Abstract
A theoretical study of two-dimensional magnetohydrodynamics viscous incompressible free convective boundary layer flow of an electrically conducting, chemically reacting nanofluid from a convectively heated permeable vertical surface is presented. Scaling group of transformations is used in the governing equations and the boundary conditions to determine absolute invariants. A third-order ordinary differential equation which corresponds to momentum conservation and two second-order ordinary differential equations which correspond to energy and nanoparticle volume fraction (species) conservation are derived. Our (group) analysis indicates that, for the similarity solution, the convective heat transfer coefficient and mass transfer velocity are proportional tox-1/4whilst the reaction rate is proportional tox-1/2, wherexis the axial distance from the leading edge of the plate. The effects of the relevant controlling parameters on the dimensionless velocity, temperature, and nanoparticle volume fraction are examined. The accuracy of the technique we have used was tested by performing comparisons with the results of published work and the results were found to be in good agreement. The present computations indicate that the flow is accelerated and temperature enhanced whereas nanoparticle volume fractions are decreased with increasing order of chemical reaction. Furthermore the flow is strongly decelerated, whereas the nanoparticle volume fraction and temperature are enhanced with increasing magnetic field parameter. Increasing convection-conduction parameter increases velocity and temperatures but has a weak influence on nanoparticle volume fraction distribution. The present study demonstrates the thermal enhancement achieved with nanofluids and also magnetic fields and is of relevance to nanomaterials processing.
Highlights
Nanofluids have a significant impact on heat transfer enhancement in modern years
(i) Dimensionless velocity is depressed whereas the temperature and the nanoparticle volume fraction are increased with an increase in magnetohydrodynamic parameter, M
(ii) Dimensionless temperature is enhanced slightly, and nanoparticle volume fraction is elevated whereas velocity is reduced with a rise in the order of chemical reaction, n
Summary
Nanofluids have a significant impact on heat transfer enhancement in modern years They have been utilized in diverse technologies including turbulent flows [1], propulsion [2], geothermics [3], porous media solar collectors [4, 5], and chemical engineering coating processes [6]. The convective boundary condition was utilized by a variety of researchers including Yao et al [27] for stretching/shrinking flows, Makinde and Aziz [28] for nanofluids, Yacob et al [29] for nanofluids, Uddin et al [30] for nanofluid flow in porous media, and Aziz and Khan [31] for natural convective nanofluid These studies have neglected chemical reaction effects. The influences of chemical reaction, magnetic field, wall transpiration, convective-conductive boundary condition, Brownian parameter, thermophoresis parameter and Lewis number on the dimensionless fluid velocity, temperature, and nanoparticle volume fraction distributions are explored. A good area of applications of the present problem is nanofluid synthesis for medicine
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