fluids Review Mathematical Modeling and Computer Simulations of Nanofluid Flow with Applications to Cooling and Lubrication Clement Kleinstreuer * and Zelin Xu Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7910, USA; zxu4@ncsu.edu * Correspondence: ck@ncsu.edu; Tel.: +1-919-515-5261 Academic Editors: Phuoc X. Tran and Mehrdad Massoudi Received: 31 March 2016; Accepted: 20 May 2016; Published: 27 May 2016 Abstract: There is a growing range of applications of nanoparticle-suspension flows with or without heat transfer. Examples include enhanced cooling of microsystems with low volume-fractions of nanoparticles in liquids, improved tribological performance with lubricants seeded with nanoparticles, optimal nanodrug delivery in the pulmonary as well as the vascular systems to combat cancer, and spray-coating using plasma-jets with seeded nanoparticles. In order to implement theories that explain experimental evidence of nanoparticle-fluid dynamics and predict numerically optimum system performance, a description of the basic math modeling and computer simulation aspects is necessary. Thus, in this review article, the focus is on the fundamental understanding of the physics of nanofluid flow and heat transfer with summaries of microchannel-flow applications related to cooling and lubrication. Keywords: nanofluids; mathematical modeling; computer simulations; heat transfer enhancement; improved lubrication 1. Introduction Over the last several decades, there has been an ever-increasing interest in nanofluids, i.e., liquids with all sorts of solid nanoparticles (NPs) well dispersed at low concentrations. Application areas for nanofluids range from engineering to medicine, taking advantage of their unique properties in heat transfer [1–3], drug delivery [4–7], mass transport [8,9], boiling phenomena [10,11], absorption and radiation [12–15], optics [16,17], reacting surfaces and catalysts [18], spray-coating [19,20], and lubrication [21–24]. Though initially investigated in the heat transfer community (see [25]), the concept of “nanofluids” is being continuously expanded in developing more and more useful applications. Three application-schematics are given in Figure 1. Clearly, in order to achieve optimal system performance in present and future applications, the underlying physics has to be clearly understood via benchmark experiments as well as sound theories. Focusing here on various aspects of mathematical modeling and computer simulations, transport processes of nanofluids are analyzed and system performances numerically predicted. Fluids 2016, 1, 16; doi:10.3390/fluids1020016 www.mdpi.com/journal/fluids