Tribology International 190 (2023) 109038 Available online 28 October 2023 0301-679X/© 2023 Elsevier Ltd. All rights reserved. Thermal and solutal slip impacts of tribological coatings on the fow and heat transfer of reiner-philippoff nanofuid lubrication toward a stretching surface: The applications of Darcy-Forchheimer theory M. Israr Ur Rehman a , Haibo Chen a, * , Aamir Hamid b , Shami A.M. Alsallami c , A. Al-Zubaidi d , S. Saleem d a School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, PR China b Department of Mathematics, Women University of Azad Jammu and Kashmir, Bagh 12500, Pakistan c Department of Mathematical Sciences, College of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia d Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia A R T I C L E INFO Keywords: Reiner Philippoff fuid Magnetic feld Thermal radiation Mixed convection Darcy-Forchheimer Slip conditions ABSTRACT Numerous non-Newtonian fuid models are formulated as an alternative to Newton’s Law of viscosity, which describes absolute viscous sources as a function of shear rate rather than constantly. In this paper, the Reiner- Philippoff fuid (RPF) model is considered out of many existing models since it can capture certain non- Newtonian characteristics in certain cases. An adopted underlying mathematical model employs a partial dif- ferential system, which is reduced to the system of ordinary differential system with the help of suitable simi- larity variables. The resultant system is computed with the Runga-Kutta-Fehlberg (RK-F) method to boost-up the confdence of its accuracy. It is found that the porosity and Darcy-Forchheimer parameters improve the fow rate of RPF. On the other hand, heat transfer is positively affected by thermal slip in contrast to the outcomes of radiation parameter, which, however, are inauspicious. Furthermore, the mass diffusion rate is noticed to be signifcantly infuenced by the Schmidt number along with the chemical reaction parameter. In conclusion, all the results are expected to beneft numerous transport phenomena of industrial, biomedical, and thermal sciences. 1. Introduction One of the most crucial fow parameters is viscosity, also known as the measure of internal fuid friction, which causes viscous fuid to stagnate when it strikes a rigid body [1]. As a result, stagnation point fow is ensued, which characterizes viscous layer fow evolved in the neighborhoods of a stagnation locus [2]. First and foremost, such fows were studied for two-dimensional external fow of aqueous medium past a cylinder, which was mathematically elaborated by Hiemenz et al. [3]. In follow-up studies, many researchers employed different factors to extend the Hiemenz fow model, such as Homann et al. [4] studied the three-dimensional case, Ariel [5] examined the magnetohydrodynamics (MHD) effects, Chiam et al. [6] elaborated on the stagnation point fow induced by stretching plate, Wang et al. [7] scrutinized the streaming over a shrinking surface, and many more. All these studies concluded that the stagnation locii are very infuential in transport phenomena since other fow properties becomes optimal rather than velocity and pressure, that drops eventually. In recent years, many studies have been devoted to non-Newtonian mediums since a wide class of industrial, scientifc, and engineering applications beneft from their versatility, controllability, and unique fow characteristics. For instance, drag reducers, printers, pharmaceu- ticals, biomedical engineering, damping and braking equipment, and food processing are some of the common implementations that use non- Newtonian fuids [8]. It is essential to have a better understanding of the rheological properties of these materials to optimize simulations and design effective models. As an alternative to Newton’s Law of Viscosity, non-Newtonian fuid models have been developed where viscous mea- sures are not constant but rather depend on shear rate. Streams of non-Newtonian liquids along stretching surfaces have remained in the limelight for decades. Considering viscous dissipation infuences, Chen et al. [9] investigated convective heat transfer in a thin, power-law liquid flm formed due to an unsteadily stretching sheet. A * Corresponding author. E-mail address: math_chb@csu.edu.cn (H. Chen). Contents lists available at ScienceDirect Tribology International journal homepage: www.elsevier.com/locate/triboint https://doi.org/10.1016/j.triboint.2023.109038 Received 11 July 2023; Received in revised form 15 October 2023; Accepted 22 October 2023