Hybrid Nanofluid Flow Past A Permeable Moving Thin Needle

The problem of a steady flow and heat transfer past a permeable moving thin needle in a hybrid nanofluid is examined in this study. Here, we consider copper (Cu) and alumina (Al2O3) as hybrid nanoparticles, and water as a base fluid. In addition, the effects of thermophoresis and Brownian motion are taken into consideration. A similarity transformation is used to obtain similarity equations, which are then solved numerically using the boundary value problem solver, bvp4c available in Matlab software (Matlab_R2014b, MathWorks, Singapore). It is shown that heat transfer rate is higher in the presence of hybrid nanoparticles. It is discovered that the non-uniqueness of the solutions is observed for a certain range of the moving parameter λ. We also observed that the bifurcation of the solutions occurs in the region of λ > 0, i.e., when the needle moved toward the origin. Furthermore, we found that the skin friction coefficient and the heat transfer rate at the surface are higher for smaller needle sizes. A reduction in the temperature and nanoparticle concentration was observed with the increasing of the thermophoresis parameter. It was also found that the increase of the Brownian motion parameter leads to an increase in the nanoparticle concentration. Temporal stability analysis shows that only one of the solutions was stable and physically reliable as time evolved

Hybrid Nanofluid Flow Towards A Stagnation Point On A Stretching/Shrinking Cylinder

This paper examines the stagnation point flow towards a stretching/shrinking cylinder in a hybrid nanofluid. Here, copper (Cu) and alumina (Al2O3) are considered as the hybrid nanoparticles while water as the base fluid. The governing equations are reduced to the similarity equations using a similarity transformation. The resulting equations are solved numerically using the boundary value problem solver, bvp4c, available in the Matlab software. It is found that the heat transfer rate is greater for the hybrid nanofluid compared to the regular nanofluid as well as the regular fluid. Besides, the non-uniqueness of the solutions is observed for certain physical parameters. It is also noticed that the bifurcation of the solutions occurs in the shrinking regions. In addition, the heat transfer rate and the skin friction coefficients increase in the presence of nanoparticles and for larger Reynolds number. It is found that between the two solutions, only one of them is stable as time evolves

Squeezed Hybrid Nanofluid Flow Over A Permeable Sensor Surface

This paper examines the squeezed hybrid nanofluid flow over a permeable sensor surface with magnetohydrodynamics (MHD) and radiation effects. The alumina (Al2O3) and copper (Cu) are considered as the hybrid nanoparticles, while water is the base fluid. The governing equations are reduced to the similarity equations, using the similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain the numerical solutions. It was found that the heat transfer rate was greater for the hybrid nanofluid, compared to the regular nanofluid. It was observed that dual solutions exist for some values of the permeable parameter S. The upper branch solutions of the skin friction coefficient (Re1/2 x Cf) and the heat transfer rate at the surface (Re−1/2x Nux) enhance with the added Cu nanoparticle (ϕ2) and for larger magnetic strength (M). Moreover, the values of Re1/2x Cf decrease, whereas the values of Re−1/2x Nux increase for both branches, with the rise of the squeeze flow index (b). Besides, an increment of the heat transfer rate at the sensor surface for both branches was observed in the presence of radiation (R). Temporal stability analysis was employed to determine the stability of the dual solutions, and it was discovered that only one of them was stable and physically reliable as time evolve

Nanofluid Flow On A Shrinking Cylinder With Al2O3 Nanoparticles

This study investigates the nanofluid flow towards a shrinking cylinder consisting of Al2O3 nanoparticles. Here, the flow is subjected to prescribed surface heat flux. The similarity variables are employed to gain the similarity equations. These equations are solved via the bvp4c solver. From the findings, a unique solution is found for the shrinking strength λ ≥ −1. Meanwhile, the dual solutions are observed when λc < λ < −1. Furthermore, the friction factor Re1/2 x Cf and the heat transfer rate Re−1/2 x Nux increase with the rise of Al2O3 nanoparticles ϕ and the curvature parameterγ. Quantitatively, the rates of heat transfer Re−1/2 x Nux increase up to 3.87% when ϕ increases from 0 to 0.04, and 6.69% when γ increases from 0.05 to 0.2. Besides, the profiles of the temperature θ(η) and the velocity f 0 (η) on the first solution incline for larger γ, but their second solutions decline. Moreover, it is noticed that the streamlines are separated into two regions. Finally, it is found that the first solution is stable over time

