Activation energy and binary chemical reaction effects in mixed convective nanofluid flow with convective boundary conditions

Dhlamini, Mlamuli; Kameswaran, Peri K.; Sibanda, Precious; Motsa, S. S.; Mondal, Hiranmoy

doi:10.1016/j.jcde.2018.07.002

Cited by 100 publications

(51 citation statements)

References 31 publications

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“…To maintain the strength of the bioconvection tendency, we assumed that nanoparticle concentrations were diluted in water and the movement of micro‐organisms is free from nanoparticles and the nanofluid suspension is stable for the survival of micro‐organisms. So, we formulated the governing equations as conservation of mass, momentum equation, thermal energy, nanoparticle concentration equations, and density of the unsteady MHD Williamson nanofluid with gyrotactive micro‐organisms by extending Dhlamini et al 5 and taking into account the Williamson fluid along with nanofluids in the presence of motile gyrotactic micro‐organisms:

\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0,

\frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} = ν \frac{\partial^{2} u}{\partial y^{2}} + \sqrt{2 ν} Γ \frac{\partial u}{\partial y} \frac{\partial^{2} u}{\partial y^{2}} - \frac{σ B_{0}^{2} u}{ρ},

\frac{\partial T}{\partial t} + u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} = α_{m} \frac{\partial^{2} T}{\partial y^{2}} + τ true[D_{B} \frac{\partial C}{\partial y} \frac{\partial T}{\partial y} + \frac{D_{T}}{T_{\infty}} {(\frac{\partial T}{\partial y})}^{2} true] + \frac{μ}{ρ c_{p}} {(\frac{\partial u}{\partial y})}^{2},

\frac{\partial C}{\partial t} + u \frac{\partial C}{\partial x} + v \frac{\partial C}{\partial y} = D_{B}

…”

Section: Problem Descriptionmentioning

confidence: 99%

“…Khan et al 4 considered a stretched surface to investigate the impact of activation energy in a binary chemical reaction of Tio 2 ‐CuO‐H 2 O nanomaterials. Dhlamini et al 5 used the spectral quasilinearization method to study mixed convective nanofluid flow and consider the influence of the binary chemical reaction and activation energy. Bilal et al 6 investigated three‐dimensional (3D) magnetohydrodynamics (MHD) rotating flow in consideration of the binary chemical reaction and activation energy.…”

Section: Introduction and Literature Surveymentioning

confidence: 99%

“…Based on the advantageous applications toward industry, the author was motivated to extend Dhlamini et al 5 by adding the Williamson fluid in the momentum equation and gyrotactic micro‐organisms density equations. The governing equations are solved by similarity transformation and numerically using the fifth‐order RK method using the shooting technique.…”

Section: Introduction and Literature Surveymentioning

confidence: 99%

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Activation energy and binary chemical reaction on unsteady MHD Williamson nanofluid containing motile gyrotactic micro‐organisms

Gorji

2020

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The author presents the influence of Arrhenius activation energy and binary chemical reaction on an unsteady magnetohydrodynamics Williamson nanofluid with motile gyrotactic micro‐organisms. The governing equations are converted to coupled ordinary differential equations with similarity transformations and the fifth‐order Runge‐Kutta Fehlberg method and the shooting algorithm is applied to solve these equations using the appropriate boundary conditions. A detailed investigation considering the effects of different physical parameters on the profiles like velocity, temperature, concentration, and density of motile gyrotactic micro‐organisms was done and plotted graphically. It is found that the thermal boundary layer enhances for the chemical reaction rate and the solutal boundary layer increases for activation energy. Furthermore, the nondimensional Williamson parameter reduces for the velocity profile. The author studied the wall temperature gradient of different fluids and found that temperature gradient decreased for the present study. Comparisons of the present result with published work were done to verify the present code.

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\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0,

\frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} = ν \frac{\partial^{2} u}{\partial y^{2}} + \sqrt{2 ν} Γ \frac{\partial u}{\partial y} \frac{\partial^{2} u}{\partial y^{2}} - \frac{σ B_{0}^{2} u}{ρ},

\frac{\partial T}{\partial t} + u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} = α_{m} \frac{\partial^{2} T}{\partial y^{2}} + τ true[D_{B} \frac{\partial C}{\partial y} \frac{\partial T}{\partial y} + \frac{D_{T}}{T_{\infty}} {(\frac{\partial T}{\partial y})}^{2} true] + \frac{μ}{ρ c_{p}} {(\frac{\partial u}{\partial y})}^{2},

\frac{\partial C}{\partial t} + u \frac{\partial C}{\partial x} + v \frac{\partial C}{\partial y} = D_{B}

…”

Section: Problem Descriptionmentioning

confidence: 99%

Section: Introduction and Literature Surveymentioning

confidence: 99%

Section: Introduction and Literature Surveymentioning

confidence: 99%

See 1 more Smart Citation

Activation energy and binary chemical reaction on unsteady MHD Williamson nanofluid containing motile gyrotactic micro‐organisms

Gorji

2020

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“…Thermal radiation effect with viscous dissipation in the fluid flow over a nonlinear stretching sheet was investigated by Cortell 14 . One of the most important properties of thermal conductivity for nanofluids is working with viscous dissipation and thermal radiation, which is discussed by different authors 15‐19 . Most of the scientists and engineers aim to work at high temperature for various catalytic processes.…”

Section: Introductionmentioning

confidence: 99%

Influence of an inclined stretching cylinder over MHD mixed convective nanofluid flow due to chemical reaction and viscous dissipation

2020

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This paper analyzed the steady two-dimensional magnetohydrodynamic mixed convective viscous nanofluid and heat transfer toward an inclined stretching cylinder with chemical reaction and uniform magnetic field. The governing partial differential equation in a cylindrical form is reduced to a set of nonlinear ordinary differential equations by using appropriate similarity transformation and solved numerically by spectral quasilinearization methods (SQLMs). A new approach of this method is employed to derive numerical expressions for velocity, temperature, and concentration profile. The convergence and accuracy of our numerical scheme are observed. The SQLM is employed to find out the convergent series solution. There is an increase in the temperature profiles due to the increase in the thermophoresis parameter. The increase in effective Eckert number results in the increase of the temperature profile. K E Y W O R D SMHD flow, stretching cylinder, viscous dissipation

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“…Hayat et al 26 inspected the influence of the mixed convection flow model with non‐Darcy's resistance, activation energy, chemical reaction, thermophoresis, Brownian motion, and thermal radiation with vertical asymmetric compliant channel walls for magnetoperistalsis of a Jeffrey nanomaterial. Dhlamini et al 27 reported unsteady mixed convective flow of binary chemical reaction and activation energy with thermophoresis, Brownian motion, and viscous dissipation on the concentration of chemical species, temperature of the fluid, and velocity of the fluid for a boundary of infinite length.…”

Section: Introductionmentioning

confidence: 99%

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

Ibrahim

Gizewu

2020

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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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Activation energy and binary chemical reaction effects in mixed convective nanofluid flow with convective boundary conditions

Cited by 100 publications

References 31 publications

Activation energy and binary chemical reaction on unsteady MHD Williamson nanofluid containing motile gyrotactic micro‐organisms

Activation energy and binary chemical reaction on unsteady MHD Williamson nanofluid containing motile gyrotactic micro‐organisms

Influence of an inclined stretching cylinder over MHD mixed convective nanofluid flow due to chemical reaction and viscous dissipation

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

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