Heat transfer from a particle in laminar flows of a variable thermal conductivity fluid

We revisit the classical problem of steady-state heat transfer from a single particle in a uniform laminar flow with the assumption that the thermal conductivity of the fluid changes linearly with the temperature. We use a combination of asymptotic and scaling analyses to derive approximate expressions for the dimensionless heat transfer coefficient, i.e., the Nusselt number Nu, of arbitrarily shaped particles. The results cover the entire range of the Peclet number Pe. We find that, for a constant temperature boundary condition and fixed geometry, the Nusselt number is essentially equal to the product of two terms, one of which is only a function of Pe while the other one is nearly independent of Pe and mainly depends on the proportionality constant of the conductivity-temperature relation. We also show that, in contrast, when a uniform heat flux is imposed on the surface of the particle, Nu can be estimated as a summation of a Pe-dependent piece and one that solely varies with the proportionality constant. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This study revisits the classical problem of steady-state heat transfer from a single particle in a uniform laminar flow, assuming the thermal conductivity of the fluid changes linearly with temperature. Through a combination of asymptotic and scaling analyses, approximate expressions for the dimensionless heat transfer coefficient Nu of arbitrarily shaped particles are derived, covering the entire range of the Peclet number Pe. The results show that Nu can be decomposed into two parts under constant temperature boundary conditions, one related to Pe and the other mainly dependent on the proportionality constant of the conductivity-temperature relation; while under a uniform heat flux, Nu can be decomposed into a Pe-dependent part and a part solely varying with the proportionality constant.