The Variation Formula for Solutions of Differential Equations

The study of the entropy generation in a thin film flow with variable fluid properties past over a stretching sheet

Advances in Mechanical Engineering ◽

10.1177/1687814018789522 ◽

2018 ◽

Vol 10 (11) ◽

pp. 168781401878952 ◽

Cited By ~ 21

Author(s):

Taza Gul ◽

Irfan Haleem ◽

Ibrar Ullah ◽

Muhammad Altaf Khan ◽

Ebenezer Bonyah ◽

...

Keyword(s):

Differential Equations ◽

Thermal Radiation ◽

Liquid Film ◽

Entropy Generation ◽

Stretching Sheet ◽

Film Flow ◽

Variable Viscosity ◽

Bejan Number ◽

Variation Formula ◽

Number Formula

This research inspects the liquid film flow of the nanofluid in a permeable medium with the consequence of thermal radiation over a stretching sheet. The viscidness and thermal conduction of the nanofluid varies with temperature in such a manner that the thermal conductivity considered in direct relation while the viscosity considered inversely proportional to the temperature field. The invariable magnetic field applies vertically to the flow field in the existence of entropy generation. For the above-mentioned nanofluid study, Buongiorno’s model is used. The leading equations are changed into a set of third- and second-order nonlinear coupled differential equations. These nonlinear ordinary differential equations are solved using the optimal approach of homotopy analysis method. The physical appearance of the modelled parameters based on the liquid film thickness is mainly focused. Furthermore, the influence of embedded parameters like variable viscosity parameter [Formula: see text] Prandtl number [Formula: see text] Schmidt number [Formula: see text] Brinkman number [Formula: see text] Brownian motion constraint [Formula: see text] thermophoresis constraint [Formula: see text] magnetic parameter [Formula: see text] thermal radiation parameter [Formula: see text] Reynolds number [Formula: see text] diffusion coefficient [Formula: see text] non-dimension temperature variation [Formula: see text] and non-dimension concentration variation [Formula: see text] is observed on the velocity pitch, temperature gradient and concentration sketch. The consequence of parameters due to entropy generation and Bejan number has also been observed in this work. The important physically quantities of skin friction coefficient, the local Nusselt number and Sherwood number have also been studied. Residual error and optimal values have been calculated for the range of each physical parameter. The present work is compared with the published work and the comparison has been shown physically and numerically.

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