M Ijaz Khan1, Sohail A Khan2, T Hayat3, M Imran Khan4, A Alsaedi5. 1. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan. Electronic address: ijazfmg_khan@yahoo.com. 2. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan. 3. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University P. O. Box 80207, Jeddah 21589, Saudi Arabia. 4. Heriot Watt University, Edinburgh Campus, Edinburgh EH14 4AS, United Kingdom. Electronic address: mk42@hw.ac.uk. 5. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University P. O. Box 80207, Jeddah 21589, Saudi Arabia.
Abstract
BACKGROUND: Nanomaterials have higher inspiration in the growth of pioneering heat transportation fluids and good efforts were made in this field during the recent year. Nowadays numerous scientists and researchers have focused their struggle on nanomaterials study. Nanoliquids have advanced properties which make them efficient in various applications including engine cooling, hybrid-power engine, pharmaceutical processes, refrigerator and vehicle thermal management etc. Therefore such implication in mind the entropy optimization in magnetohydrodynamic nanomaterials (TiO2 - GO) flow between two stretchable rotating disks is discussed here. Energy expression subject to Joule heating, thermal radiation and viscous dissipation is modeled. Entropy optimization rate is based upon thermodynamic second law. Here titanium dioxide (TiO2) and graphene oxide (GO) and water (H2O) are used as nanoliquids. Homogeneous and heterogeneous reactions have been accounted. METHODS: Transformation process reduced nonlinear PDE's to ordinary differential systems. Formulated systems are solved due to implementation of Newton built in shooting method. RESULTS: Salient behavior of influential variables on velocity, entropy optimization, temperature, Bejan number and concentration graphically illustrated for (TiO2 and GO). Surface drag force and gradient of temperature ((Cf1, Cf2) and (Nux1, Nux2)) are numerically computed for various interesting parameters at lower and upper disks respectively. Axial and radial velocities components boost up for larger (Re) but opposite is hold for tangential velocity. Entropy optimization and temperature are increased for higher Brinkman number (Br). CONCLUSIONS: A significant augmentation occurs in radial and axial velocities (f'(ξ) and f(ξ)) versus stretching parameter, while opposite is hold for tangential velocity (g(ξ)). For larger values of Reynold and Brinkman numbers the temperature increases. Temperature and entropy optimization have opposite effect for radiation parameter. Concentration has similar results for Reynold and Schmidt numbers. Entropy optimization and Bejan number for radiation parameter have similar outcome. Bejan number decays for Brinkman number.
BACKGROUND: Nanomaterials have higher inspiration in the growth of pioneering heat transportation fluids and good efforts were made in this field during the recent year. Nowadays numerous scientists and researchers have focused their struggle on nanomaterials study. Nanoliquids have advanced properties which make them efficient in various applications including engine cooling, hybrid-power engine, pharmaceutical processes, refrigerator and vehicle thermal management etc. Therefore such implication in mind the entropy optimization in magnetohydrodynamic nanomaterials (TiO2 - GO) flow between two stretchable rotating disks is discussed here. Energy expression subject to Joule heating, thermal radiation and viscous dissipation is modeled. Entropy optimization rate is based upon thermodynamic second law. Here titanium dioxide (TiO2) and graphene oxide (GO) and water (H2O) are used as nanoliquids. Homogeneous and heterogeneous reactions have been accounted. METHODS: Transformation process reduced nonlinear PDE's to ordinary differential systems. Formulated systems are solved due to implementation of Newton built in shooting method. RESULTS: Salient behavior of influential variables on velocity, entropy optimization, temperature, Bejan number and concentration graphically illustrated for (TiO2 and GO). Surface drag force and gradient of temperature ((Cf1, Cf2) and (Nux1, Nux2)) are numerically computed for various interesting parameters at lower and upper disks respectively. Axial and radial velocities components boost up for larger (Re) but opposite is hold for tangential velocity. Entropy optimization and temperature are increased for higher Brinkman number (Br). CONCLUSIONS: A significant augmentation occurs in radial and axial velocities (f'(ξ) and f(ξ)) versus stretching parameter, while opposite is hold for tangential velocity (g(ξ)). For larger values of Reynold and Brinkman numbers the temperature increases. Temperature and entropy optimization have opposite effect for radiation parameter. Concentration has similar results for Reynold and Schmidt numbers. Entropy optimization and Bejan number for radiation parameter have similar outcome. Bejan number decays for Brinkman number.