The porous media approach is being adapted to a system of nanoparticles that are attached to a solid surface (a metal wire) embedded into a stagnant fluid, forming by design nanofins around the wire. The analyzed system resembles the Transient Hot Wire experimental method used in evaluating the thermal conductivity of a fluid or nanofluid suspensions. Since the attachment of the nanoparticles to the wire is done by design (as distinct from uncontrolled agglomeration around the wire), one major objective in such a design is attempting to enhance the heat transfer from the wire. The latter objective is analyzed via a short times approximation of the solution. Preliminary results based on the leading order solution shows that such a heat transfer enhancement is indeed possible and presents major advantages compared to commonly used macro-fins.