If the fluid is heated only at one point or small region, or a small tube is introduced which supplies a source of additional fluid at one point, the fluid there will expand, pushing fluid particles around it outward in all directions. This will cause an outward velocity field throughout the fluid, centered on the heated point. Any closed surface enclosing the heated point will have a flux of fluid particles passing out of it, so there is positive divergence at that point. However any closed surface "not" enclosing the point will have a constant density of fluid inside, so just as many fluid particles are entering as leaving the volume, thus the net flux out of the volume is zero. Therefore the divergence at any other point is zero.