Nanomaterials

Research

19 pages, 920 KiB

Open AccessArticle

Instability of Liquid Film with Odd Viscosity over a Non-Uniformly Heated and Corrugated Substrate

by Danting Xue, Ruigang Zhang, Quansheng Liu and Zhaodong Ding

Nanomaterials 2023, 13(19), 2660; https://doi.org/10.3390/nano13192660 - 28 Sep 2023

Cited by 1 | Viewed by 1084

The effect of odd viscosity on the instability of liquid film along a wavy inclined bottom with linear temperature variation is investigated. By utilizing the long-wave approximation, the non-linear evolution equation of the free surface is derived. By applying the normal mode method, [...] Read more.

The effect of odd viscosity on the instability of liquid film along a wavy inclined bottom with linear temperature variation is investigated. By utilizing the long-wave approximation, the non-linear evolution equation of the free surface is derived. By applying the normal mode method, the linear instability of thin film flow is investigated. With the help of multi-scale analysis methods, the weakly non-linear instability of thin film flow is also investigated. The results reveal that the Marangoni effect caused by non-uniform temperature distribution promotes the instability of the liquid film, while the odd viscosity has a stabilizing effect. In addition, for a positive local inclination angle

θ

, an increase in bottom steepness

ζ

inhibits the instability of the liquid film flow. In contrast, with a negative local inclination angle

θ

, increased bottom steepness

ζ

promotes the instability of the liquid film flow. The results of the temporal linear instability analysis and the weakly non-linear instability analysis have been substantiated through numerical simulations of the non-linear evolution equations. Full article

(This article belongs to the Special Issue Advances of Nanoscale Fluid Mechanics)

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15 pages, 368 KiB

Open AccessArticle

Exact Solutions for Non-Isothermal Flows of Second Grade Fluid between Parallel Plates

by Evgenii S. Baranovskii

Nanomaterials 2023, 13(8), 1409; https://doi.org/10.3390/nano13081409 - 19 Apr 2023

Cited by 11 | Viewed by 1202

Abstract

In this paper, we obtain new exact solutions for the unidirectional non-isothermal flow of a second grade fluid in a plane channel with impermeable solid walls, taking into account the fluid energy dissipation (mechanical-to-thermal energy conversion) in the heat transfer equation. It is [...] Read more.

In this paper, we obtain new exact solutions for the unidirectional non-isothermal flow of a second grade fluid in a plane channel with impermeable solid walls, taking into account the fluid energy dissipation (mechanical-to-thermal energy conversion) in the heat transfer equation. It is assumed that the flow is time-independent and driven by the pressure gradient. On the channel walls, various boundary conditions are stated. Namely, we consider the no-slip conditions, the threshold slip conditions, which include Navier’s slip condition (free slip) as a limit case, as well as mixed boundary conditions, assuming that the upper and lower walls of the channel differ in their physical properties. The dependence of solutions on the boundary conditions is discussed in some detail. Moreover, we establish explicit relationships for the model parameters that guarantee the slip (or no-slip) regime on the boundaries. Full article

(This article belongs to the Special Issue Advances of Nanoscale Fluid Mechanics)

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17 pages, 635 KiB

Open AccessArticle

Influence of Stress Jump Condition at the Interface Region of a Two-Layer Nanofluid Flow in a Microchannel with EDL Effects

by Muhammad Raees ul Haq, Ammarah Raees, Hang Xu and Shaozhang Xiao

Nanomaterials 2023, 13(7), 1198; https://doi.org/10.3390/nano13071198 - 28 Mar 2023

Viewed by 1425

Abstract

The influence of stress jump conditions on a steady, fully developed two-layer magnetohydrodynamic electro-osmotic nanofluid in the microchannel, is investigated numerically. A nanofluid is partially filled into the microchannel, while a porous medium, saturated with nanofluid, is immersed into the other half of [...] Read more.

