)' * tau;
@ -226,14 +249,13 @@ Twarm = NaN;
for k = 1:Nt
b = (1/tau)*M*u + F;
u = A\b;
% Average inner wall temperature
innerWallTemp(k) = mean(u(innerWallNodes));
%innerWallTemp(k) = max(u(innerWallNodes));
% Check heating criterion
if innerWallTemp(k) >= T_target
if innerWallTemp(k) >= T_target
Twarm = k * tau;
fprintf('Task 9 (i): Inner wall reaches %.1f°C at T = %.1f s\n', ...
T_target, Twarm);
@ -241,14 +263,14 @@ for k = 1:Nt
end
end
% figure(9)
% plot(timeVec(1:k), innerWallTemp(1:k), 'LineWidth', 2)
% hold on
% yline(T_target,'r--','67°C','LineWidth',1.5)
% xlabel('Time [s]')
% ylabel('Average inner wall temperature [°C]')
% title('Heating of the inner ceramic wall')
% grid on
figure(9)
plot(timeVec(1:k), innerWallTemp(1:k), 'LineWidth', 2)
hold on
yline(T_target,'r--','67°C','LineWidth',1.5)
xlabel('Time [s]')
ylabel('Average inner wall temperature [°C]')
title('Heating of the inner ceramic wall')
grid on
%% CHECK: Insulated mug – transient redistribution
[K_neu, F_neu] = CalculateLaplace_mult_rot(model,lambda_wall,lambda_fluid,lambda_air);
@ -258,7 +280,7 @@ M_neu = AddMass_mult_rot(model,M_neu,c_wall,c_fluid,c_air);
% Time stepping parameters
tau = 0.5;
T_end = 400;
T_end = 100;
Nt = ceil(T_end / tau);
A_neu = (1/tau) * M_neu + K_neu;