On The Stability Of The Flow And Heat Transfer Over A Moving Thin Needle With Prescribed Surface Heat Flux

The steady flow and heat transfer over a moving thin needle with prescribed surface heat flux is studied. The similarity equations are obtained by using similarity transformation technique. The problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The plots of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented and their behaviors are discussed for different values of the needle size and the velocity ratio parameter. Results show that the decreasing of the needle size enhance the skin friction coefficient and the local Nusselt number on the needle surface. It is found that dual solutions exist (upper and lower branches) for a certain range of the velocity ratio parameter. A stability analysis of the solutions are performed and it shows that the upper branch solution is stable, while the lower branch solution is unstable

Unsteady boundary layer flow over a sphere in a porous medium

This study focuses on the problem of unsteady boundary layer flow over a sphere in a porous medium. The governing equations which consists of a system of dimensional partial differential equations is applied with dimensionless parameter in order to obtain non-dimensional partial differential equations. Later, the similarity transformation is performed in order to attain nonsimilar governing equations. Afterwards, the governing equations are solved numerically by using the Keller-Box method in Octave programme. The effect of porosity parameter is examined on separation time, velocity profile and skin friction of the unsteady flow. The results attained are presented in the form of table and graph

Unsteady Flow And Heat Transfer Past A Stretching/Shrinking Sheet In A Hybrid Nanofluid

The unsteady flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid is studied. The governing equations of the problem are transformed to the similarity equations by using similarity transformation technique. The problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The plots of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for selected parameters are presented. It is found that dual solutions exist for a certain range of the unsteadiness parameter. A temporal stability analysis is performed to determine the stability of the dual solutions in a long run, and it is reveals that only one of them is stable while the other is unstable

Hiemenz Flow Over A Shrinking Sheet In A Hybrid Nanofluid

This study investigates the Hiemenz flow of hybrid nanofluid over a shrinking sheet. The similarity equations are obtained using similarity variables and then solved using the bvp4c solver. The outcomes showed that dual solutions occur for the shrinking case, in the range of 1.24657 1.1 1.1. Besides, the heat transfer rate is intensified with the rise of hybrid nanoparticles. Moreover, as hybrid nanoparticles increases, the friction on the surface is increased for 1, and no friction occurs when = 1. Finally, these solutions are tested using the stability analysis where the outcomes found that the first solution is stable and acceptable

MHD Glauert Flow Of A Hybrid Nanofluid With Heat Transfer

This paper examines the wall jet flow and heat transfer of the Glauert problem with the effect of the hybrid nanoparticles. Also, the influence of the magnetic field and the variable surface temperature are taken into consideration. Here, we consider copper (Cu) and alumina (Al2O3) as the hybrid nanoparticles while water is the base fluid. The governing equations are reduced to the similarity equations using similarity transformations. Then, the numerical solutions are obtained by using the bvp4c function in MATLAB software. The findings reveal that hybrid nanofluid provides a higher heat transfer rate compared to regular nanofluid. Besides, the heat transfer rate and the skin friction coefficient increase in the presence of nanoparticles. Moreover, the rise of the temperature index parameter contributes to the enhancement of the heat transfer rate, but it does not affect the skin friction coefficient. The stronger magnetic strength led to the reduction of the heat transfer rate and the skin friction coefficient

Multiple solutions of the unsteady hybrid nanofluid flow over a rotating disk with stability analysis

The present study attempts to analyze the unsteady flow over a rotating disk in a hybrid nanofluid with suction and deceleration effects. The partial derivatives of multivariable differential equations are converted to ordinary differential equations using appropriate transformations. The bvp4c function in MATLAB software is employed to solve the mathematical model. The outcomes show that multiple solutions are verifiable in certain operating parameters. The stability of the multiple solutions over time is investigated. It is discovered that the first and the second solutions are stable and physically relevant, whereas the third solution is unstable as time evolves. Moreover, the stronger deceleration contributes to enhancing the skin friction coefficient in the radial direction Rer1/2Cf and in the azimuthal direction Rer1/2Cg, for the first and third solutions whereas the second solution reduces. The values of Rer1/2Cf and Rer1/2Cg for the third solution enhance in the presence of suction, while the opposite behaviors​ are observed for the first and second solutions. The enhancement of the local Nusselt number Rer−1/2Nur on all solutions is noticed with the imposition of suction on the surface and stronger deceleration strength