# Slip Effects on MHD Squeezing Flow of Jeffrey Nanofluid in Horizontal Channel with Chemical Reaction

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Formulation

## 3. Results and Discussion

## 4. Physical Quantities of Interest

## 5. Conclusions

- The flow velocity increases as the plates move closer $(S>0)$ and it decreases as the plates move apart $(S<0)$ near the vicinity of the upper plate.
- The wall shear stress increases as S, $\gamma $ and $Ha$ rise, while it reduces with an increase in ${\lambda}_{1}$, $Da$ and $De$.
- The enhancement of ${\lambda}_{1}$ and $Ha$ decelerate the fluid velocity, temperature, and concentration.
- The flow velocity adjacent to the upper plate region slows down for increasing $\gamma $, $Da$ and $De$.
- The fluid temperature and heat transfer rate enhance when $Pr$, $Ec$ and ${N}_{t}$ increases, whereas the opposite effect is observed with an increase in ${N}_{b}$.
- The rise of ${N}_{b}$ increases the nanoparticle concentration and decreases the mass transfer rate.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

Roman letters | |

B | magnetic field |

${c}_{f}$ | concentration susceptibility |

${c}_{p}$ | specific heat of nanoparticles |

C | nanoparticle concentration |

${C}_{w}$ | concentration at upper plate |

${D}_{B}$ | Brownian diffusion coefficient |

${D}_{T}$ | Thermophoretic diffusion coefficient |

$De$ | Deborah Number |

$Da$ | Darcy Number |

$Ec$ | Eckert Number |

$Ha$ | Hartmann number |

h | distance between two plates |

${k}_{1}$ | permeability of porous medium |

${k}_{f}$ | thermal conductivity of fluid |

${k}_{c}$ | rate of chemical reaction |

$Le$ | Lewis number |

l | initial distance between two surfaces (at $t=0$) |

${N}_{1}$ | velocity slip |

${N}_{b}$ | Brownian motion parameter |

${N}_{t}$ | thermophoresis parameter |

$Pr$ | Prandtl number |

S | squeeze number |

R | chemical reaction parameter |

T | fluid temperature |

${T}_{w}$ | temperature at upper plate |

${T}_{m}$ | ambient temperature |

t | time |

u | fluid velocity in x direction |

v | fluid velocity in y direction |

${v}_{w}$ | velocity at upper plate |

$(x,y)$ | cartesian coordinates |

Greek symbols | |

$\alpha $ | constant |

${\alpha}_{f}$ | thermal diffusivity of Jeffrey fluid |

$\gamma $ | slip parameter |

f | dimensionless velocity parameter |

$\theta $ | dimensionless temperature parameter |

$\delta $ | dimensionless length |

$\varphi $ | Dimensionless concentration parameter |

$\eta $ | boundary layer thickness |

${\nu}_{f}$ | kinematic viscosity |

$\sigma $ | electrical conductivity |

${\rho}_{f}$ | fluid density |

${\rho}_{p}$ | density of nanoparticles |

$\phi $ | porosity of porous medium |

${\lambda}_{1}$ | ratio of relaxation to retardation times |

${\lambda}_{2}$ | retardation time |

$\tau $ | ratio of heat capacities of nanoparticles and fluid |

## References

- Eastman, J.A.; Choi, S.U.S.; Li, S.; Yu, W.; Thompson, L.J. Anomalously increased effective thermal conductivities of eth-ylene glycol-based nanofluids containing copper nanoparticles. Appl. Phys. Lett.
