Dear Nawal El-kahina Khelalfa, to my opinion, there is no any principal peculiarities of modelling of heat transfer in case of objects which you take into a mind. You may use usual approaches and software for this goal. Good luck.

You can use the normal fin equations as far as your case is concerned.Miniaturization has effects on fluid flow studies as it violates continuum assumption but in case of fin heat transfer ,you can use usual procedure

The "traditional heat transfer fin model is limited by the Biot number when this last is very small. 

Good question! When dimensions get smaller, there is a limit as to when the continuum assumptions break down, also for conduction in solids. Normally, one shold be aware when the dimension of the geometry becomes the same order-of-magnitude in size as the fundamental mechanism at hand for heat transport (in this case electron and 'phonon' mean free paths). Fortunately, these dimensions are normally typically in the nano-to-micron size range (unless you are operating at very low cryogenic temperatures). So, if your fin thickness is thicker than, say 10 microns, the continuum approach is sufficient and the standard fin efficiency calculatons may be applied using the standard thermal conductivity of the fin material. If the thickness becomes smaller, the fin material thermal conductivity may need modifications, but the overall approach for fin efficiency calculation is the same.

For the convection part: If the flow channel dimension restricts the free molecular motion of the flowing fluid, the momentum and heat transfer processes are hampered, and the continuum assumption is no longer valid. Typically, this applies for geometries less than 50-100 microns in diameter. 

Not exactly: it is only "simplified" via the assumption that the temperature is the same all over in the considered body. A small Biot number means that the convective effect is small in comparison to the conduction or diffusibility of heat. Basic equations are not eliminated!

As far as I understand, you are interested in the conduction heat transfer along the fin and not the convective heat transfer from the fin to the fluid. The conductive part should not be affected by the reduction in dimensions, as it is the case of convective part. 

Therefore, you should be able to use same models as in macroscopic theory. The only difference occurs at the value of convection heat transfer coefficient, for heat dissipation from fin surface. Here, indeed the decrease in dimensions has an important role, BUT depends of the order of magnitude you are talking about. For fluid flow in meso-scale channels (millimeter-size hydraulic diameter) there is no significant change in value for HT coefficient. For micro-scale channels (down to 100 microns hydraulic diameter), there is a difference, up to 25% decrease in Nusselt number, that is in HT coefficient, respectively. For lower dimensions, you have to decide upon the efficiency of miniaturization in technical applications. If such miniaturization is required beyond 10 microns, then read Erling's comments above.

Good luck.

I have employed heat diffusion equation and thermal radiation on dimensions as small as 100 microns, and it works well after fabrication. I think you can use the same equations for micro scale safely.

Basic design  of fin of small size is as usual. However, Biot number is affected leading to effect on  fin effectiveness and efficiency.