As far as I can tell, Matlab does exactly what you're telling it to do, but its a bit hard to understand what you're actually trying to achieve. It looks a bit as if you're trying to convolve a temperature signal (q) with some sort of impulse response (g) of your system. If so, g should propbably be normalised such that sum(g) = 1.

Reza,

To solve a temporal superposition problem through a convolution in the spectral domain, you have to convolve the incremental heat flux function f, not the heat flux signal itself.

Using the infinite line source model to get the normalized transfer function g for a field composed of a single borehole, a solution is easily obtained in Matlab with:

ks=2; % Ground thermal conductivity (W/mK)

Cs=2.2e6; % Ground volumetric heat capacity (J/m^3K)

rb=0.04; % Borehole radius (m)

q=[1 10 5 6 8 16 20 13 25 30]; % Heat flux signal (W/m)

t=[3600:3600:10*3600]; % Evaluation time (s)

nt=numel(t);

f=[diff([0 q])]; % Incremental heat flux function f

g=1/(4*pi*ks)*expint(rb^2./(4*ks/Cs*t)); % Normalized transfer function g

a=fft(f,2*nt);

b=fft(g,2*nt);

c=ifft(a.*b);

Tb=c(1:nt) % Temperature along the borehole wall as a function of time.

Cheers

Philippe

Thank you , as you mentioned my problem was in the incremental heat flux function f...with your help i recognized my mistake