experimentally it is noticed that the rate of heat flow does not change in both cases of flow through thin or thick insulator. i urgently need scientific explanation
It would help to have more information. We must be overlooking something. We know from theory that for heat flow in a solid, q = - k∇T where ∇T is the thermal gradient and k is a thermal diffusion coefficient (conductivity) which may be a constant or a tensor, depending on the nature of the material. For a simple one-dimensional experiment, ∇T translates to dT/dx--the temperature difference divided by the thickness.
In some real-world situations, the thermal resistance of a material will have two terms, a surface R value and an internal value. And, if you are dealing with a fluid, as in a double-pane window with a gas between, then "thickness" has an entirely different effect. Convection and radiation become important.
I guess we have to know more about the experiment.
I agree with Ernest Rogers that probably some detail is overlooked. It may be that there is an additional insulating layer between your heat source and your heat sink (bad thermal contact of your heater?). Or there is a thermal leak, and the heat bypasses your measuring devices?
Are you dealing with flat layers or curved walls such as insulation of thin pipes or thin wires? The latter could provide the explanation for your problem.
The rate of heat depends on the thermalconductivity so it does not change when the thickness change. Also, the thickness will affect the amount of heat transfer, the thicker wall, the smaller heat transfer