The Research and Impact of the Works by Don Nield

The problem

Heat and dissolved substances move through porous materials in many engineered systems, including heat exchangers and filters. Don Nield, a mathematician in the Department of Engineering Science at the University of Auckland, spent more than 50 years developing theory for these flows. His main subject was convection, the flow that develops when differences in density make warm or light fluid rise, and the conditions under which that flow begins. His book with Adrian Bejan, Convection in Porous Media, has introduced many researchers to the fundamentals of heat and mass transfer in porous media (Nield and Bejan, 1992, 2017). Engineers also refer to it in the design and analysis of systems involving porous media.

This paper is a commemoration of his work. Our goal was to summarise his main contributions and to report citation counts, publication numbers and collaborations as measures of his influence.

What we did

We reviewed the works by Don Nield indexed in Scopus, a database of publications and the citations between them. We grouped the works by year of publication. For each year we totalled the citations to date of the works published in that year. We did this for all his works, for his single-author works, and for his works with Andrey Kuznetsov, who worked in Raleigh, North Carolina (Figs 1 to 3 of the paper). Table 1 of the paper lists the number of works and total citations for each of his 26 collaborators.

One of us (Sid Becker) was a research student of Andrey Kuznetsov from 2002 to 2007. We include his account of how that collaboration operated.

What we found

Don Nield published more than 270 works. Table 1 counts 249 indexed in Scopus, with 22,480 citations. Thirty-five of his works have each been cited more than 100 times, and 20 of these more than 200 times. His most cited work has nearly 7,000 citations. More than 190 of his works concern flow in porous media, and more than 160 of those concern convective heat transfer. About a third concern stability analysis and the onset of convection. Stability analysis determines whether a small disturbance to a steady flow, or to a fluid at rest, grows or decays.

His 70 single-author works have 3,921 citations. Among his earliest papers, his 1964 paper on surface tension and buoyancy in cellular convection has been cited more than 500 times (Nield, 1964). His 1968 paper on the onset of thermohaline convection in a porous medium has been cited more than 550 times (Nield, 1968b). Thermohaline convection is driven by gradients in both temperature and salt concentration. He also examined common modelling choices critically, including where the Brinkman–Forchheimer equation for flow in a porous medium applies (Nield, 1991c).

Don was a mathematician. He published results from computer models of heat and mass transfer only with collaborators.

Nield and Kuznetsov modelled convection in nanofluids, fluids that contain a suspension of nanoparticles. Their models included Brownian motion and thermophoresis, two ways that nanoparticles move relative to the fluid. They showed that oscillatory instability, in which a disturbance grows while oscillating, can occur when the nanoparticles are concentrated towards the bottom of a layer (Nield and Kuznetsov, 2006c, 2009a, 2010c, 2010f, 2011c, 2013c, 2014b, 2014d, 2015b, 2016b; Kuznetsov and Nield, 2010f; Nield et al., 2015). In the same papers they showed that the particles affect the flow mainly through buoyancy, the upward or downward force that arises from differences in density, and less through how heat is carried. They also showed that oscillatory convection can be suppressed by changing what the model assumes about nanoparticles crossing the top and bottom of the layer (the boundary condition on nanoparticle flux).

In nanofluid-saturated porous media, Kuznetsov and Nield found that local thermal non-equilibrium, a temperature difference between the fluid and the solid, is significant in some cases but generally minimal for typical dilute nanofluids (Kuznetsov and Nield, 2011a).

Don's first joint work with Kuznetsov appeared in 1999. The collaboration produced 128 Scopus-indexed works with 8,979 citations (Table 1). By our arithmetic, that is about half of his 249 indexed works. Their output was highest in 2010, with 16 publications. Kuznetsov and Nield's 2010 paper on natural convection of a nanofluid past a vertical plate has been cited 1,387 times (Kuznetsov and Nield, 2010c).

Don worked in Auckland and Andrey in Raleigh, more than 12 hours apart. When Don stopped work, he sent his updates to Andrey, whose day was beginning. In Sid's words, for years their work "went on around the clock".

His 4 Scopus-indexed works with Adrian Bejan have 8,056 citations (Table 1). Convection in Porous Media appeared in five editions between 1992 and 2017, and the fourth edition alone has been cited more than 6,900 times. Later editions added topics, including heat transfer in nanofluids and local thermal non-equilibrium.

Limitations

We note in the paper that his impact cannot be fully quantified. Citation counts and publication numbers are only partial measures of it. In two places the text of the paper gives higher citation counts than Table 1, for the Bejan books and for the Kuznetsov collaboration. This explainer and the chart use the Table 1 values. All of the counts are citations to date. They also cover only the 249 works indexed in Scopus, out of more than 270 in total.

Glossary

Porous medium: a solid with connected pore spaces through which a fluid can flow.

Convection: fluid flow driven by differences in density, for example warm fluid rising above cooler fluid.

Onset of convection: the conditions at which a fluid at rest first begins to convect.

Stability analysis: a calculation of whether a small disturbance to a steady flow or a fluid at rest grows or decays.

Thermohaline (double-diffusive) convection: convection driven by gradients in both temperature and dissolved solute concentration.

Nanofluid: a fluid carrying a suspension of particles with sizes measured in nanometres (billionths of a metre).

Brownian motion: the random movement of small particles caused by collisions with the molecules of the surrounding fluid.

Thermophoresis: the drift of particles in a fluid driven by a temperature gradient.

Buoyancy: the upward or downward force on a parcel of fluid that is lighter or heavier than the fluid around it.

Oscillatory instability: an instability in which the disturbance grows while oscillating in time.

Local thermal non-equilibrium: a difference in temperature between the fluid and the solid at the same point in a porous medium.

Brinkman–Forchheimer equation: an extension of the basic law for flow through a porous medium that adds terms for viscous shear and for drag at high flow speeds.

Scopus: a database of scholarly publications and the citations between them.

Citation: a reference to a work in a later publication. A citation count is the number of such references to date.