Symmetry analysis for film boiling of nanofluids on a vertical plate using a nonlinear approach

Abstract

This paper focuses on developing a self-similar model to be used in modeling of transport processes of heat, momentum and concentration in a nanofluid at its stable film boiling over a vertical surface. Novelty of the model consists in finding self-similar forms of variables and differential equations for a nanofluid via application of the Lie group theory. In the process of finding the self-similar forms, functional dependence of physical properties (viscosity, thermal conductivity and diffusion coefficient) on the nanoparticle concentration and temperature have been taken into account. As a result, novel self-similar functions for flow rate, enthalpy and nanoparticle concentration have been derived. The self-similar model proposed in the paper is universal since it does not involve any specific form of functional dependence of physical properties. The model incorporates also effects of the Brownian and thermophoretic diffusion. Six major non-dimensional parameters have been revealed, which stand for effects of the nanoparticles on heat transfer and fluid flow in the vapor film. They include the Schmidt number Sc; nanoparticle concentration ϕ∞; normalized densities of the nanoparticles rpυ and rpL (being dependent parameters); relative thermal conductivity of the nanoparticles κ and the complex parameter Ja/Pr. The subsequent simulations are based on the numerical solution of momentum, energy and mass transport equations in a self-similar form. It was shown that increased nanoparticle concentration enhances heat transfer.