Similarity transform-based numerical analysis of natural convection over an inclined flat plate using nanofluid

Nanofluids serve as a working medium in many state-of-the-art heating and cooling systems, where natural convection is a primary medium of thermal energy transfer. Based on the review of recently published literature, the present study is devoted to heat transfer analysis, based on similarity transformations and numerical solutions. The study aims to provide reliable, predictive analytical expressions for heat transfer coefficients and heat transfer rates in a schematic of the natural convection phenomenon. The objective is to analyse laminar free convection across a stagnant Al2O3-water nanofluid layer, spread over an inclined plane surface and exposed to the ambient. A novel similarity transformation method is applied to laminar boundary layer flow, capable of handling coupled influences of flow parameters, thermal boundary conditions and temperature-dependent thermophysical properties. This analysis also considers the effects of concentration and shape factor of nanoparticles on heat transfer. The physical properties are transformed into equivalent (temperature-dependent) physical property factors, along with similarity transformations of velocity and temperature fields. The fifth-order Runge-Kutta method is used to solve the coupled governing equations. The solutions are compared with predictive formulae for wall temperature gradients, heat transfer rates, and the convection heat transfer coefficient. Calculations based on predictive formulae agree well with published data.