A study of quadratic thermal radiation and quadratic convection on viscoelastic material flow with two different heat source modulations

Al‐Kouz, Wael; Mahanthesh, B.; Alqarni, M.S.; Thriveni, K.

doi:10.1016/j.icheatmasstransfer.2021.105364

Cited by 39 publications

(8 citation statements)

References 26 publications

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“…Table 1 displays the thermo physical property values. Equations ( 1)-( 4) reflect the flow-driven equations [35,36] and Equation ( 5) indicates the suitable conditions based on the foregoing assumptions.…”

Section: Formulationmentioning

confidence: 99%

“…Equations ()–() reflect the flow‐driven equations [35, 36] and Equation () indicates the suitable conditions based on the foregoing assumptions.

\begin{equation} {u_x} + {v_y} = 0 \end{equation}

\begin{equation} \def\eqcellsep{&}\begin{array}{l} u{u_x} + v{u_y} = \frac{{{\mu _{thnf}}}}{{{\rho _{thnf}}}}{u_{yy}} + {\beta _c}\left( {C - {C_\infty }} \right)g\cos \alpha + {\beta _T}\left( {T - {T_\infty }} \right)g\cos \alpha \\[10pt] + {\beta _{1T}}{\left( {T - {T_\infty }} \right)^2}g\cos \alpha - {\rho _{thnf}}^{ - 1}\sigma u{B_0}^2 \end{array} \end{equation}

\begin{matrix} u T_{x} + v T_{y} + λ * [\begin{matrix} left u^{2} T_{x x} goodbreak+ v^{2} T_{y y} goodbreak+ 2 u v T_{x y} + \\ left ((), u u_{x} + v u_{y}) T_{x} + ((), u v_{x} + v v_{y}) T_{y} \end{matrix}] = \frac{μ_{t h n f}}{(ρ C_{p})} \end{matrix}

…”

Section: Formulationmentioning

confidence: 99%

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Significance of non‐Fourier flux on a chemically reactive ternary hybrid nanofluid flow (water + Al₂O₃ + ZnO + Fe₃O₄) by a quadratically radiated tended elongating surface

Ramakrishna¹,

Avula²,

Sadananda³

et al. 2022

Z Angew Math Mech

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This study compares the dynamics of dissipative water–alumina–zinc oxide–iron (II, III) oxide ternary hybrid nanofluid (THNF) and water–alumina–zinc oxide binary hybrid nanofluid flows across an inclined surface when quadratic thermal radiation and chemical reaction are important. This report presents the governing equations for the transportation of both dynamics using the thermo‐physical properties of water (base fluid), alumina nanoparticles, zinc oxide nanoparticles and iron (II, III) oxide nanoparticles. To analyse heat transmission phenomena, the Cattaneo–Christov heat flux model was added into the energy equation. With proper similarity transformations, flow‐driven equations are transformed into nonlinear ordinary differential equations and then solved using the bvp4c solver. Slope of linear regression (SLR) is used to determine the rate at which physical parameters increase or decrease as a result of the influence of relevant factors. It is noticed that, when volume percent of nanoparticles (ϕ1) takes input in the range 0≤ϕ1≤0.3$0 \le {\phi _1} \le 0.3$, skin friction coefficient decreases at a rate of 16.548 (in case of THNF) and 14.2018 (in case of binary hybrid nanofluid) per unit value of volume percent of nanoparticles. It is detected that when radiation parameter false(Rdfalse)$( {{R_d}} )$ increases, Nusselt number decreases. The decrement rates are observed as 2.9451 (in case of THNF) and 1.15337 (in case of binary hybrid nanofluid) when radiation parameter takes input in the range 0≤Rd≤0.3$0 \le {R_d} \le 0.3$. Furthermore, it is noticed that, when chemical reaction parameter false(Krfalse)$( {{K_r}} )$ increases, Sherwood number increases. The increment rates are observed as 0.1259 (in case of THNF) and 1.1263 (in case of binary hybrid nanofluid) when chemical reaction parameter takes input in the range 0≤Kr≤0.3$0 \le {K_r} \le 0.3$. There was also good agreement in a validation study between the current and previous results.

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Section: Formulationmentioning

confidence: 99%

“…Equations ()–() reflect the flow‐driven equations [35, 36] and Equation () indicates the suitable conditions based on the foregoing assumptions.

\begin{equation} {u_x} + {v_y} = 0 \end{equation}

\begin{equation} \def\eqcellsep{&}\begin{array}{l} u{u_x} + v{u_y} = \frac{{{\mu _{thnf}}}}{{{\rho _{thnf}}}}{u_{yy}} + {\beta _c}\left( {C - {C_\infty }} \right)g\cos \alpha + {\beta _T}\left( {T - {T_\infty }} \right)g\cos \alpha \\[10pt] + {\beta _{1T}}{\left( {T - {T_\infty }} \right)^2}g\cos \alpha - {\rho _{thnf}}^{ - 1}\sigma u{B_0}^2 \end{array} \end{equation}

\begin{matrix} u T_{x} + v T_{y} + λ * [\begin{matrix} left u^{2} T_{x x} goodbreak+ v^{2} T_{y y} goodbreak+ 2 u v T_{x y} + \\ left ((), u u_{x} + v u_{y}) T_{x} + ((), u v_{x} + v v_{y}) T_{y} \end{matrix}] = \frac{μ_{t h n f}}{(ρ C_{p})} \end{matrix}

…”

Section: Formulationmentioning

confidence: 99%

Significance of non‐Fourier flux on a chemically reactive ternary hybrid nanofluid flow (water + Al₂O₃ + ZnO + Fe₃O₄) by a quadratically radiated tended elongating surface