**2001**, 78, 718–720. [Google Scholar] [CrossRef] - Wong, K.V.; De Leon, O. Applications of nanofluids: Current and future. Adv. Mech. Eng.
**2010**. [Google Scholar] [CrossRef] [Green Version] - Buongiorno, J. Convective Transport in Nanofluids. ASME J. Heat Transf.
**2006**, 128, 240–250. [Google Scholar] [CrossRef] - Kuznetsov, A.V.; Nield, D.A. The onset of double-diffusive nanofluid convection in a layer of a saturated porous medium. Transp. Porous Medium
**2010**, 85, 941–951. [Google Scholar] [CrossRef] - Sheikholeslami, M.; Hatami, M.; Domairry, G. Numerical simulation of two phase unsteady nanofluid flow and heat transfer between parallel plates in presence of time dependent magnetic field. J. Taiwan Inst. Chem. Eng.
**2015**, 46, 43–50. [Google Scholar] [CrossRef] - Noor, N.A.M.; Shafie, S.; Admon, M.A. Effects of Viscous Dissipation and Chemical Reaction on MHD Squeezing Flow of Casson Nanofluid between Parallel Plates in a Porous Medium with Slip Boundary Condition. Eur. Phys. J. Plus
**2020**, 135. [Google Scholar] [CrossRef] - Stefan, M. Experiments on apparent adhesion. Lond. Edinb. Dublin Philos. Mag. J. Sci.
**1874**, 47, 465–466. [Google Scholar] [CrossRef] - Reynolds, O. On the theory of lubrication and its application to Mr. Beauchamp tower’s experiments, including an experimental determination of the viscosity of olive oil. Philos. Trans. R. Soc. Lond.
**1886**, 177, 157–234. [Google Scholar] [CrossRef] - Archibald, F.R. Load capacity and time relations for squeeze films. Trans. ASME
**1956**, 78, 231–245. [Google Scholar] [CrossRef] - Jackson, J.D. A study of squeezing flow. Applied Scientific Research. Trans. ASME
**1963**, 11, 148–152. [Google Scholar] [CrossRef] - Ishizawa, S. The unsteady flow between two parallel discs with arbitrary varying gap width. Bull. Jpn. Soc. Mech. Eng.
**1966**, 9, 533–550. [Google Scholar] [CrossRef] - Leider, P.J.; Bird, R.B. Squeezing Flow between Parallel Disks: Theoretical Analysis. Ind. Eng. Chem. Fundam.
**1974**, 13, 336–341. [Google Scholar] [CrossRef] - Grimm, R.J. Squeezing flows of Newtonian liquid films: An analysis including fluid inertia. Appl. Sci. Res.
**1976**, 32, 149–166. [Google Scholar] [CrossRef] - Wang, C.Y. The squeezing of a fluid between two plates. J. Appl. Mech.
**1976**, 43, 579–583. [Google Scholar] [CrossRef] - Bujurke, N.M.; Achar, P.K.; Pai, N.P. Computer extended series for squeezing flow between plates. Fluid Dyn. Res.
**1995**, 16, 173–187. [Google Scholar] [CrossRef] - Noor, N.A.M.; Shafie, S.; Admon, M.A. Unsteady MHD squeezing flow of Jeffrey fluid in a porous medium with thermal radiation, heat generation/absorption and chemical reaction. Phys. Scr.
**2020**, 95. [Google Scholar] [CrossRef] - Khan, U.; Ahmed, N.; Khan, S.I.; Zaidi, Z.A.; Xiao-Jun, Y.; Mohyud-Din, S.T. On unsteady two-dimensional and axisymmet-ric squeezing flow between parallel plates. Alex. Eng. J.
**2014**, 53, 463–468. [Google Scholar] [CrossRef] [Green Version] - Gaffar, S.A.; Prasad, V.R.; Bég, O.A. Numerical study of flow and heat transfer of non-Newtonian tangent hyperbolic fluid from a sphere with Biot number effects. Alex. Eng. J.
**2015**, 54, 829–841. [Google Scholar] [CrossRef] [Green Version] - Ali, A.; Asghar, S. Analytic solution for oscillatory flow in a channel for Jeffrey fluid. J. Aerosp. Eng.
**2012**, 27, 644–651. [Google Scholar] [CrossRef] - Sharma, B.D.; Yadav, P.K.; Filippov, A. A Jeffrey-fluid model of blood flow in tubes with stenosis. Colloid J.
**2017**, 79, 849–856. [Google Scholar] [CrossRef] - Mukhopadhyay, S. MHD boundary layer flow and heat transfer over an exponentially stretching sheet embedded in a thermally stratified medium. Alex. Eng. J.
**2013**, 52, 259–265. [Google Scholar] [CrossRef] [Green Version] - Hayat, T.; Sajjad, R.; Asghar, S. Series solution for MHD channel flow of a Jeffrey fluid. Commun. Nonlinear Sci. Numer. Simul.
