Development of a lumped capacitance model for heat transfer from a nanoparticle suspended in a fluids medium

Abstract

The purpose of this study is to examine the feasibility of using a lumped capacitance approach to model the transient heat transfer behavior from a nanoparticle suspended in a fluid. Since the Cattaneo-Vernotte (CV) constitutive model involves solving using complex numerical procedures a new model is developed in this study that can give a simple closed form solution to heat transfer problems when nanoscale regimes are considered. A nanoscale lumped capacitance model is developed by modifying Cattaneo-Vernotte (CV) constitutive relation. The CV relation, which is a hyperbolic heat equation, is based on the correction made to the assumption of infinite speed of heat propagation proposed in Fourier law. An electrical analogy of the proposed nanoscale lumped capacitance model has been developed and solved using the electrical design software. It is observed that the Vernotte number plays an important role in nanoscale heat transfer problems. Since Vernotte number is very low for common macroscale structure it is neglected in classical lumped capacitance model but it should be included when heat transfer at nanoscale levels is considered because of higher Vernotte numbers. The results of nanoscale model differs significantly with that of classical lumped capacitance model for higher values of Vernotte number and as the Vernotte number approaches zero the nanoscale model returns to the classical lumped capacitance model as expected. The accuracy of this model is still in question and needs to be validated with experimental data and/or by comparison with a computational model employing the CV constitutive relation before drawing any further conclusions on the correctness of the model developed in this study.