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Change in internal energy of viscoelastic fluid flow between two rotating parallel plates having variable fluid properties

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Abstract

In this study, second-grade fluid is taken into account in order to examine its rotating behavior with heat and mass transfer effects. The analysis is carried out between two parallel plates. The study of heat and mass transfer is accomplished by taking the effects of non-constant diffusivity, conductivity and viscosity. A chemical reaction is taken in the form of activation energy. Moreover, it is assume that the kinetic energy of the fluid particles is converted into internal energy. Signifying fundamental equations are tracked by constructing numerical form solutions for velocity, temperature and concentration distributions, while assuming variable fluid properties and internal energy change. Bvp4c technique is employed by considering second-grade fluid parameter and variable fluid properties to be very small. The impact of emerging parameters on velocity, temperature and concentration distributions is examined through graphical depiction. A direct relation is taken between concentration and diffusivity, temperature and thermal conductivity, whereas the indirect relation is assumed for viscosity. Heat transfer is minor for a fluid with variable conductivity and viscosity as likened to the fluid with constant conductivity and viscosity. For uplifting values of rotation parameter, the fluid velocity magnifies.

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Abbreviations

ρ :

Density

μ :

Dynamic viscosity

Ω:

Angular velocity

\(k_{r}^{2}\) :

Reaction rate

k :

Boltzmann constant

\(\alpha_{1} ,\alpha_{2}\) :

Viscoelastic parameters

K :

Thermal conductivity

D :

Mass diffusivity

K 2 :

Rotation parameter

R :

Viscosity parameter

u w :

Velocity of the stretched sheet

\(\delta\) :

Temperature difference parameter

\(\sigma_{m}\) :

Chemical reaction parameter

x, y, z :

Cartesian coordinates

u, v, w :

Velocity components

Ec:

Eckert number

Sc:

Schmidt number

Re:

Renolds number

T h :

Wall temperature

C h :

Wall concentration

\(\tau_{w}\) :

Wall shear stress

\(q_{w}\) :

Surface heat flux

\(j_{w}\) :

Surface mass flux

\(\theta\) :

Dimensionless temperature

\(\varphi\) :

Dimensionless concentration

E :

Activation energy

Nu:

Nusselt number

Sh:

Sherwood number

c p :

Specific heat

C f :

Skin friction coefficient

Pr:

Prandtl number

\(\theta_{r}\) :

Variable viscosity parameter

n :

Fitted rate constant

\(\varepsilon\) :

Thermal conductivity parameter

\(\varepsilon_{1}\) :

Mass diffusivity parameter

\(L\) :

Dimensionless length parameter

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Authors and Affiliations

  1. Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur, AJK, 10250, Pakistan

    T. Salahuddin, Maryam Arshad & Nazim Siddique

  2. Department for Management of Science and Technology Development, Ton Duc Thang University, Hochi Minh City, Vietnam

    I. Tlili

  3. Faculty of Applied Sciences, Ton Duc Thang University, Hochi Minh City, Vietnam

    I. Tlili

Authors
  1. T. Salahuddin
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  2. Maryam Arshad
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  3. Nazim Siddique
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  4. I. Tlili
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Correspondence to Maryam Arshad.

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Salahuddin, T., Arshad, M., Siddique, N. et al. Change in internal energy of viscoelastic fluid flow between two rotating parallel plates having variable fluid properties. Indian J Phys 95, 1801–1811 (2021). https://doi.org/10.1007/s12648-020-01833-0

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