**2010**, 15, 2400–2406. [Google Scholar] [CrossRef] - Muhammad, T.; Hayat, T.; Alsaedi, A.; Qayyum, A. Hydromagnetic unsteady squeezing flow of Jeffrey fluid between two parallel plates. Chin. J. Phys.
**2017**, 55, 1511–1522. [Google Scholar] [CrossRef] - Ahmad, K.; Ishak, A. Magnetohydrodynamic flow and heat transfer of a Jeffrey fluid towards a stretching vertical surface. Therm. Sci.
**2015**. [Google Scholar] [CrossRef] [Green Version] - Hayat, T.; Abbas, T.; Ayub, M.; Muhammad, T.; Alsaedi, A. On Squeezed Flow of Jeffrey Nanofluid between Two Parallel Disks. Appl. Sci.
**2016**, 6, 346. [Google Scholar] [CrossRef] - Sheikholeslami, M.; Ganji, D.D.; Ashorynejad, H.R. Investigation of squeezing unsteady nanofluid flow using ADM. Powder Technol.
**2013**, 239, 259–265. [Google Scholar] [CrossRef] - Pourmehran, O.; Rahimi-Gorji, M.; Gorji-Bandpy, M.; Ganji, D.D. Analytical investigation of squeezing unsteady nanofluid flow between parallel plates by LSM and CM. Alex. Eng. J.
**2014**, 54, 17–26. [Google Scholar] [CrossRef] [Green Version] - Gorgani, H.H.; Maghsoudi, P.; Sadeghi, S. An innovative approach for study of thermal behavior of an unsteady nanofluid squeezing flow between two parallel plates utilizing artificial neural network. Eur. J. Sustain. Dev. Res.
**2019**, 3. [Google Scholar] [CrossRef] [Green Version] - Acharya, N.; Das, K.; Kundu, P.K. The squeezing flow of Cu-water and Cu-kerosene nanofluids between two parallel plates. Alex. Eng. J.
**2016**, 55, 1177–1186. [Google Scholar] [CrossRef] [Green Version] - Azimi, M.; Riazi, R. MHD unsteady GO-water squeezing nanofluid flow heat and mass transfer between two infinite parallel moving plates: Analytical investigation. Sadhana
**2017**, 42, 335–341. [Google Scholar] [CrossRef] [Green Version] - Sheikholeslami, M.; Ganji, D.D.; Rashidi, M.M. Magnetic field effect on unsteady nanofluid flow and heat transfer using Buongiorno model. J. Magn. Magn. Mater.
**2016**, 416, 164–173. [Google Scholar] [CrossRef] - Madaki, A.G.; Roslan, R.; Rusiman, M.S.; Raju, C.S.K. An innovative approach for study of thermal behavior of an unsteady nanofluid squeezing flow between two parallel plates utilizing artificial neural network. Alex. Eng. J.
**2017**, 57, 1033–1040. [Google Scholar] [CrossRef] - Ullah, I.; Shafie, S.; Khan, I. Soret and Dufour effects on unsteady mixed convection slip flow of Casson fluid over a nonlinearly stretching sheet with convective boundary condition. Sci. Rep.
**2017**, 7. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Khan, U.; Ahmed, N.; Asadullah, M.; Mohyud-din, S.T. Effects of viscous dissipation and slip velocity on two dimensional and axisymmetric squeezing flow of Cu-water and Cu-kerosene nanofluids. Propuls. Power Res.
**2015**, 4, 40–49. [Google Scholar] [CrossRef] [Green Version] - Singh, K.; Rawat, S.K.; Kumar, M. Heat and mass transfer on squeezing unsteady MHD nanofluid flow between parallel plates with slip velocity effect. J. Nanosci.
**2016**. [Google Scholar] [CrossRef] [Green Version] - Sobamowo, G.M.; Jayesimi, L.O. Squeezing Flow Analysis of Nanofluid Under the Effects of Magnetic Field and Slip Boundary Conditions Using Chebychev Spectral Collocation Method. Fluid Mech.
**2017**, 3, 54–60. [Google Scholar] [CrossRef] [Green Version] - Sobamowo, M.G.; Akinshilo, A.T.; Yinusa, A.A. Thermo-Magneto-Solutal Squeezing Flow of Nanofluid between Two Parallel 564 Disks Embedded in a Porous Medium: Effects of Nanoparticle Geometry, Slip and Temperature Jump Conditions. Model. Simul. Eng.
