This paper discusses the model of the boundary layer(BL)flow and the heat transfer characteristics of hybrid nanofluid(HNF)over shrinking/stretching disks.In addition,the thermal radiation and the impact of velocity a...This paper discusses the model of the boundary layer(BL)flow and the heat transfer characteristics of hybrid nanofluid(HNF)over shrinking/stretching disks.In addition,the thermal radiation and the impact of velocity and thermal slip boundary conditions are also examined.The considered hybrid nano-fluid contains silver(Ag)and iron oxide(Fe_(3)O_(4))nanoparticles dispersed in the water to prepare the Ag-Fe_(3)O_(4)/water-based hybrid nanofluid.The requisite posited partial differential equations model is converted to ordinary differential equations using similarity transformations.For a numerical solution,the shooting method in Maple is employed.Moreover,the duality in solutions is achieved for both cases of the disk(stretching(λ>0)and shrinking(λ<0)).At the same time,a unique solution is observed for λ=0.No solution is found for them at λ<λ_(c),whereas the solutions are split at the λ=λ_(c).Besides,the value of the λ_(c) is dependent on the φ_(hnf).Meanwhile,the values of f″(0)and -θ′(0)intensified with increasing φ_(hnf).Stability analysis has been applied using bvp4c in MATLAB software due to a dual solution.Furthermore,analysis shows that the first solution is stable and feasible physically.For the slip parameters,an increase in the velocity slip parameter increases the velocity and shear stress profiles while increasing the temperature profile in the first solutions.While the rise in thermal slip parameter reduces the temperature profile nanoparticle volume fractions increase it.展开更多
This study investigates the heat transfer and flow dynamics of a ternary hybrid nanofluid comprising alumina,copper,and silica/titania nanoparticles dispersed in water.The analysis considers the effects of suction,mag...This study investigates the heat transfer and flow dynamics of a ternary hybrid nanofluid comprising alumina,copper,and silica/titania nanoparticles dispersed in water.The analysis considers the effects of suction,magnetic field,and Joule heating over a permeable shrinking disk.Amathematicalmodel is developed and converted to a systemof differential equations using similarity transformation which then,solved numerically using the bvp4c solver in Matlab software.The study introduces a novel comparative analysis of alumina-copper-silica and alumina-coppertitania nanofluids,revealing distinct thermal conductivity behaviors and identifying critical suction values necessary for flow stabilization.Dual solutions are found within a specific range of parameters such that the minimum required suction values for flow stability,with S_(c)=1.2457 for alumina-copper-silica/water and S_(c)=1.2351 for alumina-coppertitania/water.The results indicate that increasing suction by 1%enhances the skin friction coefficient by up to 4.17%and improves heat transfer efficiency by approximately 1%,highlighting its crucial role in stabilizing the opposing flow induced by the shrinking disk.Additionally,the inclusion of 1%silica nanoparticles reduces both skin friction and heat transfer rate by approximately 0.28%and 0.85%,respectively,while 1%titania concentration increases skin friction by 3.02%but results in a slight heat transfer loss of up to 0.61%.These findings confirm the superior thermal performance of alumina-copper-titania/water,making it a promising candidate for enhanced cooling systems,energy-efficient heat exchangers,and industrial thermal management applications.展开更多
基金the Researchers Supporting Project number(RSPD2025R997),King Saud University,Riyadh,Saudi Arabia.
文摘This paper discusses the model of the boundary layer(BL)flow and the heat transfer characteristics of hybrid nanofluid(HNF)over shrinking/stretching disks.In addition,the thermal radiation and the impact of velocity and thermal slip boundary conditions are also examined.The considered hybrid nano-fluid contains silver(Ag)and iron oxide(Fe_(3)O_(4))nanoparticles dispersed in the water to prepare the Ag-Fe_(3)O_(4)/water-based hybrid nanofluid.The requisite posited partial differential equations model is converted to ordinary differential equations using similarity transformations.For a numerical solution,the shooting method in Maple is employed.Moreover,the duality in solutions is achieved for both cases of the disk(stretching(λ>0)and shrinking(λ<0)).At the same time,a unique solution is observed for λ=0.No solution is found for them at λ<λ_(c),whereas the solutions are split at the λ=λ_(c).Besides,the value of the λ_(c) is dependent on the φ_(hnf).Meanwhile,the values of f″(0)and -θ′(0)intensified with increasing φ_(hnf).Stability analysis has been applied using bvp4c in MATLAB software due to a dual solution.Furthermore,analysis shows that the first solution is stable and feasible physically.For the slip parameters,an increase in the velocity slip parameter increases the velocity and shear stress profiles while increasing the temperature profile in the first solutions.While the rise in thermal slip parameter reduces the temperature profile nanoparticle volume fractions increase it.
基金funded by Universiti Teknikal Malaysia Melaka,through Fakulti Teknologi dan Kejuruteraan Mekanikal(FTKM)’s publication fund-K23003.
文摘This study investigates the heat transfer and flow dynamics of a ternary hybrid nanofluid comprising alumina,copper,and silica/titania nanoparticles dispersed in water.The analysis considers the effects of suction,magnetic field,and Joule heating over a permeable shrinking disk.Amathematicalmodel is developed and converted to a systemof differential equations using similarity transformation which then,solved numerically using the bvp4c solver in Matlab software.The study introduces a novel comparative analysis of alumina-copper-silica and alumina-coppertitania nanofluids,revealing distinct thermal conductivity behaviors and identifying critical suction values necessary for flow stabilization.Dual solutions are found within a specific range of parameters such that the minimum required suction values for flow stability,with S_(c)=1.2457 for alumina-copper-silica/water and S_(c)=1.2351 for alumina-coppertitania/water.The results indicate that increasing suction by 1%enhances the skin friction coefficient by up to 4.17%and improves heat transfer efficiency by approximately 1%,highlighting its crucial role in stabilizing the opposing flow induced by the shrinking disk.Additionally,the inclusion of 1%silica nanoparticles reduces both skin friction and heat transfer rate by approximately 0.28%and 0.85%,respectively,while 1%titania concentration increases skin friction by 3.02%but results in a slight heat transfer loss of up to 0.61%.These findings confirm the superior thermal performance of alumina-copper-titania/water,making it a promising candidate for enhanced cooling systems,energy-efficient heat exchangers,and industrial thermal management applications.