The influence of stress jump conditions on a steady, fully developed two-layer magnetohydrodynamic electro-osmotic nanofluid in the microchannel, is investigated numerically. A nanofluid is partially filled into the microchannel, while a porous medium, saturated with nanofluid, is immersed into the other half of the microchannel. The Brinkmann-extended Darcy equation is used to effectively explain the nanofluid flow in the porous region. In both regions, electric double layers are examined, whereas at the interface, Ochoa-Tapia and Whitaker’s stress jump condition is considered. The non-dimensional velocity, temperature, and volume fraction of the nanoparticle profiles are examined, by varying physical parameters. Additionally, the Darcy number, as well as the coefficient in the stress jump condition, are investigated for their profound effect on skin friction and Nusselt number. It is concluded that, taking into account the change in shear stress at the interface has a significant impact on fluid flow problems. Full article

(This article belongs to the Special Issue Advances of Nanoscale Fluid Mechanics)

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15 pages, 2721 KiB

Open AccessArticle

Spherical Hybrid Nanoparticles for Homann Stagnation-Point Flow in Porous Media via Homotopy Analysis Method

by Xiangcheng You and Jifeng Cui

Nanomaterials 2023, 13(6), 1000; https://doi.org/10.3390/nano13061000 - 9 Mar 2023

Cited by 4 | Viewed by 1458

Abstract

Non-axisymmetric stagnant-point flows for flat plates in porous media containing spherical Cu-Al₂O₃-H₂O nanoparticles are studied using the homotopy analysis method (HAM). The governing equations are transformed into three coupled non-linear ordinary differential equations through similarity transformations. A [...] Read more.

Non-axisymmetric stagnant-point flows for flat plates in porous media containing spherical Cu-Al₂O₃-H₂O nanoparticles are studied using the homotopy analysis method (HAM). The governing equations are transformed into three coupled non-linear ordinary differential equations through similarity transformations. A large degree of freedom is provided by HAM when selecting auxiliary linear operators. By transforming nonlinear coupled ordinary differential equations with variable coefficients into linear ordinary differential equations with constant coefficients, nonlinear coupled ordinary differential equations can be solved. Over the entire domain, these equations can be solved approximately analytically. The analysis involves a discussion of the impact of many physical parameters generated in the proposed model. The results have shown that skin friction coefficients of Cf_x and Cf_y increase with volume fraction of hybrid nanofluid and the coefficient of permeability increasing. For the axisymmetric case of γ = 0, when volume fraction, φ, φ₁, φ₂ = 0, 5%, 10%, 20%, Cf_x = Cf_y = 1.33634, 1.51918, 1.73905, 2.33449, it can be found that the wall shear stress values increase by 13.68%, 30.14%, and 74.69%, respectively. In response to an increase in hybrid nanofluid volume fractions, local Nusselt numbers Nu_x increase. Nu_x decrease and change clearly with the coefficient of permeability increasing in the range of γ < 0; the values of Nu_x are less affected in the range of γ > 0. Full article

(This article belongs to the Special Issue Advances of Nanoscale Fluid Mechanics)

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15 pages, 4022 KiB

Open AccessArticle

Shape-Factor Impact on a Mass-Based Hybrid Nanofluid Model for Homann Stagnation-Point Flow in Porous Media

by Shiyuan Li and Xiangcheng You

Nanomaterials 2023, 13(6), 984; https://doi.org/10.3390/nano13060984 - 8 Mar 2023

Cited by 4 | Viewed by 1535

Abstract

This paper studies the impact of shape factor on a mass-based hybrid nanofluid model for Homann stagnation-point flow in porous media. The HAM-based Mathematica package BVPh 2.0 is suitable for determining approximate solutions of coupled nonlinear ordinary differential equations with boundary conditions. This [...] Read more.

This paper studies the impact of shape factor on a mass-based hybrid nanofluid model for Homann stagnation-point flow in porous media. The HAM-based Mathematica package BVPh 2.0 is suitable for determining approximate solutions of coupled nonlinear ordinary differential equations with boundary conditions. This analysis involves discussions of the impact of the many physical parameters generated in the proposed model. The results show that skin friction coefficients of Cf_x and Cf_y increase with the mass of the first and second nanoparticles of the hybrid nanofluids w₁ and w₂ and with the coefficient of permeability in porous media. For the axisymmetric case of γ = 0, when w₁ = w₂ = 10 gr, w_f = 100 gr and Cf_x = Cf_y = 2.03443, 2.27994, 2.50681, and 3.10222 for σ = 0, 1, 2, and 5. Compared with w₁ = w₂ = 10 gr, w_f = 100 gr, and σ = 0, it can be found that the wall shear stress values increase by 12.06%, 23.21%, and 52.48%, respectively. As the mass of the first and second nanoparticles of the mass-based hybrid nanofluid model increases, the local Nusselt number Nu_x increases. Values of Nu_x obviously decrease and change with an increase in the coefficient of permeability in the range of γ < 0; otherwise, Nu_x is less affected in the range of γ > 0. According to the calculation results, the platelet-shaped nanoparticles in the mass-based hybrid nanofluid model can achieve maximum heat transfer rates and minimum surface friction. Full article