**2018**. [Google Scholar] [CrossRef] - Ullah, I.; Bhattacharyya, K.; Shafie, S.; Khan, I. Unsteady MHD mixed convection slip flow of Casson fluid over nonlinearly stretching sheet embedded in a porous medium with chemical reaction, thermal radiation, heat generation/absorption and convective boundary conditions. PLoS ONE
**2016**, e0165348. [Google Scholar] [CrossRef] [Green Version] - Ullah, I.; Waqas, M.; Hayat, T.; Alsaedi, A.; Khan, M. Thermally radiated squeezed flow of magneto-nanofluid between two parallel disks with chemical reaction. J. Therm. Anal. Calorim.
**2019**, 135, 1021–1030. [Google Scholar] [CrossRef] - Mohamed, R.A.; Rida, S.Z.; Arafa, A.A.M.; Mubarak, M.S. Heat and mass transfer in an unsteady Magnetohydrodynamics Al2O3-water nanofluid squeezed between two parallel radiating plates embedded in porous media with chemical reaction. J. Heat Transf. Trans. ASME
**2020**, 142. [Google Scholar] [CrossRef] - Raju, C.S.K.; Babu, M.J.; Sandeep, N. Chemically reacting radiative MHD Jeffrey nanofluid flow over a cone in porous medium. Int. J. Eng. Res. Afr.
**2016**, 19, 75–90. [Google Scholar] [CrossRef] - Shankar, U.; Naduvinamani, N.B. Magnetized impacts of Brownian motion and thermophoresis on unsteady squeezing flow 578 of nanofluid between two parallel plates with chemical reaction and Joule heating. Heat Transf. Asian Res.
**2019**, 48, 4174–4202. [Google Scholar] [CrossRef] - Noor, N.A.M.; Shafie, S.; Admon, M.A. MHD Squeezing Flow of Casson Nanofluid with Chemical Reaction, Thermal Radiation and Heat Generation/Absorption. J. Adv. Res. Fluid Mech. Therm. Sci.
**2020**, 68, 94–111. [Google Scholar] [CrossRef] - Song, J.; An, W.; Wu, Y.; Tian, W. Neutronics and Thermal Hydraulics Analysis of a Conceptual Ultra-High Temperature MHD Cermet Fuel Core for Nuclear Electric Propulsion. Front. Energy Res.
**2018**, 6. [Google Scholar] [CrossRef] - Sharma, D.; Pandey, K.M.; Debbarma, A.; Choubey, G. Numerical Investigation of heat transfer enhancement of SiO2-water based nanofluids in light water nuclear reactor. Mater. Today Proc.
**2017**, 4, 10118–10122. [Google Scholar] [CrossRef] - Noor, N.A.M.; Shafie, S.; Admon, M.A. Unsteady MHD flow of Casson nanofluid with chemical reaction, thermal radiation 592 and heat generation/absorption. MATEMATIKA
**2019**, 35, 33–52. [Google Scholar] [CrossRef] [Green Version] - Naduvinamani, N.B.; Shankar, U. Thermal-diffusion and thermo-diffusion effects on squeezing flow of unsteady magnetohydrodynamic Casson fluid between two parallel plates with thermal radiation. Sadhana
**2019**, 44. [Google Scholar] [CrossRef] [Green Version] - Mustafa, M.; Hayat, T.; Obaidat, S. On heat and mass transfer in the unsteady squeezing flow between parallel plates. Meccanica
**2012**, 47, 1581–1589. [Google Scholar] [CrossRef] - Gupta, A.K.; Ray, S.S. Numerical treatment for investigation of squeezing unsteady nanofluid flow between two parallel plates. Powder Technol.
**2015**, 279, 282–289. [Google Scholar] [CrossRef] - Celik, I. Squeezing flow of nanofuids of Cu-water and kerosene between two parallel plates by Gegenbauer wavelet collocation method. Eng. Comput.
**2019**. [Google Scholar] [CrossRef] - Noor, N.A.M.; Shafie, S.; Admon, M.A. Impacts of chemical reaction on squeeze flow of MHD Jeffrey fluid in horizontal porous channel with slip condition. Phys. Scr.
**2021**, 96. [Google Scholar] [CrossRef]

