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Heat Transfer of MHD Channel Flow of Viscoelastic (PTT) Fluid

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New Trends in Applied Analysis and Computational Mathematics

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1356))

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Abstract

The study presents the heat transfer aspect of MHD channel flow of Phan-Thien-Tanner (PTT) conducting flow accounting for the viscous dissipation. The role of Deborah number substantiates the dual behavior of Newtonian and non-Newtonian aspects of the flow model. The inclusion of two body forces due to magnetic field (force act at a distance) and porosity of the medium enrich the analysis. The important findings are the role of magnetic parameter is to enhance the temperature across the flow domain, whereas Deborah number and other parameters act adversely. Thus, the simulation of the flow parameters provides ample scopes to meet the design requirements in cooling/heating. The most interesting observation is that contribution of viscous dissipative heat seems to be insignificant due to linear variation across the temperature field in the present PTT model indicating the preservation of thermal energy loss.

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Abbreviations

\(\vec{B}\) :

Magnetic flux

\(B_{0}\) :

Constant flux density

D/Dt:

Material time derivative

De:

Deborah number

\(\vec{J}\) :

Electric current density

I:

Identity tensor

Kp:

Porosity parameter

L:

Characteristic length

M:

Magnetic parameter

p:

Pressure

\(\overrightarrow {{T^{*} }}\) :

Cauchy stress tensor

\(\vec{V}\) :

Velocity vector

\(\vec{\tau }\) :

Extra stress tensor

λ :

Relaxation time

μ :

Constant viscosity coefficient

σ :

electrical conductivity

ρ :

fluid density

ε :

elongation parameter

\(\nabla\) :

Gradient operator

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Authors and Affiliations

  1. Department of Mathematics, IGIT, Sarang, Dhenknal, Odisha, India

    B. K. Swain

  2. Department of Mathematics, S.O.A, Deemed to Be University, Bhubaneswar, Odisha, India

    M. Das & G. C. Dash

Authors
  1. B. K. Swain
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  2. M. Das
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  3. G. C. Dash
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Correspondence to B. K. Swain .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Odisha, India

    Susanta Kumar Paikray

  2. Department of Mathematics, Gauhati University, Guwahati, India

    Hemen Dutta

  3. Department of Mathematics, Center for Mathematics of Uncertainty, Creighton University, Omaha, NE, USA

    John N. Mordeson

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Swain, B.K., Das, M., Dash, G.C. (2021). Heat Transfer of MHD Channel Flow of Viscoelastic (PTT) Fluid. In: Paikray, S.K., Dutta, H., Mordeson, J.N. (eds) New Trends in Applied Analysis and Computational Mathematics. Advances in Intelligent Systems and Computing, vol 1356. Springer, Singapore. https://doi.org/10.1007/978-981-16-1402-6_4

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