%% Housekeeping clear; close all; clc; format short %% Given Data: del_T = 10; Phi = linspace(0,1); % Volume fraction of metal Phif = 0.75; % Volume fraction of fields metal k_f = 18.75; % Thermal conductivity of fields metal in W/mK h_f = 25400; % Latent Heat of fields matal in J/kg rho_f = 7880; % Density of fields metal in Kg/m^3 cp_f = 325; % Specific heat capacity of fields metal in J/KgK Cp_f = cp_f*rho_f; % Specific heat capacity of fields metal in J/kgK H_f = h_f*rho_f; % Latent heat of fields metal in J/m^3 k_p = 0.2; % Thermal conductivity of paraffin in W/mK h_p = 243500; % Latent Heat of paraffin in J/kg rho_p = 774; % Density of paraffin in Kg/m^3 cp_p = 2160; % Specific heat capacity of paraffin in J/KgK Cp_p = cp_p*rho_p; % Specific heat capacity of paraffin in J/kgK H_p = h_p*rho_p; % Latent heat of paraffin in J/m^3 k_Cu = 385; % Thermal conductivity of copper in W/mK rho_Cu = 8960; % Density of copper in Kg/m^3 cp_Cu= 390; % Specific heat capacity of copper in J/KgK Cp_Cu = cp_Cu*rho_Cu; % Specific heat capacity of copper in J/m^3K k_Al = 205; % Thermal conductivity of Aluminum in W/mK rho_Al = 2700; % Density of Aluminum in kg/m^3 cp_Al = 900; % Specific heat capacity of Aluminum in J/kgK Cp_Al = cp_Al*rho_Al; % Specific heat capacity of Aluminum in J/m^3K k_GCF = 600; % Thermal conductivity of copper in W/mK rho_GCF = 2266; % Density of copper in Kg/m^3 cp_GCF = 720; % Specific heat capacity of GCF in J/kgK Cp_GCF = cp_GCF*rho_GCF; % Specific heat capacity of GCF in J/m^3K h_pcm = h_f.*Phif + (h_p.*(1-Phif)); % Effective Latent heat of pcm in J/kg cp_pcm = cp_f.*Phif + (cp_p.*(1-Phif)); % Effective Specific heat capacity of pcm in J/kgK rho_pcm = rho_f.*Phif + (rho_p.*(1-Phif)); % Effective density of pcm in Kg/m^3 H_pcm = h_pcm.*rho_pcm; % Effective Latent heat of pcm in J/m^3 Cp_pcm = cp_pcm.*rho_pcm; % Effective Specific heat capacity of pcm in J/m^3K %% Setting up: % Thermal conductivity: k1 = k_f.*Phif + (k_p.*(1-Phif)); % Effective Thermal conductivity of pcm in W/mK k2 = k_Cu.*Phi + (k1.*(1-Phi)); % Effective Thermal conductivity of Cu+pcm(k1) W/mK k3 = k_Cu.*Phi + (k_p.*(1-Phi)); % Effective Thermal conductivity of Cu+paraffin W/mK k4 = k_Al.*Phi + (k_p.*(1-Phi)); % Effective Thermal conductivity of Al+paraffin in W/mK k5 = k_GCF.*Phi + (k_p.*(1-Phi)); % Effective Thermal conductivity of GCF+paraffin in W/mK k6 = k_GCF.*Phi + (k1.*(1-Phi)); % Effective Thermal conductivity of GCF+pcm in W/mK k7 = k_Al.*Phi + (k1.*(1-Phi)); % Effective Thermal conductivity of Al+pcm in W/mK % Energy density: E_eff_1 = Phi*0 + ((H_pcm + (Cp_pcm*del_T)))*0.000001; % Effective Energy density of pcm in J/cm^3 E_eff_2 = ((((Cp_Cu*del_T)).*Phi) + ((H_pcm + (Cp_pcm*del_T)).*(1-Phi)))*0.000001; % Effective Energy density of Cu+pcm in J/cm^3 E_eff_3 = ((((Cp_Cu*del_T)).*Phi) + ((H_p + (Cp_p*del_T)).*(1-Phi)))*0.000001; % Effective Energy density of Cu+paraffin in J/cm^3 E_eff_4 = ((((Cp_Al*del_T)).*Phi) + ((H_p + (Cp_p*del_T)).*(1-Phi)))*0.000001; % Effective Energy density of Al+paraffin in J/cm^3 E_eff_5 = ((((Cp_GCF*del_T)).*Phi) + ((H_p + (Cp_p*del_T)).*(1-Phi)))*0.000001; % Effective Energy density of GCF+paraffin in J/cm^3 E_eff_6 = ((((Cp_GCF*del_T)).*Phi) + ((H_pcm + (Cp_pcm*del_T)).*(1-Phi)))*0.000001; % Effective Energy density of GCF+pcm in J/cm^3 E_eff_7 = ((((Cp_Al*del_T)).*Phi) + ((H_pcm + (Cp_pcm*del_T)).*(1-Phi)))*0.000001; % Effective Energy density of Al+pcm in J/cm^3 X1 = times(k1,E_eff_1/0.000001); X2 = times(k2,E_eff_2/0.000001); X3 = times(k3,E_eff_3/0.000001); X4 = times(k4,E_eff_4/0.000001); X5 = times(k5,E_eff_5/0.000001); X6 = times(k6,E_eff_6/0.000001); X7 = times(k7,E_eff_7/0.000001); Eta_eff1 = sqrt(X1); % Figure of merit of pcm in (Wsec^0.5)/Km^2 Eta_eff2 = sqrt(X2); % Figure of merit of Cu+pcm in (Wsec^0.5)/Km^2 Eta_eff3 = sqrt(X3); % Figure of merit of Cu+paraffin in (Wsec^0.5)/Km^2 Eta_eff4 = sqrt(X4); % Figure of merit of Al+paraffin in (Wsec^0.5)/Km^2 Eta_eff5 = sqrt(X5); % Figure of merit of GCF+paraffin in (Wsec^0.5)/Km^2 Eta_eff6 = sqrt(X6); % Figure of merit of GCF+pcm in (Wsec^0.5)/Km^2 Eta_eff7 = sqrt(X7); % Figure of merit of Al+pcm in (Wsec^0.5)/Km^2 %% Plot colors = [60/255 133/255 244/255; 225/255 68/255 55/255; 244/255 160/255 0; 15/255 157/255 88/255; 144/255 103/255 167/255; 128/255 133/255 133/255]; set(0, 'DefaultLineLineWidth', 1); set(groot, 'defaultAxesColorOrder', colors); figure(1); clf; grid on; y = [Eta_eff2; Eta_eff3; Eta_eff4; Eta_eff5; Eta_eff6; Eta_eff7]; x = [E_eff_2; E_eff_3; E_eff_4; E_eff_5; E_eff_6; E_eff_7]; loglog(x(1,:),y(1,:),'*-') hold on; loglog(x(2,:),y(2,:)) hold on loglog(x(3,:),y(3,:)) hold on loglog(x(4,:),y(4,:)) hold on loglog(x(5,:),y(5,:),'o-') hold on loglog(x(6,:),y(6,:),'s-') ylabel('FoM [ Wsec^(0.5)/Km^2]'); xlabel('Effective energy density [J/cm^3]'); xlim([10 1000]) ylim([1000 1000000]) title('Volume fraction of FM = 0.75') ltag = {'Cu+FM+P','Cu+P','Al+P','GCF+P','GCF+FM+P','Al+FM+P'}; legend(ltag,'Location','Southeast'); hold off;