Radiative flow of Maxwell nanofluid containing gyrotactic microorganism and energy activation with convective Nield conditions

Waqas, Hassan; Khan, Sami Ullah; Shehzad, Sabir Ali; Imran, Muhammad

doi:10.1002/htj.21451

Cited by 52 publications

(25 citation statements)

References 44 publications

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“…Before compute the solution of above equations, let us transform the equations into dimensionless form by using the following similarity variable

ψ goodbreakinfix= \sqrt{true(a ν true)} x^{⁎} f (η) goodbreakinfix, η goodbreakinfix= \sqrt{\frac{a}{ν}} y^{⁎} goodbreakinfix, u^{⁎} goodbreakinfix= a x^{⁎} f false' (η) goodbreakinfix, v^{⁎} goodbreakinfix= - \sqrt{a ν} f (η) goodbreakinfix, K goodbreakinfix= a x^{⁎} \sqrt{\frac{a}{ν}} w (η),

θ (η) goodbreakinfix= \frac{T - T_{\infty}}{T_{w} - T_{\infty}} goodbreakinfix, ϕ (η) goodbreakinfix= \frac{C - C_{\infty}}{C_{w} - C_{\infty}} goodbreakinfix, χ (η) goodbreakinfix= \frac{n - n_{\infty}}{n_{w} - n_{\infty}} .

…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…Before compute the solution of above equations, let us transform the equations into dimensionless form by using the following similarity variable 25,26 ψ…”

Section: Similarity Variablesmentioning

confidence: 99%

“…The highly nonlinear transformed system (21)(22)(23)(24)(25) with conditions (26,27) is evaluated numerically by using the shooting method (Appendix B). According to this scheme, the BVP is transmuted into IVP by following the below procedure:…”

Section: Numerical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…This mobility of microorganisms is simulated by various stimulators such as chemotaxis, photosynthesis, gyrotactic, and so on. Many recent advancements on this topic can be visualized through Kuznetsov et al [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] Recently, the activation energy has attained the interests of engineers, which was originally proposed by Arrhenius in 1889. This is known as base energy supplied to reactants in chemical processing for the conversion of products.…”

mentioning

confidence: 99%

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Significance of the nonlinear radiative flow of micropolar nanoparticles over porous surface with a gyrotactic microorganism, activation energy, and Nield's condition

Waqas

Khan

Shehzad

et al. 2019

Heat Trans. Asian Res.

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Current continuation presents the numerical study regarding stretched flow micropolar nanofluid over moving the sheet in the existence of activation energy and microorganisms. Furthermore, nonlinear aspects of thermal radiation are also utilized in the energy equation which results in the energy equation becomes highly nonlinear. This investigation has been performed by using convective Nield boundary conditions. First, useful dimensionless variables are implemented to reduce the partial differential into ordinary ones. Later on, the approximate solution of the transformed physical problem is computed by using the shooting scheme. A detailed physical interpretation of obtained results is also presented for velocity, temperature, motile microorganisms density, and mass concentration profiles. A detailed graphical explanation for each engineering parameter has been discussed for some specified range like 0 goodbreakinfix≤ K 1 goodbreakinfix≤ 1.5 , 0.1 goodbreakinfix≤ m goodbreakinfix≤ 0.7 , 0.1 goodbreakinfix≤ K goodbreakinfix≤ 0.7 , 0.1 goodbreakinfix≤ N t goodbreakinfix≤ 2.4 , 0.1 goodbreakinfix≤ γ goodbreakinfix≤ 0.4 , 1.0 goodbreakinfix≤ italicPr goodbreakinfix≤ 1.8 , 0.4 goodbreakinfix≤ R d goodbreakinfix≤ 1.0 , 0.2 goodbreakinfix≤ N b goodbreakinfix≤ 0.8 , 0.1 goodbreakinfix≤ E goodbreakinfix≤ 7.0, and 0.4 goodbreakinfix≤ L b goodbreakinfix≤ 1.0 . The theoretical computations based presented here can be more proficient to attain the maximum efficiency of various thermal extrusion systems and microbial fuel cells.