(This article belongs to the Special Issue Advances of Nanoscale Fluid Mechanics)

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15 pages, 2906 KiB

Open AccessArticle

Theoretical Analysis of the Effects of Exothermic Catalytic Chemical Reaction on Transient Mixed Convection Flow along a Curved Shaped Surface

by Hossam A. Nabwey, Muhammad Ashraf, Uzma Ahmad, Ahmed. M. Rashad, Sumayyah I. Alshber and Miad Abu Hawsah

Nanomaterials 2022, 12(24), 4350; https://doi.org/10.3390/nano12244350 - 7 Dec 2022

Cited by 5 | Viewed by 1326

Abstract

The present problem addressed the transient behavior of convective heat and mass transfer characteristics across a curved surface under the influence of exothermic catalytic chemical reactions. The governing non-linear mathematical model wastransformed into a convenient form with the help of a primitive variable [...] Read more.

The present problem addressed the transient behavior of convective heat and mass transfer characteristics across a curved surface under the influence of exothermic catalytic chemical reactions. The governing non-linear mathematical model wastransformed into a convenient form with the help of a primitive variable formulation. The final primitive formed model wassolved numerically by applying the finite difference method. The analysis of the above said computed numerical data in terms of oscillatory heat transfer, skin friction, and oscillatory mass transfer for various emerging parameters, such as the mixed convection parameter

λ_{T}

, modified mixed convection parameter

λ_{c}

, index parameter

n

, activation energy parameter

E

, exothermicparameter

β

, temperature relative parameter

γ

, chemical reaction parameter

λ

, and Schmidt number

S_{c}

is plotted in graphical form. An excellent agreement is depicted for oscillatory heat transfer behavior at the large value of activation energy

E

. The amplitude of heat transfer and prominent fluctuating response in mass transfer with a certain height is found at each value of the index parameter

n

with a good alteration. An increase in the activation energy led to an increase in the surface temperature, which yielded more transient heat transfer in the above-said mechanism. The main novelty of the current study is that first, we ensured the numerical results for the steady state heat and fluid flow and then these obtained results wereused in the unsteady part to obtain numerical results for the transient behavior of the heat and mass transfer mechanism. Full article

(This article belongs to the Special Issue Advances of Nanoscale Fluid Mechanics)

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16 pages, 5385 KiB

Open AccessArticle

Thermal Analysis of Radiative Darcy–Forchheimer Nanofluid Flow Across an Inclined Stretching Surface

by Jifeng Cui, Ahmed Jan, Umer Farooq, Muzamil Hussain and Waseem Asghar Khan

Nanomaterials 2022, 12(23), 4291; https://doi.org/10.3390/nano12234291 - 2 Dec 2022

Cited by 42 | Viewed by 1628

Abstract

Nanofluids have unique features that make them potentially valuable in a variety of medicinal, technical, and industrial sectors. The widespread applications of nanotechnology in modern science have prompted researchers to study nanofluid models from different perspectives. The objective of the current research is [...] Read more.

Nanofluids have unique features that make them potentially valuable in a variety of medicinal, technical, and industrial sectors. The widespread applications of nanotechnology in modern science have prompted researchers to study nanofluid models from different perspectives. The objective of the current research is to study the flow of non-Newtonian nanofluid over an inclined stretching surface immersed in porous media by employing the Darcy–Forchheimer model. Both titanium oxide (

T i O_{2}

) and aluminum oxide (

A l_{2} O_{3}

) are nanoparticles which can be found in blood (based fluid). The consequences of viscous dissipation, thermal radiations, and heat generation are also incorporated. Boundary layer approximations are employed to model the governing system of partial differential equations (PDEs). The governing PDEs with their associated boundary conditions are further altered to a dimensionless form by employing appropriate transformations. The results of the transformed model are collected using local non-similarity approach up to the second level of truncation in association with the built-in finite difference code in MATLAB (bvp4c). Additionally, the impacts of emerging factors on the fluid flow and thermal transport features of the considered flow problem are displayed and analyzed in graphical forms after achieving good agreement between accomplished computational results and published ones. Numerical variations in drag coefficient and Nusselt number are elaborated through the tables. It has been perceived that the enhancement in Casson fluid parameter diminishes the velocity profile. Moreover, it is noted that the porosity parameter and Lorentz’s forces reinforce the resulting frictional factor at the inclined stretching surface. Full article

