Prediction of Convective Heat Transfer of Nanofluids Based on Fractal-Monte Carlo Simulations

Abstract

With the consideration of the Brownian motion of nanoparticles in°uids, the probability model for the size of nanoparticles and the model for convective heat transfer of nano°uids are derived based on the fractal character of nanoparticles. The proposed model is expressed as a function of the size of nanoparticles, the volumetric nanoparticle concentration, the thermal conductivity of base°uids, fractal dimension of nanoparticles and the temperature, as well as the random number. It is found that the convective heat°ux of nano°uids decreases with increasing of the average diameter of nanoparticles. This model has the characters of both analytical and numerical solutions. The Monte Carlo simulations combined with the fractal geometry theory are performed. Every parameter of the proposed formula on convective heat transfer of nano°uids has clear physical meaning. So the proposed model can reveal the physical mechanisms of convective heat transfer of nano°uids.

Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation

“…The average diameter ' av λ of the all nanoparticles calculated in the presented Monte Carlo simulations can be written as [90]…”

“…If the converged heat flux from CHTNs is obtained in one run, set the heat flux from CHTNs as ( ) n t q(n= 1, 2, 3,…, Y). Then, the average t q is calculated by[90]…”

Bioconvective Non-Newtonian Nanofluid Transport in Porous Media Containing Micro-Organisms in a Moving Free Stream

“…We will show how linear group transformations combine two independent variables ðx; yÞ into a single independent variable and reduce the boundary value problem of partial differential Eqs. (10)- (14) into the boundary value problem of ordinary differential equations. We scale all independent and dependent variables as follows:…”

“…36,37 We investigate the values of i so that the form of the Eqs. (10)- (14) is invariant under the transformations in (16). Substituting (16) into Eqs.…”

“…Brownian motion of nanoparticles can elevate thermal conduction via a variety of mechanisms, prominent among which are the direct effect owing to nanoparticles that transport heat or the indirect contribution due to micro-convection of fluid surrounding individual nanoparticles. 14,16,17 For small particles, Brownian motion is strong, and the parameter Nb will have high values; the converse is the case for large particles. The coupling of thermal and nanoparticle species fields via the differential conservation equations and indeed via the buoyancy ratio parameter, manifests in a great sensitivity of the nanoparticle mass transfer process to thermal effects and in particular Brownian motion.…”