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“…Before compute the solution of above equations, let us transform the equations into dimensionless form by using the following similarity variable

ψ goodbreakinfix= \sqrt{true(a ν true)} x^{⁎} f (η) goodbreakinfix, η goodbreakinfix= \sqrt{\frac{a}{ν}} y^{⁎} goodbreakinfix, u^{⁎} goodbreakinfix= a x^{⁎} f false' (η) goodbreakinfix, v^{⁎} goodbreakinfix= - \sqrt{a ν} f (η) goodbreakinfix, K goodbreakinfix= a x^{⁎} \sqrt{\frac{a}{ν}} w (η),

θ (η) goodbreakinfix= \frac{T - T_{\infty}}{T_{w} - T_{\infty}} goodbreakinfix, ϕ (η) goodbreakinfix= \frac{C - C_{\infty}}{C_{w} - C_{\infty}} goodbreakinfix, χ (η) goodbreakinfix= \frac{n - n_{\infty}}{n_{w} - n_{\infty}} .

…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…Before compute the solution of above equations, let us transform the equations into dimensionless form by using the following similarity variable 25,26 ψ…”

Section: Similarity Variablesmentioning

confidence: 99%

Section: Numerical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Significance of the nonlinear radiative flow of micropolar nanoparticles over porous surface with a gyrotactic microorganism, activation energy, and Nield's condition

Waqas

Khan

Shehzad

et al. 2019

Heat Trans. Asian Res.

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Numerical study of hydrodynamic flow of a Casson nanomaterial past an inclined sheet under porous medium

Anwar

Rafique

Misiran

et al. 2019

Heat Trans. Asian Res.

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The main aim of the current paper is to investigate the mass and heat transportation of a Casson nanomaterial generated by the inclination of the surface. The magnetic field effect along with suction or injection are considered. The working nanomaterial is taken into consideration based on the concept of the Buongiorno nanofluid theory, which explores the thermal efficiencies of liquid flows under movement of Brownian and thermophoretic phenomena. The emergent system of differential expressions is converted to dimensionless form with the help of the appropriate transformations.This system is numerically executed by the implementation of Keller-Box and Newton's schemes. A good agreement of results can be found with the previous data in a limiting approach. The behavior of the physical quantities under concern, including energy exchange, Sherwood number, and wall shear stress are portrayed through graphs and in tabular form. The Nusselt number and Sherwood number are found to diminish against the altered magnitudes of Brownian motion and the inclination parameter. Moreover, the velocity profile decreases with the growth of the inclination effect. In the same vein, the buoyancy force and solutal buoyancy effects show a direct relation with the velocity field. The outcomes have promising technological uses in liquidbased systems related to stretchable constituents. K E Y W O R D S Casson nanofluid, inclined surface, Keller-Box method, MHD ′ ′ ′ ′ J J J J J j j j j

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Nonlinear mixed convection flow of a tangent hyperbolic fluid with activation energy

Ibrahim

Gizewu

2020

Heat Trans

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In this communication, the dynamics of a non‐Newtonian tangent hyperbolic fluid with nanoparticles past a nonuniformly thickened stretching surface is discussed. We examine the impact of nonlinear mixed convection flow of a hyperbolic tangent fluid with the Cattaneo‐Christov heat and mass diffusion model past a bidirectional stretching surface. The effects of activation energy and magnetic field are incorporated in the analysis. The variables of transformations are used to change the nonlinear partial differential equations into ordinary differential equations (ODEs). Then, these ODEs are numerically solved using the Matlab routine of the bvp4c algorithm. The derailed analysis of the influences of the governing parameters on velocities along the x‐ and y‐axes, temperature and concentration profiles are presented using tables and figures. The outcomes of these parameters reveal that the velocities along the x‐ and y‐axes are decreased for the values of We increasing but the opposite behavior is observed as the value of A increases. The results also show that the values of e and N b rise as the temperature profiles increase. Similar influences are observed on the profile of concentration as the values of F and f rise. As the values of N 1 go from 0.27 to 0.25, the skin‐friction coefficient increases, and similarly, as N b goes from 0.3 to 0.1, − θ false′ false( 0 false) is enhanced.

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Radiative flow of Maxwell nanofluid containing gyrotactic microorganism and energy activation with convective Nield conditions

Abstract: On the account of industrial and technological applica-Arrhenius activation energy, bioconvection, Maxwell nanofluid, thermal radiation, shooting method.

Cited by 52 publications

References 44 publications

Significance of the nonlinear radiative flow of micropolar nanoparticles over porous surface with a gyrotactic microorganism, activation energy, and Nield's condition

Significance of the nonlinear radiative flow of micropolar nanoparticles over porous surface with a gyrotactic microorganism, activation energy, and Nield's condition

Numerical study of hydrodynamic flow of a Casson nanomaterial past an inclined sheet under porous medium

Nonlinear mixed convection flow of a tangent hyperbolic fluid with activation energy

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