Physical Analysis of Thermophoresis and Variable Density Effects on Heat Transfer Assessment along a Porous Stretching Sheet and Their Applications in Nanofluid Lubrication

Nanofluids are engineered colloidal suspensions of nanoparticles in the base fluids. At very low particle concentration, nanofluids have a much higher and strongly temperature-dependent thermal conductivity, which enables them to enhance the performance of machining applications such as the cooling and lubrication of the cutting zone during any machining process, the vehicle’s braking system, enhanced oil recovery (EOR), engine oil, and the drilling process of crude oil. In the current work, the density is assumed as an exponential function of temperature due to larger temperature differences. The main focus of this mechanism is the variable density effects on heat and mass characteristics of nanoparticles across the stretching porous sheet with thermophoresis and Brownian motion to reduce excessive heating in high-temperature systems. This is the first temperature-dependent density problem of nanofluid across the stretching surface. The coupled partial differential equations (PDEs) of the present nanofluid mechanism are changed into nonlinear coupled ordinary differential equations (ODEs) with defined stream functions and similarity variables for smooth algorithm and integration. The changed ODEs are again converted in a similar form for numerical outcomes by applying the Keller Box approach. The numerical outcomes are deduced in graphs and tabular form with the help of the MATLAB (R2013a created by MathWorks, Natick, MA, USA) program. In this phenomenon, the velocity, temperature, and concentration profile, along with their slopes, have been plotted for various parameters pertaining to the current issue. The range of parameters has been selected according to the Prandtl number $0.07\le Pr\le 70.0$ and buoyancy parameter $0<\lambda <\infty$, respectively. The novelty of the current work is its use of nanoparticle fraction along the porous stretching sheet with temperature-dependent density effects for the improvement of lubrication and cooling for any machining process and to reduce friction between tool and work piece in the cutting zone by using nanofluid. Moreover, nanoparticles can also be adsorbed on the oil/water surface, which alters the oil/water interfacial tension, resulting in the formation of emulsions.