Abstract
Abstract In this study we use a new spectral relaxation method to investigate heat transfer in a nanofluid flow over an unsteady stretching sheet with thermal dispersion and radiation. Three water-based nanofluids containing copper oxide CuO, aluminium oxide Al2O3 and titanium dioxide TiO2 nanoparticles are considered in this study. The transformed governing system of nonlinear differential equations was solved numerically using the spectral relaxation method that has been proposed for the solution of nonlinear boundary layer equations. Results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity, temperature and nanoparticle fraction profiles for some values of the governing physical and fluid parameters. Validation of the results was achieved by comparison with limiting cases from previous studies in the literature. We show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to common numerical methods for solving nonlinear boundary value problems. We show that the convergence rate of the spectral relaxation method is significantly improved by using the method in conjunction with the successive over-relaxation method.
Highlights
In recent years flow and heat transfer over a stretching surface has been extensively investigated due to its importance in industrial and engineering applications such as in the heat treatment of materials manufactured in extrusion processes and the casting of materials
We considered three different nanoparticles, copper oxide (CuO), aluminium oxide (Al O ) and titanium oxide (TiO ), with water as the base fluid
The spectral relaxation method algorithm ( )-( ) has been used to solve the nonlinear coupled boundary value problem due to flow over a steady stretching sheet in a nanofluid
Summary
In recent years flow and heat transfer over a stretching surface has been extensively investigated due to its importance in industrial and engineering applications such as in the heat treatment of materials manufactured in extrusion processes and the casting of materials. Wire drawing, the manufacture of plastic and rubber sheets and polymer extrusion are some of the important processes that take place subject to stretching and heat transfer. The development of a boundary layer over a stretching sheet was first studied by Crane [ ], who found an exact solution for the flow field. This problem was extended by Gupta and Gupta [ ] to a permeable surface. Since the pioneering work of Sakiadis [ ], various aspects of the stretching problem involving Newtonian and non-Newtonian fluids have been extensively studied by several authors (see Cortell [ ], Hayat and Sajid [ ], Liao [ ], Xu [ ])
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