38 research outputs found
Multiple Solutions and Stability Analysis of Boundary Layer Flows over a Stretching/Shrinking Sheet in Nanofluids
No full textStudies of multiple solutions on boundary layer flows have gained much attention in the field of fluid dynamics in the recent years. In this regard, stability analysis is also important to identify the stable and unstable solutions. In this thesis, the possibility of occurrence of multiple solutions has been studied for boundary layer flows over stretching/shrinking sheet in nanofluids. Five different problems have been considered where two of the problems used nanofluid model proposed by Buongiomo and the remaining three problems used nanofluid model proposed by Tiwari and Das. The base fluids considered in this study are viscous fluid, Casson fluid and micropolar fluid. The mathematical models which govern the flows of five different problems have been constructed. Similarity transformations have been employed to transform the governing equations of partial differential equations to nonlinear ordinary differential equations. The resulting system is then solved numerically using shooting method with the aid of shootlib function in Maple software. To validate the results obtained in this study, comparison for specific cases have been done and in good agreement with existing solutions in literature. From this study, it is found that an increase of suction parameters will increase the rate of heat transfer in both stretching and shrinking cases. However, it causes the rate of skin friction to decrease for stretching case but to increase for shrinking case. Further, suction parameter, Casson parameter and Biot number decrease the temperature profiles but radiation, Brownian motion and thermophoresis parameters contribute towards the opposite. The results also displayed the occurrence of multiple solutions in all the problems considered. Therefore, the stability analysis has been performed to identify the stability of multiple solutions by using bvp4c solver in Matlab. The stability analysis indicates that the first solution is stable while the second and third solutions are unstable
Description of a new actinosporean type from South African freshwaters
No full textActinospore infection of oligochaetes collected from the mud of 2 freshwater biotopes in South Africa was studied. Using the 'cell-well plate method', a new aurantiactinomyxon type was found in 1.1% of the examined Branchiura sowerbyi oligochaete specimens from the Rietvlei River, north of Johannesburg, Gauteng, South Africa. In 1.5% of B. sowerbyi collected in a pond (Padda Dam), near the Rand Afrikaans University, Johannesburg, the same aurantiactinomyxon type was found. Infected oligochaetes were found only after collection and no actinosporean release was recorded in Branchiura specimens kept alive for several weeks. Actinospore infection showed a high intensity in oligochaetes in both positive cases. Until now, no actinosporean stages of myxosporeans have been described from South Africa. The aurantiactinospore type presented in this communication differs from the known types already described in the literature
Stefan blowing and slip effects on unsteady nano fluid transport past a shrinking sheet: multiple solutions
No full textThe aim of a present article is to investigate the laminar unsteady two‐dimensional boundary layer flow of a nanofluid with Stefan blowing and slip effect. First, governing boundary layer equations are converted in the ordinary form of the differential equations (ODEs) from partial differential equations using appropriate coordinate transformations. The obtained ODEs are then solved by applying a shooting method with the Runge‐Kutta fourth order method by implementation of the Maple software. The influences of different controlling dimensionless parameters over the dimensionless velocity, temperature, concentration, friction factor, local heat as well as mass transfer have been discussed and represented by plots. It is found that there exist dual solutions for the different applied nanofluid parameters along with the blowing parameter. The results reveal that by increasing the values of the Brownian motion (Nb), thermophoresis (Nt) and blowing parameters (fw), the skin friction increases (decreases) in the first (second) solutio
Effects of the viscous dissipation and chemical reaction on Casson nanofluid flow over the permeable stretching/shrinking sheet
No full textMHD micropolar nanofluid flow over an exponentially stretching/shrinking surface: triple solutions
No full textIn this study, the problem of MHD micropolar nanofluid boundary layer flows over an exponentially stretching/shrinking sheet with radiation and suction effect is considered. The Buongiorno’s nanofluid model is applied to the problem. The governing equations are first transformed to the coupled nonlinear similarity
equations by using similarity transformations. The resulting equations which is in ordinary differential equations form are then solved numerically by using shooting method.Triple solutions are observed to exist for the flows. A comparison with existing solutions in literature for specific case are made to assess the accuracy of the present results. Further, the flows profiles are examined, and it is found that the presence of suction parameter will contribute the occurrences of triple solutions
Linear stability analysis of MHD flow of micropolar fluid with thermal radiation and convective boundary condition: Exact solution
No full textMagnetohydrodynamic (MHD) flow of micropolar fluid by including the thermal radiation and convective condition on a shrinking surface in the presence of mass suction effects has been investigated. The momentum, angular momentum and energy equations, and the solutions of these equations are valid for whole Navier stokes, and microrotational and energy equations have been solved exactly. We obtain the solution in the form of an incomplete γ function for the energy equation. The results reveal that dual solutions exist for certain domains of different physical parameters. Furthermore, high suction produces the high effect of drag force, and as a result, coefficient of skin friction increases in the first solution. Stability analysis has been performed and determined that the first solution is more stable
