IHTC.rar_INVERSE HEAT_heat_heat conduction_ihtc_inverse

%SHEDEMO5: The surface temperature on a particle board is computed % using interior measurements. % % datasets % % d29f10MT3B.dat - Temperature measurement 2.9mm below surface % d29f10MT1B.dat - The measured air temperature close to the surface. % (not used, available only for reference) clear,close all,echo on % Set the parameters that correspond to the physical properties of % the problem. T0=50; % The measurements were sampled during test || initial value 857s. L0=0.458e-3;% The distance between the Thermocouple and the surface. L1=12.0e-3; % The thickness of the Particle board. k=6.9; % Thermal conductivity [W/m/K] Rho=4300; % Density [kg/m3] c=600; % Specific heat [W*s/kg/K] % Draw a picture that explain the experimental setup. The details of % the experiment are also summarized. echo off f1=figure; FigurePos=get(f1,'Position'); set(f1,'Name','SHEDEMO5: Experimental setup') a1=axes;set(a1,'Position',[0.1 0.1 0.4 0.8]); set(a1,'Visible','off');axis([0.05,0.4,0.1,0.8]);hold on xpos=[0.1 0.1 0.13 0.15 0.16 0.17 0.18 0.2 0.2 0.19 0.17 0.15 0.13 0.12 0.11 0.10]; ypos=[0.2 0.7 0.71 0.69 0.73 0.71 0.75 0.73 0.19 0.18 0.23 0.19 0.18 0.20 0.17 0.2]; plot(xpos,ypos,'k-');% cross section of the board xpos=[0.2 0.13 0.13 0.2]; ypos=[0.5 0.5 0.45 0.45]; plot(xpos,ypos,'k-'); plot([0.13],[0.475],'r.','MarkerSize',20) xpos=[0.14 0.22]; ypos=[0.475 0.49]; plot(xpos,ypos,'m-');text([0.225], [0.49],'G_m(t)','FontSize',14) plot([0.1],[0.475],'b.','MarkerSize',20) xpos=[0.09 0.05];ypos=[0.475 0.485]; plot(xpos,ypos,'m-');text([0.03], [0.505],'F(t)','FontSize',14) hSize=FigurePos(3);vSize=FigurePos(4); EditPos=[0.4*hSize,0.05*vSize,(0.95-0.4)*hSize,0.9*vSize]; u1=uicontrol('Style','Text','Position',EditPos); set(u1,'BackgroundColor',[0.95 0.95 0.95]); set(u1,'HorizontalAlignment','Left');set(u1,'Max',1000,'FontSize',12); str='SHEDEMO5: The temperature history inside a particle board is'; str=strcat(str,' measured by a thermocouple. From these measurements'); str=strcat(str,' we attempt to compute the temperatute history at the'); str=strcat(str,' surface of the board. In the sketch the red dot'); str1=strcat(str,' correspond to the thermocouple.'); str='EXPERIMENTAL DETAILS: A particle board, initially heated to 70'; str=strcat(str,' degrees, was suddenly placed to cool in air of room'); str=strcat(str,' temperature. The thermocouple, located 2.9 mm from'); str=strcat(str,' the surface of the board, recorded the temperature'); str=strcat(str,' history in the interior of the particle board.'); str2=strcat(str,' The measurements were conducted during 14.3 minutes.'); str3='REFERENCES:'; str='L. Elden, F. Berntsson, and T. Reginska. Wavelet and Fourier'; str=strcat(str,' methods for solving the sideways heat equation.'); str4=strcat(str,' SIAM J. Sci. Comput., 21(6):2187-2205.'); %uitext(u1,str1,'-',str2,'-',str3,str4); input('Press return>>');echo on % Load the measured temperature data, i.e. the function T(L0,t)=G_m. G = dlmread('Channel-4.txt'); G0= dlmread('Channel-8.txt'); % The initial temperature is supposed to be equal to zero. (in the % numerical model) T_INIT=mean(G(1:20)); G=G-T_INIT*ones(size(G)); N=length(G); % First we assume that the temperature in the particle board is symmetric % with respect to the center. This allows us to compute the heat flux as % a function of time at the location of the thermocouple. For this particular % experiment this assumption should be very good. This is a well-posed % problem. kappa=k*T0/c/Rho/(L1-2*L0)^2; [tmp1,tmp2,H]=crnhs(N,24,kappa,G,G); for i = 1:N if(H(i) > 1.0) H(i) = -20.0; end end %H=H*L0/(L1-2*L0); %H= (G-G0)/0.2; % Now we use the Cauchy data [G,H] and compute the temperature and % heat-flux at the surface of the particle board. The solution is % not very sensitive with respect to the choice of the cut off % frequency xi_c. It should be instructive to experiment a bit with % different values for this parameter. tol=1e-5; xi_c=200; kappa=k*T0/c/Rho/(L0*L0); [uu,xx]=ifftrk45(H,G,kappa,xi_c,tol); F=uu(length(uu(:,1)),:); % Present the computational results. First we restore the original % temperature scale. The blue curve illustrate the measured data % and the red curve correspond to the computed surface temperature. F=F+T_INIT*ones(size(F));G=G+T_INIT*ones(size(G)); f2=figure('Name','SHEDEMO5: Computational results'); tt=T0*(0:N-1)/(N-1); plot(tt,F,'r-',tt,G,'b-'); xlabel('Time [s]','FontSize',14); ylabel('Temperature [ ^oC]','FontSize',14); set(gca,'Fontsize',14); grid on; echo off input('Press return>>');echo on echo off