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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
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
References
N. Phan-Thien, R.I. Tanner, A new constitutive equation derived from network theory. J. Nonnewton. Fluid Mech. 2, 353–365 (1977)
N. Phan-Thein, J. Rheol. 22, 259–283 (1978)
R.I. Tanner, Engineering Rheology (Clarendon Press, Oxford, 2000)
P.J. Oliveira, F.T. Pinho, Analytical solution for the fully-developed channel and pipe flow of Phan-Thien-Tanner fluids. J. Fluid Mech. 387, 271–280 (1999)
F.T. Pinho, P.J. Oliveira, Analysis of forced convection in pipes and channels with simplified Phan-Thien-Tanner fluid. Int. J. Heat Mass Transf. 43, 2273–2287 (2000)
F.T. Pinho, P.J. Oliveria, Axial annular flow of a nonlinear viscoelastic fluid: an analytical solution. J. Nonnewton. Fluid Mech. 93, 325–337 (2000)
M.A. Alves, F.T. Pinho, P.J. Oliveira, Study of steady pipe and channel flows of single-mode Phan-Thien-Tanner fluid. J. Nonnewton. Fluid Mech. 101, 55–76 (2001)
M.F. Letelier, D.A. Siginer, On the fully developed tube flow of a class of non-linear viscoelastic fluids. Int. J. Non-Linear Mech. 40, 485–493 (2005)
A.M. Siddiqui, R. Mahmood, Q.K. Ghori, Some exact solutions for the thin film flow of a PTT fluid. Phys. Lett. A 356, 353–356 (2006)
S. Nasseri, L. Bilston, B. Fasheun, R. Tanner, Modelling the biaxial elongational deformation of soft solids. Rheol. Acta 43, 68–79 (2004)
J.H. He, Int. J. Nonlinear Sci. Numer. Simul. 6(2), 207 (2005)
P. Loraih, Magneto Fluid Dynamics, Second edn. (Springer), p. 85
R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids.Vol. 1 Fluid Mechanics, 2nd edn. (John Wiley and Sons, Inc., Hoboken, New Jersey, 1987)
T. Hayat, S. Noreen, A. Hendi, Peristaltic motion of Phan-Thien-Tanner fluid in the presence of slip condition. J. Biorheol. 25(1), 8–17 (2011)
T. Hayat, S. Noreen, N. Ali, S. Abbasbanday, Peristaltic motion of Phan-Thien-Tanner fluid ina planar channel. Numer. Methods Partial Differ. Equ. 28(3), 737–748 (2012)
T. Hayat, S. Noreen, S. Asghar, A. Hendi, Influence of an induced magnetic field on peristaltic transport of a Phan-Thien-Tanner fluid in an asymmetric channel. Chem. Eng. Commun. 198(5), 609– 628 (2011)
N. Faraz, Y. Khan, D.S. Shankar, Decomposition-transform method for fractional differential equation. Int. J. Nonlinear Sci. Sim. 11, 305–310 (2010)
F. Talay Akyildiz, K. Vajravelu, Magnetohydrodynamic flow of a viscoelastic fluid. Physics Letters A. 372, 3380–3384 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-981-16-1402-6_4
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-1401-9
Online ISBN: 978-981-16-1402-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)