Ramakrishna¹,

Avula²,

Sadananda³

et al. 2022

Z Angew Math Mech

View full text Add to dashboard Cite

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“…The authors have discussed the impact of the nonlinear thermal radiation and observed that the velocity has a positive function with the effect. [25] analyzed the impact of linear, nonlinear, and QRTR, and irregular heat generation on a quadratic convection viscoelastic flow over a porous sheet. The numerical results revealed that quadratic heat radiation increases the temperature larger than linear radiation.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Quadratic Thermal Radiation on Carreau Fluid Past a Melting Stretchable Cylinder

Jiann

Mohamad

Rawi

et al. 2023

Preprint

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The melting phenomenon plays a vital role in power storage, electronic cooling, and semiconductor manufacturing. A better understanding of the phenomenon may produce an electronic device with optimal performance. In the present study, the melting effect on the flow of Carreau fluid over a stretchable cylinder is analyzed. Since the temperature difference is huge, quadratic thermal radiation is considered to simulate the real situation. To solve the governing equations, suitable similarity variables are applied to convert the complex nonlinear partial equations into ordinary equations. Semi-analytical homotopic solutions of the equation are then determined using the homotopy analysis method. The melting parameter has increased the heat transfer rate by more than 10% for both Prandhl fluids. As the temperature ratio due to the quadratic radiation increase, the local Nusselt number for the fluid with a Prandtl number, 0.71 has been reduced by 25%, and more reduction is observed for fluid with a Prandtl number, 10.

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“…Quadratic convection (nonlinear convection) occurs due to nonlinear density temperature diferences in the buoyant force term, which substantially infuences fow behavior [35,36]. In order to reduce machinery damage, it also has applications in the production of better lubricants [37,38], which prompted a number of researchers to look into the fow carried on by quadratic convective fow. Sampath Kumar et al [39] explored a quadratic convective fow of Jefrey liquid with a Cattaneo-Christov heat fux in the presence of nanoparticles and came to the conclusion that the efect of the buoyancy ratio parameter on the velocity and temperature felds is quite the opposite.…”

Section: Introductionmentioning

confidence: 99%

On the Non‐Fourier’s Heat and Non‐Fick’s Mass Flux for the Quadratic Convection Flow of a Couple Stress Nanofluid with Wu’s Slip

Ibrahim

Gamachu

Abebe

2023

Mathematical Problems in Engineering

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The overall goal of this paper is to look at how non-Fick’s and non-Fourier’s concepts affect the quadratic convection flow of a couple stress nanofluid across an extending surface under Wu’s slip, convective heating, and convective mass transfer conditions. The governing equations in the investigation are also initially stated as higher-order partial differential equations and thereafter rehabilitated into ordinary differential equations via similarity conversions. Finally, the numerical approach of the bvp5c solver in MATLAB R2019a is engaged to solve the resultant equations. It has been researched and shown using graphs and tables how physical characteristics affect the velocity, temperature, and concentration fields. The results show that the velocity profile along the x-direction grows with intensifying values of the couple stress, quadratic convection, buoyancy, and third-order slip constraints, whereas it declines with intensifying values of the fourth-order slip and magnetic field constraints. Also, the results show that as the velocity ratio constraint is increased, the velocity field along the y-axis increases. Furthermore, an augment in the values of the quadratic convection constraint and Schmidt number, respectively, causes a diminution in temperature and concentration distributions. The results of the current study can be used to increase lubricant production and reduce machinery deterioration. Furthermore, this theoretical and numerical deliberation has the potential to be beneficial in the field of bio-fluid dynamics and biomedicine.

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A study of quadratic thermal radiation and quadratic convection on viscoelastic material flow with two different heat source modulations

Cited by 39 publications

References 26 publications

Significance of non‐Fourier flux on a chemically reactive ternary hybrid nanofluid flow (water + Al₂O₃ + ZnO + Fe₃O₄) by a quadratically radiated tended elongating surface

Significance of non‐Fourier flux on a chemically reactive ternary hybrid nanofluid flow (water + Al₂O₃ + ZnO + Fe₃O₄) by a quadratically radiated tended elongating surface

Analysis of Quadratic Thermal Radiation on Carreau Fluid Past a Melting Stretchable Cylinder

On the Non‐Fourier’s Heat and Non‐Fick’s Mass Flux for the Quadratic Convection Flow of a Couple Stress Nanofluid with Wu’s Slip

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A study of quadratic thermal radiation and quadratic convection on viscoelastic material flow with two different heat source modulations

Cited by 39 publications

References 26 publications

Significance of non‐Fourier flux on a chemically reactive ternary hybrid nanofluid flow (water + Al2O3 + ZnO + Fe3O4) by a quadratically radiated tended elongating surface

Significance of non‐Fourier flux on a chemically reactive ternary hybrid nanofluid flow (water + Al2O3 + ZnO + Fe3O4) by a quadratically radiated tended elongating surface

Analysis of Quadratic Thermal Radiation on Carreau Fluid Past a Melting Stretchable Cylinder

On the Non‐Fourier’s Heat and Non‐Fick’s Mass Flux for the Quadratic Convection Flow of a Couple Stress Nanofluid with Wu’s Slip

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Significance of non‐Fourier flux on a chemically reactive ternary hybrid nanofluid flow (water + Al₂O₃ + ZnO + Fe₃O₄) by a quadratically radiated tended elongating surface

Significance of non‐Fourier flux on a chemically reactive ternary hybrid nanofluid flow (water + Al₂O₃ + ZnO + Fe₃O₄) by a quadratically radiated tended elongating surface