a=2;
b=1;
bb[n_]=(-1)^(Floor[n/2])(1-(-1)^n)^2 a/(n^2 Pi^2);
CC[n_]=bb[n]/Sinh[n Pi b/a];

u[x_,y_]=Sum[CC[n] Sinh[n Pi y/a] Sin[n Pi x/a],{n,1,100}];

Manipulate[Plot[u[x,y],{x,0,a},PlotRange->{0,1}],{y,0,b}];

ParametricPlot3D[{x,y,u[x,y]},{x,0,a},{y,0,b}];

a=2;
b=1;
bb[n_]=1/n^2;
CC[n_]=bb[n]/Sinh[n Pi b/a];

u2[x_,y_]=Sum[CC[n] Sinh[n Pi y/a] Sin[n Pi x/a],{n,1,50}];

Manipulate[Plot[u2[x,y],{x,0,a},PlotRange->{0,1.1}],{y,0,b}];

ParametricPlot3D[{x,y,u2[x,y]},{x,0,a},{y,0,b}];