This research will explore the issue of stagnation point flow in carbon nanotubes with suction/injection impacts by a nonlinear stretching/shrinking sheet. By practising a similarity transformation, the governing partial differential equations (PDEs) are converted to a scheme of nonlinear ordinary differential equations (ODEs). Then, settled numerically with applying a bvp4c solver in Matlab. Two types of carbon nanotubes (CNTs) are used which are SWCNTs (single-walled) and MWCNTs (multiwalled) and the base fluid used is water. In the form of graphs, the impact of the velocity, temperature, skin friction and numbers of Nusselts parameter is researched and displayed and interpreted physically. It is found that if only suction rises, the range of solutions will increase.
The boundary layer flow with heat and mass transfer are important since the quality of final product depends on factors such as the rate of cooling and stretching phenomenon. The pivotal aim of this research is to address magnetohydrodynamics (MHD) copper-aluminium oxide hybrid nanoparticles containing gyrotactic microorganisms over a stretching vertical cylinder with suction. The mathematical model has been formulated based on Tiwari-Das nanofluid model. Two types of nanofluid containing Copper (Cu) and Aluminum Oxide (Al2O3) immersed in water is considered in this study. In the analysis, the governing partial differential equations (PDEs) are transformed into a set of ordinary differential equations (ODEs) by a similarity transformation. Corresponding boundary conditions are analysed numerically along with these equations and are programmed in MATLAB software through the bvp4c method to obtain the solutions. The numerical solutions are obtained for the skin friction coefficient, the local Nusselt number, local Sherwood number and local density of motile microorganism as well as velocity, temperature, concentration, and microorganism profiles. The present analysis is validated by comparing with previously published work and found to be in good agreement. The effects of the parameter are analysed and discussed. According to the findings, suction increases shear stress, heat transport rate, mass transfer, and mass diffusivity. Moreover, hybrid nanofluid was discovered to be faster than nanofluid in terms of transit rate. Furthermore, the local density motile microorganism bioconvection Peclet number and bioconvection Lewis number increased.
The pivotal aim of this research is to address a natural stagnation bioconvection flow of a hybrid nanofluid containing gyrotactic microorganisms over an exponentially stretching and shrinking vertical sheet. The mathematical formulation of simplified Navier-Stokes equations is made in the presence of a few parameters such as Prandtl number, concentration to thermal buoyancy ratio, microorganism to thermal buoyancy ratio, Lewis number, bioconvection Peclet number, bioconvection Lewis number, microorganisms concentration difference and buoyancy parameter. The two types of nanofluid containing titanium alloy (Ti6Al4V) and aluminium alloy (AA7075) immersed in water are considered for the investigation. In the analysis, the governing partial differential equations (PDEs) are transformed into a set of ordinary differential equations (ODEs) by a similarity transformation. The resulting equations are rewritten in MATLAB software through the Bvp4c method to obtain the solutions. The effects of hybrid nanofluid of titanium alloy (Ti6Al4V) and aluminium alloy (AA7075), microorganisms’ concentration difference parameter, and bioconvection Lewis Number are observed in this mathematical model in the presence of stretching and shrinking sheets. The numerical values are obtained for the skin friction coefficient, local Nusselt number, local Sherwood number, and local density of motile microorganisms for the reporting purpose. In addition, the profiles of the velocity, temperature, concentration, and microorganism are visualized as the main findings of this article.
The problem of hyperbolic tangent fluid model for stagnation flow of hybrid nanofluid over a stretching sheet is investigated. Constitutive relation of an incompressible hyperbolic tangent model as well as consideration of thermal radiation and Newtonian heating is taken into account. The boundary layer problem is formulated to nonlinear partial differential equations which is then transformed into ordinary differential equations by using similarity transformation. The equations including the boundary conditions are solved numerically using bvp4c in the MATLAB software. A comparison with previous findings shows an excellent agreement. The effect of governing parameters such as power law index, Weissenberg number, suction/injection, radiation and Biot number is investigated. The changes in the value of volume fraction of diamond and silicon dioxide are also analyzed. Characteristics for the significant variables are graphically presented and the numerical results are tabulated. The velocity behavior is significantly influenced by the volume fraction of diamond and silicon dioxide and other physical parameters. Meanwhile, the temperature is influenced by the radiation parameter. This study provides conclusive evidence that increasing the volume fraction of diamond nanoparticles significantly enhances the heat transfer rate. The increment by 0.1 (10%) of the volume fraction of diamond nanoparticles increases the heat transfer rate approximately by 3%. These findings underscore the potential of integrating these nanoparticles to improve thermal performance across diverse applications.
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