Nanomatemàtiques: modelització matemàtica a la nanoescala

Abstract

In this paper we discuss three problems recently studied within the Industrial Maths Research Group at the Centre de Recerca Matemàtica, where continuum theory may be applied to describe nanoscale phenomena: 1. Heat transfer with nanofluids: Experimental results concerning the remarkable heat transfer characteristics of nanofluids are at times contradictory. We apply a boundary layer analysis to show that a standard model which has been used by many authors to predict an improvement in heat transfer with increasing nanoparticle concentration in fact shows a decrease. 2. Nanoparticle melting: Nanoparticles often exhibit a sharp increase in melting rate as the size decreases. A mathematical model will be presented which predicts this phenomena and explains the experimentally observed abrupt melting of the smallest nanoparticles. 3. Enhanced flow in carbon nanotubes (CNTs): This model shows that the experimentally observed enhancement can be explained using standard flow equations but with a depletion layer between the liquid and solid interfaces. The results also provide one physical explanation for the Navierslip condition.