(This article belongs to the Special Issue Advances of Nanoscale Fluid Mechanics)

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20 pages, 2647 KiB

Open AccessArticle

Rotating Hybrid Nanofluid Flow with Chemical Reaction and Thermal Radiation between Parallel Plates

by Mubashar Arshad, Ali Hassan, Qusain Haider, Fahad M. Alharbi, Najah Alsubaie, Abdullah Alhushaybari, Diana-Petronela Burduhos-Nergis and Ahmed M. Galal

Nanomaterials 2022, 12(23), 4177; https://doi.org/10.3390/nano12234177 - 24 Nov 2022

Cited by 24 | Viewed by 2418

Abstract

This research investigates the two different hybrid nanofluid flows between two parallel plates placed at two different heights,

y_{0}

and

y_{h}

, respectively. Water-based hybrid nanofluids are obtained by using

A l_{2} O_{3}

,

T i O_{2}

[...] Read more.

This research investigates the two different hybrid nanofluid flows between two parallel plates placed at two different heights,

y_{0}

and

y_{h}

, respectively. Water-based hybrid nanofluids are obtained by using

A l_{2} O_{3}

,

T i O_{2}

and

C u

as nanoparticles, respectively. The upper-level plate is fixed, while the lower-level plate is stretchable. The fluid rotates along the y-axis. The governing equations of momentum, energy and concentration are transformed into partial differential equations by using similarity transformations. These transformed equations are grasped numerically at MATLAB by using the boundary value problem technique. The influence of different parameters are presented through graphs. The numerical outcomes for rotation, Nusselt, Prandtl, and Schmidt numbers are obtained in the form of tables. The heat transfer rate increases by augmentation in the thermophoresis parameter, while it decays by increasing the Reynolds number. Oxide nanoparticles hybrid nanofluid proved more efficient as compared to mixed nanoparticles hybrid nanofluid. This research suggests using oxide nanoparticles for good heat transfer. Full article

(This article belongs to the Special Issue Advances of Nanoscale Fluid Mechanics)

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20 pages, 3981 KiB

Open AccessArticle

Dynamic Instability of Functionally Graded Graphene Platelet-Reinforced Porous Beams on an Elastic Foundation in a Thermal Environment

by Jing Zhang, Ying Lv and Lianhe Li

Nanomaterials 2022, 12(22), 4098; https://doi.org/10.3390/nano12224098 - 21 Nov 2022

Cited by 6 | Viewed by 1657

Abstract

Under thermal environment and axial forces, the dynamic instability of functionally graded graphene platelet (GPLs)-reinforced porous beams on an elastic foundation is investigated. Three modes of porosity distributions and GPL patterns are considered. The governing equations are given by the Hamilton principle. On [...] Read more.

Under thermal environment and axial forces, the dynamic instability of functionally graded graphene platelet (GPLs)-reinforced porous beams on an elastic foundation is investigated. Three modes of porosity distributions and GPL patterns are considered. The governing equations are given by the Hamilton principle. On the basis of the differential quadrature method (DQM), the governing equations are changed into Mathieu–Hill equations, and the main unstable regions of the porous composite beams are studied by the Bolotin method. Thermal buckling and thermo-mechanical vibration problems are also studied. The effects of porosity coefficients and GPL weight fraction, dispersion pattern, initial thermal loading, slenderness ratio, geometry and size, boundary conditions, and foundation stiffness are discussed. The conclusions show that an elastic foundation has an obvious enhancement effect on thermal buckling, free vibration, and dynamic instability, which improves the stiffness of the beam. Full article

(This article belongs to the Special Issue Advances of Nanoscale Fluid Mechanics)

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16 pages, 2769 KiB

Open AccessArticle

Convective Heat Transfer in Magneto-Hydrodynamic Carreau Fluid with Temperature Dependent Viscosity and Thermal Conductivity

by Syed Amir Ghazi Ali Shah, Ali Hassan, Najah Alsubaie, Abdullah Alhushaybari, Fahad M. Alharbi, Ahmed M. Galal, Diana-Petronela Burduhos-Nergis and Costica Bejinariu

Nanomaterials 2022, 12(22), 4084; https://doi.org/10.3390/nano12224084 - 20 Nov 2022

Cited by 7 | Viewed by 1756

Abstract

This study is aimed to explore the magneto-hydrodynamic Carreau fluid flow over a stretching/shrinking surface with a convectively heated boundary. Temperature-dependent variable thermophysical properties are utilized to formulate the problem. The flow governing equations are obtained with boundary layer approximation and constitutive relation [...] Read more.