**Table 1.**Numerical outputs of $-{f}^{\u2033}\left(1\right)$ for S as ${\lambda}_{1}\to \infty $, $Da\to \infty $, $De=$${N}_{b}={10}^{-10}$, $Ha=\gamma =Ec=\delta ={N}_{t}=R=0$ and $Pr=Le=1$.

$-{\mathit{f}}^{\u2033}\left(1\right)$ | |||
---|---|---|---|

$\mathit{S}$ | Wang [14] | Khan et al. [17] | Present Results |

−0.9780 | 2.235 | 2.1915 | 2.1917 |

−0.4977 | 2.6272 | 2.6193 | 2.6194 |

−0.09998 | 2.9279 | 2.9277 | 2.9277 |

0 | 3.000 | 3.000 | 3.000 |

0.09403 | 3.0665 | 3.0663 | 3.0664 |

0.4341 | 3.2969 | 3.2943 | 3.2943 |

1.1224 | 3.714 | 3.708 | 3.708 |

**Table 2.**Numerical outputs of $-{f}^{\u2033}\left(1\right)$, $-{\theta}^{\prime}\left(1\right)$ and $-{\varphi}^{\prime}\left(1\right)$ for S as ${\lambda}_{1}\to \infty $, $Da\to \infty $, $De={N}_{b}={10}^{-10}$, $Ha=\gamma ={N}_{t}=0$, $\delta =0.1$ and $Pr=Ec=Le=R=1$.

Naduvinamani and Shankar [47] | Present Outputs | |||||
---|---|---|---|---|---|---|

$\mathit{S}$ | $-{\mathit{f}}^{\u2033}\left(\mathbf{1}\right)$ | $-{\theta}^{\prime}\left(\mathbf{1}\right)$ | $-{\varphi}^{\prime}\left(\mathbf{1}\right)$ | $-{\mathit{f}}^{\u2033}\left(\mathbf{1}\right)$ | $-{\theta}^{\prime}\left(\mathbf{1}\right)$ | $-{\varphi}^{\prime}\left(\mathbf{1}\right)$ |

−1.0 | 2.170091 | 3.319899 | 0.804559 | 2.170255 | 3.319904 | 0.804558 |

−0.5 | 2.617404 | 3.129491 | 0.781402 | 2.617512 | 3.129556 | 0.781404 |

0.01 | 3.007134 | 3.047092 | 0.761225 | 3.007208 | 3.047166 | 0.761229 |

0.5 | 3.336449 | 3.026324 | 0.744224 | 3.336504 | 3.026389 | 0.744229 |

2.0 | 4.167389 | 3.118551 | 0.701813 | 4.167412 | 3.118564 | 0.701819 |

**Table 3.**Numerical outputs of the Nusselt number for $Pr$ and $Ec$ when ${\lambda}_{1}\to \infty $, $Da\to \infty $, $De={N}_{b}={10}^{-10}$, $Ha=\gamma ={N}_{t}=0$, $\delta =0.1$, $S=0.5$ and $Le=R=1$.

$-{\mathit{\theta}}^{\prime}\left(1\right)$ | |||||
---|---|---|---|---|---|

$\mathit{Pr}$ | $\mathit{Ec}$ | Mustafa et al. [48] | Gupta and Ray [49] | Celik [50] | Present Results |

