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MHD and Thermal Radiation Flow of Graphene Casson Nanofluid Stretching/Shrinking Sheet

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Abstract

A Steady 2’ D flow of graphene-water Casson nanofluid due to a stretching/shrinking sheet is examined. The thermal radiation and heat source/sink parameters effects are considered. Utilizing similarity transformations, the nonlinear PDE’s are converted into a nonlinear ODE’s with reduced boundary conditions. Hence, the exact analytical solutions have been deduced. A theoretical result was apparatus to survey on axial and transverse velocities, temperature, reduced skin friction and local Nusselt number with suitable parameters. It is examined that when the values of thermal radiation, volume fraction, injection and Eckert number, increases then the graphene nanoparticles behave like a heater. And also they behave like cooler when the values of magnetic field, suction, primary and slip secondary Navier’s slip and heat source/sink increases. The present work containing engineering and industrial applications such as manufacturing of plastic and rubber sheets, annealing and thinning of copper wires, extrusion of polymer etc. Also, in the present analysis graphene nanoparticles can be used as a heater on increasing the solid volume fraction, injection, thermal radiation and Eckert number. On the other hand, they act as a cooler with an increase of magnetic field, suction, first velocity slip, second velocity slip and heat source/sink.

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Data Availability Statement

Data sharing is not applicable to this article.

Abbreviations

\(a_{ + }\) and \(a_{ - }\) :

Stretching and shrinking constants, respectively

\(A,B\) :

Slip factors

\(B_{0}\) :

Strength of magnetic field

\(C_{p}\) :

Specific heat

\(D_{1} ,\,D_{2} \,D_{3}\) :

Constants

\(m_{1}\) to \(m_{6}\) :

Dummy variables

\(Ec_{1} \,{\text{and}}\,Ec_{2}\) :

Eckert number for PST and PHF cases, respectively

\(f\) :

Transverse velocity

\(G\) :

Graphene

\(H_{2} O\) :

Water

\(k\) :

Thermal conductivity

\(k^{*}\) :

Mean absorption coefficient

\(L\left[ {a,b,z} \right]\) :

Laguerre polynomials

\(M\) :

Magnetic field

\(Nur_{1} \,{\text{and}}\,Nur_{2}\) :

Reduced Nusselt number for PST and PHF case, respectively

PHF :

Prescribed heat flux

\(\Pr\) :

Prandtl number

PST :

Prescribed surface temperature

\(Q_{0}\) :

Coefficient of heat source/sink

\(q_{r}\) :

Radiative heat flux

\(q_{w}\) :

Surface heat flux

\(R\) :

Thermal radiation

\(S\) :

Suction/injection parameter

\(Sr\) :

Reduced skin friction coefficient

\(T\) :

Temperature

\(u,v\) :

Velocity components in x and y directions, respectively,

\(\left( {x,y} \right)\) :

Cartesian coordinates

\(\gamma\) :

Heat source/sink parameter

\(\eta\) :

Similarity variable

\(\theta\) and \(g\) :

T profiles for PST and PHF cases respectively

\(\Lambda\) :

Casson fluid parameter

\(\lambda_{0} = 1\,{\text{and}}\, - 1\) :

Represents to stretching and shrinking sheet respectively

\(\lambda_{1} \,{\text{and}}\,\lambda_{2}\) :

1St and 2nd order velocity slips, respectively

\(\mu\) :

Effective dynamic viscosity

\(\nu\) :

Effective dynamic viscosityKinematic viscosity

\(\xi\) :

Inclined parameter of magnetic field

\(\rho\) :

Effective density

\(\left( {\rho C_{P} } \right)\) :

Heat capacitance

\(\sigma\) :

Electrical conductivity

\(\sigma^{*}\) :

Stefan-Boltzmann constant

\(\tau_{w}\) :

Skin friction

\(\phi\) :

Solid volume fraction

\(\infty\) :

Condition of ambient

\(c\) :

Critical value

\(f\) :

Base fluid

\(n\,f\) :

Nanofluid

\(s\) :

Particle

\(t\) :

Terminated value

\(w\) :

Wall surface

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Authors and Affiliations

  1. Department of Mathematics, Davangere University, Davangere, 577 007, Shivagangotri, India

    U. S. Mahabaleshwar & A. B. Vishalakshi

  2. Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

    Emad H. Aly

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Mahabaleshwar, U.S., Aly, E.H. & Vishalakshi, A.B. MHD and Thermal Radiation Flow of Graphene Casson Nanofluid Stretching/Shrinking Sheet. Int. J. Appl. Comput. Math 8, 113 (2022). https://doi.org/10.1007/s40819-022-01300-w

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