A semi-analytical solution of the thermal entrance problem with constant wall temperature for channel flow of Maxwell type viscoelastic fluids and Newtonian fluids, both with pressure dependent viscosity, is derived. A Fourier–Gauss pseudo-spectral scheme is developed and used to solve the variable coefficient parabolic partial differential energy equation. The dependence of the Nusselt number and the bulk temperature on the pressure coefficient is investigated for the Newtonian case including viscous dissipation. These effects are found to be closely interactive. The effect of the Weissenberg number on the local Nusselt number is explored for the Maxwell fluid with pressure-dependent viscosity. Local Nusselt number decreases with increasing pressure coefficient for both fluids. The local Nusselt number Nu for Newtonian fluid with pressure-dependent viscosity is always greater than Nu related to the viscoelastic Maxwell fluid with pressure-dependent viscosity.
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Thermally Developing Heat Transfer With Nonlinear Viscoelastic and Newtonian Fluids With Pressure-Dependent Viscosity
Dennis A. Siginer,
Dennis A. Siginer
Fellow ASME
Departamento de Ingeniería Mecánica,
Centro de Investigación en Creatividad y
Educación Superior,
Universidad de Santiago de Chile,
Santiago, Chile;
Department of Mathematics and
Statistical Sciences,
Department of Mechanical,
Energy and Industrial Engineering,
Botswana International University of
Science and Technology,
Palapye, Botswana
e-mails: dennis.siginer@usach.cl;
siginerd@biust.ac.bw
Departamento de Ingeniería Mecánica,
Centro de Investigación en Creatividad y
Educación Superior,
Universidad de Santiago de Chile,
Santiago, Chile;
Department of Mathematics and
Statistical Sciences,
Department of Mechanical,
Energy and Industrial Engineering,
Botswana International University of
Science and Technology,
Palapye, Botswana
e-mails: dennis.siginer@usach.cl;
siginerd@biust.ac.bw
Search for other works by this author on:
F. Talay Akyildiz,
F. Talay Akyildiz
Department of Mathematics and Statistics,
Al-Imam University,
Riyadh, Saudi Arabia
Al-Imam University,
Riyadh, Saudi Arabia
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Mhamed Boutaous
Mhamed Boutaous
Université de Lyon,
CNRS, INSA-Lyon, CETHIL, UMR5008,
Villeurbanne F-69621, France
CNRS, INSA-Lyon, CETHIL, UMR5008,
Villeurbanne F-69621, France
Search for other works by this author on:
Dennis A. Siginer
Fellow ASME
Departamento de Ingeniería Mecánica,
Centro de Investigación en Creatividad y
Educación Superior,
Universidad de Santiago de Chile,
Santiago, Chile;
Department of Mathematics and
Statistical Sciences,
Department of Mechanical,
Energy and Industrial Engineering,
Botswana International University of
Science and Technology,
Palapye, Botswana
e-mails: dennis.siginer@usach.cl;
siginerd@biust.ac.bw
Departamento de Ingeniería Mecánica,
Centro de Investigación en Creatividad y
Educación Superior,
Universidad de Santiago de Chile,
Santiago, Chile;
Department of Mathematics and
Statistical Sciences,
Department of Mechanical,
Energy and Industrial Engineering,
Botswana International University of
Science and Technology,
Palapye, Botswana
e-mails: dennis.siginer@usach.cl;
siginerd@biust.ac.bw
F. Talay Akyildiz
Department of Mathematics and Statistics,
Al-Imam University,
Riyadh, Saudi Arabia
Al-Imam University,
Riyadh, Saudi Arabia
Mhamed Boutaous
Université de Lyon,
CNRS, INSA-Lyon, CETHIL, UMR5008,
Villeurbanne F-69621, France
CNRS, INSA-Lyon, CETHIL, UMR5008,
Villeurbanne F-69621, France
1Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 1, 2018; final manuscript received April 29, 2018; published online June 18, 2018. Assoc. Editor: Sara Rainieri.
J. Heat Transfer. Oct 2018, 140(10): 101701 (7 pages)
Published Online: June 18, 2018
Article history
Received:
March 1, 2018
Revised:
April 29, 2018
Citation
Siginer, D. A., Talay Akyildiz, F., and Boutaous, M. (June 18, 2018). "Thermally Developing Heat Transfer With Nonlinear Viscoelastic and Newtonian Fluids With Pressure-Dependent Viscosity." ASME. J. Heat Transfer. October 2018; 140(10): 101701. https://doi.org/10.1115/1.4040153
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