% Input Parameters - Basic Radiator Dimensions radiator_length = 290; % radiator length (mm) radiator_height = 170; % radiator height (mm) radiator_width = 24; % radiator width (mm) tube_width = 24; % tube width (mm) tube_height = 1.5; % tube height(mm) fin_length = 4.7; % fin length (mm) fin_width = 24; % fin width (mm) fin_height = 0.5; % fin height (mm) N_tube = 25; % Number of Tubes N_fin = 7540; % Number of Fins % Input Parameters - Properties of Water at Average Temperature water_density = 982.2; % kg/m^3 water_specific_heat = 4185; % J/kg*K water_prandtl = 5.26; water_k = 0.59; % water thermal conductivity (W/mK) water_viscosity = 7.61E-04; % water viscosity (kg/m^2) % Input Parameters - Properties of Air at Average Temperature air_density = 1.16; % kg/m^3 air_specific_heat = 1007; % J/kg*K air_prandtl = 0.74; air_k = 2.50E-02; % air thermal conductivity air_kinematic_viscosity = 2.20E-05; % m^2/s % Input Parameters Nusselt_water = 3.93; % Nusselt number of fully developed water in rectangular tube k_aluminum = 237; % Thermal conductivity of aluminum (W/mK) T_water_in = 60; % Inlet water temperature (C) T_air_in = 25; % Inlet air temperature (C) % Define a range of air and water volumetric flow rates Q_air_range_CFM = linspace(500, 2000, 50); % Air flowrate range in CFM Q_water_range_LPM = linspace(5, 16, 50); % Water flowrate range in LPM % Convert units to SI (m^3/s) Q_air_range = Q_air_range_CFM * 0.000471947; % Conversion: 1 CFM = 0.000471947 m^3/s Q_water_range = Q_water_range_LPM * 1e-3 / 60; % Conversion: 1 LPM = 1e-3 m^3/min = 1e-3/60 m^3/s % Create a meshgrid of air and water flowrates [Q_air, Q_water] = meshgrid(Q_air_range, Q_water_range); % Calculate dependent variables for each flowrate combination % Internal Flow of Water A_tube = tube_width * tube_height * 10^-6; % Cross-sectional area of tube (m^2) P_tube = (2 * tube_width + 2 * tube_height) * 10^-3; % Perimeter of tube (m) hydraulic_diameter = 4 * A_tube / P_tube; % Hydraulic diameter (m) v_water = Q_water ./ (N_tube * A_tube); % Water velocity (m/s) Reynolds_water = water_density .* v_water .* hydraulic_diameter / water_viscosity; % Reynolds number of water h_water = Nusselt_water * water_k / hydraulic_diameter; % Convective heat transfer coefficient of water (W/m^2K) % External Flow of Air A_radiator = radiator_length * radiator_height * 10^-6; % Total radiator area (m^2) v_air = Q_air ./ (A_radiator - (N_tube * tube_height * radiator_length * 10^-6)); % Air velocity (m/s) Reynolds_air = v_air .* (fin_width * 10^-3) / air_kinematic_viscosity; % Reynolds number of air Nusselt_air = 0.664 * Reynolds_air.^(1/2) .* air_prandtl.^(1/2); % Nusselt number of air h_air = Nusselt_air .* air_k ./ (tube_width * 10^-3); % Convective heat transfer coefficient of air (W/m^2K) % Fin Dimension and Efficiency m = sqrt(2 * h_air ./ (k_aluminum * fin_height * 10^-3)); % Coefficient for fin efficiency (1/m) L_c = (fin_length + fin_height / 2) * 10^-3; % Corrected fin length (m) fin_efficiency = tanh(m .* L_c) ./ (m .* L_c); % Fin efficiency A_f = 2 * fin_width * L_c * 10^-3; % Single fin surface area (m^2) A_b = (2 * radiator_length * tube_width - fin_height * fin_width * N_fin) * 10^-6; % Base surface area (m^2) A_fin_base = N_fin * A_f + A_b; % Total fin/base surface area of a single tube (m^2) overall_efficiency = 1 - N_fin * A_f ./ A_fin_base .