0.5 | 1.0 | 1.522368 | 1.522367 | 1.522367 | 1.522401 |

1.0 | 1.0 | 3.026324 | 3.026323 | 3.026324 | 3.026389 |

2.0 | 1.0 | 5.980530 | 5.980530 | 5.980530 | 5.980652 |

5.0 | 1.0 | 14.43941 | 14.43941 | 14.43941 | 14.43965 |

1.0 | 0.5 | 1.513162 | 1.513162 | 1.513162 | 1.513194 |

1.0 | 1.2 | 3.631588 | 3.631588 | 3.631588 | 3.631667 |

1.0 | 2.0 | 6.052647 | 6.052647 | 6.052647 | 6.052778 |

1.0 | 5.0 | 15.13162 | 15.13162 | 15.13162 | 15.13194 |

**Table 4.**Numerical results of $-(1+1/{\lambda}_{1}){f}^{\u2033}\left(1\right)$, $-{\theta}^{\prime}\left(1\right)$ and ${\varphi}^{\prime}\left(1\right)$ for S when $De=\gamma =$$0.01$, $\delta =Ha=Ec={N}_{b}={N}_{t}=0.1$, ${\lambda}_{1}=Da=1$ and $Pr=Le=R=1.5$.

S | $-(1+1/{\mathit{\lambda}}_{1}){\mathit{f}}^{\u2033}\left(1\right)$ | $-{\mathit{\theta}}^{\prime}\left(1\right)$ | ${\mathit{\varphi}}^{\prime}\left(1\right)$ |
---|---|---|---|

−2.5 | 4.727939 | 1.244305 | 2.526508 |

−2.0 | 5.210547 | 1.158067 | 2.403976 |

−1.5 | 5.653556 | 1.097885 | 2.308981 |

−1.0 | 6.063763 | 1.055755 | 2.233626 |

−0.5 | 6.446384 | 1.026437 | 2.172665 |

0 | 6.805498 | 1.006412 | 2.122519 |

0.5 | 7.144352 | 0.993229 | 2.080659 |

1.0 | 7.465567 | 0.985166 | 2.045278 |

1.5 | 7.771288 | 0.980981 | 2.015046 |

2.0 | 8.063291 | 0.979766 | 1.988971 |

2.5 | 8.343065 | 0.980837 | 1.966294 |

**Table 5.**Numerical outputs of $-(1+1/{\lambda}_{1}){f}^{\u2033}\left(1\right)$ for S, ${\lambda}_{1}$, $Ha$, $Da$, $De$ and $\gamma $ when $\delta =Ec={N}_{b}={N}_{t}=0.1$ and $Pr=Le=R=1.5$.

S | ${\mathit{\lambda}}_{1}$ | $\mathit{Ha}$ | $\mathit{Da}$ | $\mathit{\gamma}$ | $\mathit{De}$ | $-(1+1/{\mathit{\lambda}}_{1}){\mathit{f}}^{\u2033}\left(1\right)$ |
---|---|---|---|---|---|---|

−1.5 | 1.5 | 0.1 | 1 | 0.01 | 0.01 | 4.444929 |

−1.0 | 4.866867 | |||||

−0.5 | 5.253721 | |||||

0 | 5.611752 | |||||

0.5 | 5.945698 | |||||

1.0 | 6.259225 | |||||

1.5 | 6.555223 | |||||

1.0 | 1.0 | 0.1 | 1 | 0.01 | 0.01 | 7.465567 |

1.5 | 6.259225 | |||||

2.0 | 5.664561 | |||||

2.5 | 5.310315 | |||||

3.0 | 5.075164 | |||||

3.5 | 4.907676 | |||||

1.0 | 1.5 | 1.0 | 1.0 | 0.01 | 0.01 | 6.430432 |

1.5 | 6.640604 | |||||

2.0 | 6.924462 | |||||

2.5 | 7.273334 | |||||

3.0 | 7.678004 | |||||

3.5 | 8.129483 | |||||

1.0 | 1.5 | 0.1 | 1.0 | 0.01 | 0.01 | 6.259225 |

1.5 | 6.161199 | |||||

2.0 | 6.111640 | |||||

2.5 | 6.081726 | |||||

3.0 | 6.061708 | |||||

3.5 | 6.047372 | |||||

1.0 | 1.5 | 0.1 | 1.0 | 0.01 | 0.01 | 6.259225 |

0.03 | 6.985274 | |||||

0.05 | 7.901794 | |||||

0.07 | 9.093433 | |||||

0.09 | 12.208567 | |||||

1.0 | 1.5 | 0.1 | 1.0 | 0.01 | 0.010 | 6.259225 |

0.011 | 6.258774 | |||||

0.012 | 6.258324 | |||||

0.013 | 6.257884 | |||||

0.014 | 6.257454 |

**Table 6.**Numerical outputs of $-{\theta}^{\prime}\left(1\right)$ for $Ec$, $Pr$, ${N}_{b}$ and ${N}_{t}$ when $De=\gamma =0.01$, $Ha=\delta =0.1$, $S=Da=1$ and ${\lambda}_{1}=Le=R=1.5$.

