Forced Convection Heat Transfer From a Particle at Small and Large Peclet Numbers

Abstract

We theoretically study forced convection heat transfer from a single particle in uniform laminar flows. Asymptotic limits of small and large Peclet numbers Pe are considered. For Pe≪1 (diffusion-dominated regime) and a constant heat flux boundary condition on the surface of the particle, we derive a closed-form expression for the heat transfer coefficient that is valid for arbitrary particle shapes and Reynolds numbers, as long as the flow is incompressible. Remarkably, our formula for the average Nusselt number Nu has an identical form to the one obtained by Brenner for a uniform temperature boundary condition (Chem. Eng. Sci., vol. 18, 1963, pp. 109–122). We also present a framework for calculating the average Nu of axisymmetric and two-dimensional (2D) objects with a constant heat flux surface condition in the limits of Pe≫1 and small or moderate Reynolds numbers. Specific results are presented for the heat transfer from spheroidal particles in Stokes flow.

Mass transfer from small spheroids suspended in a turbulent fluid

“…Here, the Péclet number is suitably redefined in terms of some characteristic strain rate E of the steady flow problem. Depending upon the particle geometry and relative flow field, various asymptotic expressions are available for the coefficient α and subsequent corrections (Acrivos & Taylor 1962;Acrivos & Goddard 1965;Sehlin 1969;Gupalo, Polianin & Riazantsev 1976;Poe & Acrivos 1976;Batchelor 1979;Acrivos 1980;Myerson 2002;Dehdashti & Masoud 2020;Lawson 2021). This is supplemented by a wealth of experimental and numerical data at finite Reynolds and Péclet numbers (Clift et al 1978;Sparrow, Abraham & Tong 2004;Kishore & Gu 2011;Ke et al 2018;Ma & Zhao 2020).…”

Mass transfer to freely suspended particles at high Péclet number

“…The shape dependence for spheroids in axisymmetric strain may be contrasted to the shape dependence observed for axisymmetric, uniform flow around a fixed spheroid shown in figure 3 (Acrivos & Taylor 1962;Sehlin 1969;Dehdashti & Masoud 2020). Here, the surface flux exhibits the same scaling Sh = α U Pe…”

“…A general solution to this problem would have great utility, because solid particles are often neither spherical nor subject to motions as simple as uniform or axisymmetric flows (Leal 2012). Specific analytical results are available for spheres in uniform flow (Acrivos 1960;Acrivos & Taylor 1962) or arbitrary linear shear (Gupalo & Riazantsev 1972;Poe & Acrivos 1976;Batchelor 1979) and axisymmetric bodies in uniform flow (Sehlin 1969;Gupalo et al 1976;Leal 2012;Dehdashti & Masoud 2020). To our knowledge, equivalent results are not available for arbitrary bodies with high Péclet numbers in an arbitrary linear shear.…”

Mass transfer to freely suspended particles at high Péclet number

“…The shape dependence for spheroids in axisymmetric strain may be contrasted to the shape dependence observed for axisymmetric, uniform flow around a fixed spheroid shown in figure 3 (Acrivos & Taylor 1962; Sehlin 1969; Dehdashti & Masoud 2020). Here, the surface flux exhibits the same scaling , where and is the magnitude of the relative velocity (slip velocity) between the free stream and particle.…”

“…A general solution to this problem would have great utility, because solid particles are often neither spherical nor subject to motions as simple as uniform or axisymmetric flows (Leal 2012). Specific analytical results are available for spheres in uniform flow (Acrivos 1960; Acrivos & Taylor 1962) or arbitrary linear shear (Gupalo & Riazantsev 1972; Poe & Acrivos 1976; Batchelor 1979) and axisymmetric bodies in uniform flow (Sehlin 1969; Gupalo, Polianin & Riazantsev 1976; Leal 2012; Dehdashti & Masoud 2020). To our knowledge, equivalent results are not available for arbitrary bodies with high Péclet numbers in an arbitrary linear shear.…”