* (1 - fin_efficiency); % Overall efficiency A_external = A_fin_base * N_tube; % Total external surface area (m^2) A_internal = ((2 * tube_width + 2 * tube_height) * radiator_length * N_tube) * 10^-6; % Total internal surface area (m^2) % Mass flow rates m_air = Q_air * air_density; % Air mass flow rate (kg/s) m_water = Q_water * water_density; % Water mass flow rate (kg/s) % Heat capacities C_air = m_air * air_specific_heat; % Total air heat capacity (J/K) C_water = m_water * water_specific_heat; % Total water heat capacity (J/K) C_min = min(C_air, C_water); % Minimum heat capacity (J/K) C_max = max(C_air, C_water); % Maximum heat capacity (J/K) C_r = C_min ./ C_max; % Heat capacity ratio % Overall Heat Transfer Coefficient UA = 1 ./ (1 ./ (overall_efficiency .* h_air .* A_external) + 1 ./ (h_water .* A_internal)); % (M^2kg/Ks^3) % Number of Transfer Units and Effectiveness NTU = UA ./ C_min; % Number of Transfer Units effectiveness = 1 - exp((NTU.^0.22 ./ C_r) .* (exp(-C_r .* NTU.^0.78) - 1)); % Effectiveness % Heat Transfer Rates q_max = C_min .* (T_water_in - T_air_in); % Maximum heat transfer rate (W) q_predicted = effectiveness .* q_max; % Predicted heat transfer rate (W) % Plot the results figure; % subplot(1,2,1) contour(Q_air_range_CFM, Q_water_range_LPM, round(q_predicted),20,"ShowText","off ", "LabelFormat","%.0f"); % 20 contour levels xlabel('Air Flowrate (CFM)'); ylabel('Water Flowrate (LPM)'); zlabel('Predicted Heat Transfer (W)'); title('Heat Transfer (W) as a Function of Air and Water Flowrates'); subtitle(['Ambient Temperature = ',int2str(T_air_in),'°C']) colorbar; % subplot(1,2,2); contour(Q_air_range_CFM, Q_water_range_LPM, effectiveness, 20,"ShowText","off ","LabelFormat","%.1f"); % 20 contour levels xlabel('Air Flowrate (CFM)'); ylabel('Water Flowrate (LPM)'); zlabel('effectiveness'); title('Effectiveness as a Function of Air and Water Flowrates'); subtitle(['Ambient Temperature = ',int2str(T_air_in),'°C']) colorbar; grid on; % --- Print Input Parameters with Name and Units --- fprintf('Input Parameters:\n\n'); % Basic Radiator Dimensions fprintf('Radiator Length: %.2f mm\n', radiator_length); fprintf('Radiator Height: %.2f mm\n', radiator_height); fprintf('Radiator Width: %.3f mm\n', radiator_width); fprintf('Tube Width: %.1f mm\n', tube_width); fprintf('Tube Height: %.4f mm\n', tube_height); fprintf('Fin Length: %.4f mm\n', fin_length); fprintf('Fin Width: %.2f mm\n', fin_width); fprintf('Fin Height: %.4f mm\n', fin_height); fprintf('Number of Tubes: %d\n', N_tube); fprintf('Number of Fins: %d\n', N_fin); fprintf('\n'); % Properties of Water at Average Temperature fprintf('Water Density: %.1f kg/m^3\n', water_density); fprintf('Water Specific Heat: %.0f J/kg*K\n', water_specific_heat); fprintf('Water Prandtl Number: %.2f\n', water_prandtl); fprintf('Water Thermal Conductivity: %.2f W/mK\n', water_k); fprintf('Water Viscosity: %.6f kg/m^2\n', water_viscosity); fprintf('\n'); % Properties of Air at Average Temperature fprintf('Air Density: %.2f kg/m^3\n', air_density); fprintf('Air Specific Heat: %.0f J/kg*K\n', air_specific_heat); fprintf('Air Prandtl Number: %.2f\n', air_prandtl); fprintf('Air Thermal Conductivity: %.3f W/mK\n', air_k); fprintf('Air Kinematic Viscosity: %.6e m^2/s\n', air_kinematic_viscosity); fprintf('\n'); % Additional Parameters fprintf('Nusselt Number (Water): %.2f\n', Nusselt_water); fprintf('Thermal Conductivity of Aluminum: %.2f W/mK\n', k_aluminum); fprintf('Inlet Water Temperature: %.1f °C\n', T_water_in); fprintf('Inlet Air Temperature: %.1f °C\n', T_air_in); fprintf('\n'); % Flow Rate Ranges fprintf('Air Flowrate Range: %.3f to %.3f CFM\n', Q_air_range_CFM(1), Q_air_range_CFM(end)); fprintf('Water Flowrate Range: %.3f to %.3f LPM\n', Q_water_range_LPM(1), Q_water_range_LPM(end));