$\mathit{Ec}$ | $\mathit{Pr}$ | ${\mathit{N}}_{\mathit{b}}$ | ${\mathit{N}}_{\mathit{t}}$ | $-{\mathit{\theta}}^{\prime}\left(1\right)$ |
---|---|---|---|---|

0.1 | 1.5 | 0.1 | 0.1 | 0.806612 |

0.2 | 1.620920 | |||

0.3 | 2.443096 | |||

0.4 | 3.273315 | |||

0.5 | 4.111761 | |||

0.6 | 4.958621 | |||

0.1 | 1.0 | 0.1 | 0.1 | 0.547527 |

1.5 | 0.806612 | |||

2.0 | 1.057583 | |||

2.5 | 1.301498 | |||

3.0 | 1.539288 | |||

0.1 | 1.5 | 0.2 | 0.1 | 0.783219 |

0.4 | 0.739423 | |||

0.6 | 0.699276 | |||

0.8 | 0.662416 | |||

1.0 | 0.628517 | |||

0.1 | 1.5 | 0.1 | 0.2 | 0.810460 |

0.4 | 0.818329 | |||

0.6 | 0.826437 | |||

0.8 | 0.834797 | |||

1.0 | 0.843423 |

**Table 7.**Numerical outputs of ${\varphi}^{\prime}\left(1\right)$ for $Le$, R, ${N}_{b}$ and ${N}_{t}$ when $De=\gamma =0.01$, $Ha=\delta =Ec=0.1$, $S=Da=1$ and ${\gamma}_{1}=Pr=1.5$.

$\mathit{Le}$ | R | ${\mathit{N}}_{\mathit{b}}$ | ${\mathit{N}}_{\mathit{t}}$ | ${\mathit{\varphi}}^{\prime}\left(1\right)$ |
---|---|---|---|---|

0.5 | 1.5 | 0.1 | 0.1 | 1.319558 |

1.0 | 1.655833 | |||

1.5 | 1.912033 | |||

2.0 | 2.121145 | |||

2.5 | 2.299830 | |||

3.0 | 2.457446 | |||

1.5 | −1.5 | 0.1 | 0.1 | −7.357027 |

−1.0 | −1.463706 | |||

−0.5 | 0.049833 | |||

0.5 | 1.280691 | |||

1.0 | 1.632325 | |||

1.5 | 1.912033 | |||

1.5 | 1.5 | 0.2 | 0.1 | 1.589931 |

0.4 | 1.429529 | |||

0.6 | 1.376588 | |||

0.8 | 1.350472 | |||

1.0 | 1.335057 | |||

1.5 | 1.5 | 0.1 | 0.2 | 2.543099 |

0.4 | 3.824886 | |||

0.6 | 5.133900 | |||

0.8 | 6.471441 | |||

1.0 | 7.838907 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mat Noor, N.A.; Shafie, S.; Admon, M.A.
Slip Effects on MHD Squeezing Flow of Jeffrey Nanofluid in Horizontal Channel with Chemical Reaction. *Mathematics* **2021**, *9*, 1215.
https://doi.org/10.3390/math9111215

**AMA Style**

Mat Noor NA, Shafie S, Admon MA.
Slip Effects on MHD Squeezing Flow of Jeffrey Nanofluid in Horizontal Channel with Chemical Reaction. *Mathematics*. 2021; 9(11):1215.
https://doi.org/10.3390/math9111215

**Chicago/Turabian Style**

Mat Noor, Nur Azlina, Sharidan Shafie, and Mohd Ariff Admon.
2021. "Slip Effects on MHD Squeezing Flow of Jeffrey Nanofluid in Horizontal Channel with Chemical Reaction" *Mathematics* 9, no. 11: 1215.
https://doi.org/10.3390/math9111215