This study is aimed to explore the magneto-hydrodynamic Carreau fluid flow over a stretching/shrinking surface with a convectively heated boundary. Temperature-dependent variable thermophysical properties are utilized to formulate the problem. The flow governing equations are obtained with boundary layer approximation and constitutive relation of the Carreau fluid. The shooting method is utilized to obtain graphical and numeric outcomes. Additionally, initial guesses are generated with the help of Newton’s method. The effect of Weissenberg number, Magnetization, stretching ratio, Prandtl number, suction/blowing parameter, and Lewis number is obtained on velocity, temperature and species continuity profile and analyzed. Shear stress rates and Nusselt number outcomes under body forces influences are present in tabulated data and discussed. It is observed that in absence of magnetization force, B = 0 and strong mass suction

5 \leq S \leq 7.5

effect high rates of Nusselt number is obtained. It is concluded that under the influence of power law index and non-linearity parameter maximum heat transfer and reduced shear stress rates are obtained. Full article

(This article belongs to the Special Issue Advances of Nanoscale Fluid Mechanics)

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18 pages, 4478 KiB

Open AccessArticle

The Thermal Performance Analysis of an Al₂O₃-Water Nanofluid Flow in a Composite Microchannel

by Mirza Farrukh Baig, Gooi Mee Chen and Chih Ping Tso

Nanomaterials 2022, 12(21), 3821; https://doi.org/10.3390/nano12213821 - 28 Oct 2022

Cited by 2 | Viewed by 1448

Abstract

Partial filling of porous medium insert in a channel alleviates the tremendous pressure drop associated with a porous medium saturated channel, and enhances heat transfer at an optimum fraction of porous medium filling. This study pioneered an investigation into the viscous dissipative forced [...] Read more.

Partial filling of porous medium insert in a channel alleviates the tremendous pressure drop associated with a porous medium saturated channel, and enhances heat transfer at an optimum fraction of porous medium filling. This study pioneered an investigation into the viscous dissipative forced convective heat transfer in a parallel-plate channel, partially occupied with a porous medium at the core, under local thermal non-equilibrium condition. Solving the thermal energy equation along the Darcy–Brinkman equation, new exact temperature fields and Nusselt number are presented under symmetrical isoflux thermal boundary condition. Noteworthy is the heat flux bifurcation at the interface between the clear fluid and porous medium driven by viscous dissipation, in cases where the combined hydrodynamic resistance to fluid flow and thermal resistance to fluid conduction is considerable in low Darcy number porous medium insert. However, viscous dissipation does not affect the qualitative variation of the Nusselt number with the fraction of porous medium filling. By using Al₂O₃-Water nanofluid as the working fluid in a uniformly heated microchannel, partially filled with an optimum volume fraction of porous medium, the heat transfer coefficient improves as compared to utilizing water. The accompanied viscous dissipation however has a more adverse impact on the heat transfer coefficient of nanofluids with an increasing Reynolds number. Full article

(This article belongs to the Special Issue Advances of Nanoscale Fluid Mechanics)

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20 pages, 8049 KiB

Open AccessArticle

The Impacts of Viscoelastic Behavior on Electrokinetic Energy Conversion for Jeffreys Fluid in Microtubes

by Na Li, Guangpu Zhao, Xue Gao, Ying Zhang and Yongjun Jian

Nanomaterials 2022, 12(19), 3355; https://doi.org/10.3390/nano12193355 - 26 Sep 2022

Cited by 1 | Viewed by 1478

Abstract

In this paper, the electrokinetic energy conversion (EKEC) efficiency, streaming potential of viscoelastic fluids in microtubes under an external transversal magnetic field, and an axial pressure gradient are investigated. The Jeffreys fluid is applied to model the viscoelastic fluid, and the analytic solution [...] Read more.

