Fawaz E Alsaadi1, T Hayat2, M Ijaz Khan3, Fuad E Alsaadi4. 1. Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University Jeddah, Saudi Arabia. 2. Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University Jeddah, Saudi Arabia; Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan. 3. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan. Electronic address: mikhan@math.qau.edu.pk. 4. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University Jeddah, Saudi Arabia.
Abstract
BACKGROUND: A newly developed approach in the field of nanotechnology for solving problems and collection of information is the use of nanoparticles. This idea has been further utilized in a better way in pharmaceutical industries. By using nanotechnology, the field of pharmaceutical science has been modernized and redeveloped. The use of nanotechnology in such industries has convinced the scientist to obtain more economical and easier applications. Therefore, with such effectiveness in mind, a theoretical study has been conducted to examine the effects of nonlinear radiative heat flux and magnetohydrodynamics for nanomaterial flow of Williamson fluid over a convectively heated stretchable surface. Brownian diffusion is utilized in mathematical modeling. Furthermore, heat source/sink, viscous dissipation and nonlinear radiative heat flux are examined. Convective boundary condition is implemented. Salient effects of chemical reaction and Arrhenius activation energy in mass transfer are considered. Total entropy rate is obtained through implementation of thermodynamics second law. METHODS: The nonlinear PDEs are reduced into ordinary ones by appropriate similarity transformations. A semi-analytical technique i.e., homotopy method is implemented to obtain the convergent series solutions. RESULTS: The obtained results indicate that the velocity of fluid particles increases versus higher fluid parameter. Schmidt number and activation energy variable have opposite effect on concentration. Entropy rate grows up with fluid parameter and Brinkman and Biot numbers while opposite trend is seen for Bejan number. CONCLUSIONS: Velocity of the material particles declines through larger estimations of magnetic variable while it upsurges for higher fluid parameter. Thermal distribution shows similar impact for radiative and magnetic variables. Mass concentration decreases against chemical reaction parameter while it increases via activation energy variable. Entropy and Bejan numbers show opposite impacts versus Brinkman number. Skin friction coefficient increases through larger Weissenberg number.
BACKGROUND: A newly developed approach in the field of nanotechnology for solving problems and collection of information is the use of nanoparticles. This idea has been further utilized in a better way in pharmaceutical industries. By using nanotechnology, the field of pharmaceutical science has been modernized and redeveloped. The use of nanotechnology in such industries has convinced the scientist to obtain more economical and easier applications. Therefore, with such effectiveness in mind, a theoretical study has been conducted to examine the effects of nonlinear radiative heat flux and magnetohydrodynamics for nanomaterial flow of Williamson fluid over a convectively heated stretchable surface. Brownian diffusion is utilized in mathematical modeling. Furthermore, heat source/sink, viscous dissipation and nonlinear radiative heat flux are examined. Convective boundary condition is implemented. Salient effects of chemical reaction and Arrhenius activation energy in mass transfer are considered. Total entropy rate is obtained through implementation of thermodynamics second law. METHODS: The nonlinear PDEs are reduced into ordinary ones by appropriate similarity transformations. A semi-analytical technique i.e., homotopy method is implemented to obtain the convergent series solutions. RESULTS: The obtained results indicate that the velocity of fluid particles increases versus higher fluid parameter. Schmidt number and activation energy variable have opposite effect on concentration. Entropy rate grows up with fluid parameter and Brinkman and Biot numbers while opposite trend is seen for Bejan number. CONCLUSIONS: Velocity of the material particles declines through larger estimations of magnetic variable while it upsurges for higher fluid parameter. Thermal distribution shows similar impact for radiative and magnetic variables. Mass concentration decreases against chemical reaction parameter while it increases via activation energy variable. Entropy and Bejan numbers show opposite impacts versus Brinkman number. Skin friction coefficient increases through larger Weissenberg number.