On Three-Dimensional Flow and Heat Transfer over a Non-Linearly Stretching Sheet: Analytical and Numerical Solutions

Khan, Jawad; Mustafa, M.; Hayat, Tasawar; Alsaedi, Ahmed

doi:10.1371/journal.pone.0107287

Cited by 72 publications

(42 citation statements)

References 40 publications

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“…In such situations, it is better to tackle the models numerically. Therefore, for the purpose of solving the models under consideration (γAl 2 O 3 -H 2 O and γAl 2 O 3 -C 2 H 6 O 2 ), a reliable numerical algorithm referred to as Runge-Kutta (RK) with the addition of the shooting technique ( [14,15]) is adopted. For this, the fourth-order RK technique is selected.…”

Section: Mathematical Analysismentioning

confidence: 99%

γ-Nanofluid Thermal Transport between Parallel Plates Suspended by Micro-Cantilever Sensor by Incorporating the Effective Prandtl Model: Applications to Biological and Medical Sciences

et al. 2020

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The flow of nanofluid between infinite parallel plates suspended by micro-cantilever sensors is significant. The analysis of such flows is a rich research area due to the variety of applications it has in chemical, biological and medical sciences. Micro-cantilever sensors play a significant role in accurately sensing different diseases, and they can be used to detect many hazardous and bio-warfare agents. Therefore, flow water and ethylene glycol (EG) composed by γ-nanoparticles is used. Firstly, the governing nanofluid model is transformed into two self-similar nanofluid models on the basis of their effective models. Then, a numerical method is adopted for solution purposes, and both the nanofluid models are solved. To enhance the heat transfer characteristics of the models, the effective Prandtl model is ingrained in the energy equation. The velocity F’(η) decreases with respect to the suction of the fluid, because more fluid particles drags on the surface for suction, leading to an abrupt decrement in F’(η). The velocity F’(η) increases for injection of the fluid from the upper end, and therefore the momentum boundary layer region is prolonged. A high volume fraction factor is responsible for the denser characteristics of the nanofluids, due to which the fluids become more viscous, and the velocity F’(η) drops abruptly, with the magnetic parameters favoring velocity F’(η). An increase in temperature β ( η ) of Al2O3-H2O and γAl2O3-C2H6O2 nanofluids was reported at higher fraction factors with permeable parameter effects. Finally, a comparative analysis is presented by restricting the flow parameters, which shows the reliability of the study.

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Section: Mathematical Analysismentioning

confidence: 99%

γ-Nanofluid Thermal Transport between Parallel Plates Suspended by Micro-Cantilever Sensor by Incorporating the Effective Prandtl Model: Applications to Biological and Medical Sciences

et al. 2020

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“…for the above streamfunctions given in (5). Plugging the ansatz defined in (5) and (6) in the momentum boundary-layer equations (3), we get the coupled nonlinear ordinary differential equations as…”

Section: Flow Theorymentioning

confidence: 99%

“…In addition, with m =0, the Blasius boundary layer has a 3‐dimensional cousin . In this line of study, Khan et al have investigated 3‐dimensional boundary‐layer flow in a still fluid in which the wedge movement has the above forms in both directions and have shown that for positive values of m (in our notation), the thickness of the boundary layer decreases. The boundary layer forms because of the flow of a viscous fluid over the 2‐ to 3‐dimensional stretching and shrinking porous deforming bodies and the longitudinal fins in rectangular duct (Turkyilmazoglu), and the flow model includes both heat transfer and magnetic effect (Turkyilmazoglu).…”

Section: Introductionmentioning

confidence: 98%

“…However, for the mainstream flows defined previously, we follow a slightly different procedure to that first used in Khan et al, Wang, Liu et al, Hayat et al, and Muhammad et al We introduce a new set of similarity transformations in the governing equations so that we get a shear‐to‐strain‐rate ratio or 3‐dimensionality parameter (which is absent in their analyses). Thus, we will focus our study on more global nature of the flow field, which would involve inevitably a full discussion of the boundary‐layer flow with respect to the shear‐to‐strain‐rate ratio parameter.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic and numerical solutions of three‐dimensional boundary‐layer flow past a moving wedge

Kudenatti

Bujurke

2018

Math Methods in App Sciences

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We consider a laminar boundary‐layer flow of a viscous and incompressible fluid past a moving wedge in which the wedge is moving either in the direction of the mainstream flow or opposite to it. The mainstream flows outside the boundary layer are approximated by a power of the distance from the leading boundary layer. The variable pressure gradient is imposed on the boundary layer so that the system admits similarity solutions. The model is described using 3‐dimensional boundary‐layer equations that contains 2 physical parameters: pressure gradient (β) and shear‐to‐strain‐rate ratio parameter (α). Two methods are used: a linear asymptotic analysis in the neighborhood of the edge of the boundary layer and the Keller‐box numerical method for the full nonlinear system. The results show that the flow field is divided into near‐field region (mainly dominated by viscous forces) and far‐field region (mainstream flows); the velocity profiles form through an interaction between 2 regions. Also, all simulations show that the subsequent dynamics involving overshoot and undershoot of the solutions for varying parameter characterizing 3‐dimensional flows. The pressure gradient (favorable) has a tendency of decreasing the boundary‐layer thickness in which the velocity profiles are benign. The wall shear stresses increase unboundedly for increasing α when the wedge is moving in the x‐direction, while the case is different when it is moving in the y‐direction. Further, both analysis show that 3‐dimensional boundary‐layer solutions exist in the range −1<α<∞. These are some interesting results linked to an important class of boundary‐layer flows.

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“…Some recent studies of boundary layer flow in presence of a magnetic field include those of Mabood and his group [19–21]. For the case of a nonlinearly stretching sheet, we note the work of Khan et al [22]. …”

Section: Introductionmentioning

confidence: 99%

The Effects of Thermal Radiation on an Unsteady MHD Axisymmetric Stagnation-Point Flow over a Shrinking Sheet in Presence of Temperature Dependent Thermal Conductivity with Navier Slip

2015

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In this paper, the magnetohydrodynamic (MHD) axisymmetric stagnation-point flow of an unsteady and electrically conducting incompressible viscous fluid in with temperature dependent thermal conductivity, thermal radiation and Navier slip is investigated. The flow is due to a shrinking surface that is shrunk axisymmetrically in its own plane with a linear velocity. The magnetic field is imposed normally to the sheet. The model equations that describe this fluid flow are solved by using the spectral relaxation method. Here, heat transfer processes are discussed for two different types of wall heating; (a) a prescribed surface temperature and (b) a prescribed surface heat flux. We discuss and evaluate how the various parameters affect the fluid flow, heat transfer and the temperature field with the aid of different graphical presentations and tabulated results.

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On Three-Dimensional Flow and Heat Transfer over a Non-Linearly Stretching Sheet: Analytical and Numerical Solutions

Cited by 72 publications

References 40 publications

γ-Nanofluid Thermal Transport between Parallel Plates Suspended by Micro-Cantilever Sensor by Incorporating the Effective Prandtl Model: Applications to Biological and Medical Sciences

γ-Nanofluid Thermal Transport between Parallel Plates Suspended by Micro-Cantilever Sensor by Incorporating the Effective Prandtl Model: Applications to Biological and Medical Sciences

Asymptotic and numerical solutions of three‐dimensional boundary‐layer flow past a moving wedge

The Effects of Thermal Radiation on an Unsteady MHD Axisymmetric Stagnation-Point Flow over a Shrinking Sheet in Presence of Temperature Dependent Thermal Conductivity with Navier Slip

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