Dual Solutions and Stability Analysis of Micropolar Nanofluid Flow with Slip Effect on Stretching/Shrinking Surfaces
No full textThe purpose of the present paper is to investigate the micropolar nanofluid flow on permeable stretching and shrinking surfaces with the velocity, thermal and concentration slip effects. Furthermore, the thermal radiation effect has also been considered. Boundary layer momentum, angular velocity, heat and mass transfer equations are converted to non-linear ordinary differential equations (ODEs). Then, the obtained ODEs are solved by applying the shooting method and in the results, the dual solutions are obtained in the certain ranges of pertinent parameters in both cases of shrinking and stretching surfaces. Due to the presence of the dual solutions, stability analysis is done and it was found that the first solution is stable and physically feasible. The results are also compared with previously published literature and found to be in excellent agreement. Moreover, the obtained results reveal the angular velocity increases in the first solution when the value of micropolar parameter increases. The velocity of nanofluid flow decreases in the first solution as the velocity slip parameter increases, whereas the temperature profiles increase in both solutions when thermal radiation, Brownian motion and the thermophoresis parameters are increased. Concentration profile increases by increasing N t and decreases by increasing N b
Multiple solutions of Cu-C6H9NaO7 and Ag-C6H9NaO7 nanofluids flow over nonlinear shrinking surface
No full textModel of Casson nanofluid flow over a nonlinear shrinking surface is considered. Model of Tiwari and Das is applied to nanofluid comprising of sodium alginate with copper and silver. The governing nonlinear equations incorporating the effects of the viscous dissipation are transformed into boundary value problems (BVPs) of ordinary
differential equations (ODEs) by using appropriate similarity transformations. The resulting equations are converted into initial value problems (IVPs) using the shooting method which are then solved by Runge-Kutta method of fourth
order. In order to determine the stability of the dual solutions obtained, stability analysis is performed and discovered that the first (second) solution is stable (unstable) and physically realizable (unrealizable). Both the thickness of the thermal boundary layer as well as temperature increase when the Casson parameter (β) is increased in the second solution
Radiative MHD flow and heat transfer characteristics of Cu-Fe3O4 /blood base hybridized nanofluid through stenotic artery
No full textThe main purpose of the present study is to examine the key role of Cu and Fe3O4 nanoparticles that are submerged in human blood in the existence of magnetohydrodynamics (MHD) flow through the stenosis artery. The reason behind the selection of Cu and Fe3O4 nanoparticles is that they show high potential usefulness in drug delivery and imaging properties. Moreover, the governing partial differential equations (PDEs) that define the flow and the heat transfer characteristics of blood-based hybrid nanofluid (HNF) are converted to non-dimensional form of ordinary differential equations (ODEs) using suitable similarity transformation. The shooting method is applied to solve the equations through Maple software to observe the effects of specified nanoparticles volume fractions and used physical parameters in stenotic arteries. The results show that the velocity of human blood gradually decreases with an increase in the size of the nanoparticles but temperature increases in both cases of the , either stretching or shrinking. Moreover, an increase in magnetic, suction/injection, and nanoparticle volume fractions decrease the velocity of the blood-based hybrid nanofluid flow through the stenotic artery. While, an increase in thermal radiation, magnetic, flow parameters, and nanoparticle volume fraction increases the temperature of the blood during flow through the stenotic artery. On the other hand, the Prandtl number and suction/injection parameter decrease the temperature of the blood during flow through the stenotic artery. The present research has the potential that be proven highly advantageous for an effective drug delivery in human blood arteries
Magnetized flow of Cu + Al2O3 + H2O hybrid nanofluid in porous medium: Analysis of duality and stability
No full textIn this analysis, we aim to examine the heat transfer and flow characteristics of a copper-aluminum/water hybrid nanofluid in the presence of viscous dissipation, magnetohydrodynamic (MHD), and porous medium effect over the shrinking sheet. The governing equations of the fluid model have been acquired by employment of the model of Tiwari and Das, with additional properties of the hybrid nanofluid. The system of partial differential equations (PDEs) has been converted into ordinary differential equations (ODEs) by adopting the exponential similarity transformation. Similarity transformation is an essential class of phenomenon where the symmetry of the scale helps to reduce the number of independent variables. Note that ODE solutions demonstrate the PDEs symmetrical behavior for the velocity and temperature profiles. With BVP4C solver in the MATLAB program, the system of resulting equations has been solved. We have compared the present results with the published results and found in excellent agreements. The findings of the analysis are also displayed and discussed in depth graphically and numerically. It is discovered that two solutions occur in definite ranges of suction and magnetic parameters. Dual (no) similarity solutions can be found in the range of Sc≤S and Mc≤M (Sc>S and Mc>M). By performing stability analysis, the smallest values of eigenvalue are obtained, suggesting that a stable solution is the first one. Furthermore, the graph of the smallest eigenvalue shows symmetrical behavior. By enhancing the Eckert number values the temperature of the fluid is raised