In this paper, the electrokinetic energy conversion (EKEC) efficiency, streaming potential of viscoelastic fluids in microtubes under an external transversal magnetic field, and an axial pressure gradient are investigated. The Jeffreys fluid is applied to model the viscoelastic fluid, and the analytic solution of velocity field is obtained using the Green’s function method. The influence of different dimensionless parameters, for instance, the Deborah numbers De and De^*, which are related to the relaxation time and retardation time, respectively; the dimensionless electro-kinetic width K; the dimensionless frequency ω; the volume fraction of the nanoparticles φ and the dimensionless Hartmann number Ha; and three different imposed axial periodic pressure gradients (cosine, triangular, and square) on fluid dynamics are discussed. The physical quantities are graphically described, and the influence of different parameters on the EKEC is analyzed. The results indicate that De promotes the streaming potential and EKEC efficiency of the microtube, while De^* inhibits them. Full article

(This article belongs to the Special Issue Advances of Nanoscale Fluid Mechanics)

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16 pages, 845 KiB

Open AccessArticle

Two-Dimensional Electromagnetohydrodynamic (EMHD) Flows of Fractional Viscoelastic Fluids with Electrokinetic Effects

by Kai Tian, Shujuan An, Guangpu Zhao and Zhaodong Ding

Nanomaterials 2022, 12(19), 3335; https://doi.org/10.3390/nano12193335 - 25 Sep 2022

Cited by 2 | Viewed by 1599

Abstract

The present study provides analytical and numerical solutions for an electromagnetohydrodynamic (EMHD) flow using a Caputo time-fractional Maxwell model. The flow is a typical rectangular channel flow. When the scale of the cross-stream is much smaller than the streamwise and spanwise scales, the [...] Read more.

The present study provides analytical and numerical solutions for an electromagnetohydrodynamic (EMHD) flow using a Caputo time-fractional Maxwell model. The flow is a typical rectangular channel flow. When the scale of the cross-stream is much smaller than the streamwise and spanwise scales, the model is approximated as a two-dimensional slit parallel plate flow. Moreover, the influence of the electric double layer (EDL) at the solid–liquid interface is also considered. The electro-osmotic force generated by the interaction between the electric field and the EDL will induce a flow (i.e., electro-osmotic flow). Due to the application of the electric field at the streamwise and the vertical magnetic field, the flow is driven by Lorentz force along the spanwise direction. Simultaneously, under the action of the magnetic field, the electro-osmotic flow induces a reverse Lorentz force, which inhibits the electro-osmotic flow. The result shows that resonance behavior can be found in both directions in which the flow is generated. However, compared with the classical Maxwell fluid, the slip velocity and resonance behavior of fractional Maxwell fluid are suppressed. In the spanwise direction, increasing the strength of magnetic field first promotes the slip velocity and resonance behavior, and then suppresses them, while in the streamwise direction, both the electro-osmotic flow and resonance behavior are suppressed with the magnetic field. Full article

(This article belongs to the Special Issue Advances of Nanoscale Fluid Mechanics)

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20 pages, 844 KiB

Open AccessArticle

Explicit Solutions of MHD Flow and Heat Transfer of Casson Fluid over an Exponentially Shrinking Sheet with Suction

by Ling Liu, Jing Li and Shijun Liao

Nanomaterials 2022, 12(19), 3289; https://doi.org/10.3390/nano12193289 - 21 Sep 2022

Cited by 5 | Viewed by 2435

Abstract

In this study, the magnetohydrodynamic (MHD) flow and heat transfer of a Casson fluid over an exponentially shrinking sheet with suction is investigated using the homotopy analysis method (HAM). Different from previous numerical methods and analytical techniques, we have obtained an explicit formula [...] Read more.

In this study, the magnetohydrodynamic (MHD) flow and heat transfer of a Casson fluid over an exponentially shrinking sheet with suction is investigated using the homotopy analysis method (HAM). Different from previous numerical methods and analytical techniques, we have obtained an explicit formula solution to the presented nonlinear problem. The explicit solutions of

f (η)

and

θ (η)

are obtained and are valid in the whole domain. The changes in velocity and temperature profiles are studied in cases of different Casson fluid parameter

γ

, magnetic interaction parameter M, suction parameter s, and Prandtl number

P r

. The convergent solutions are verified by comparison with the numerical results. In addition, the skin friction coefficient

C_{f}

and local Nusselt number

N u_{x}

are analyzed using the analytic formulas of

f^{″} (0)

and

θ^{'} (0)

, respectively. The analytical formulas help us intuitively analyze the influence of various parameters at the theoretical level. The effects of different physical quantities on

C_{f}

and

N u_{x}

are thoroughly investigated. Full article

(This article belongs to the Special Issue Advances of Nanoscale Fluid Mechanics)

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