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Research Papers: Forced Convection

Thermally Developing Heat Transfer With Nonlinear Viscoelastic and Newtonian Fluids With Pressure-Dependent Viscosity

[+] Author and Article Information
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

F. Talay Akyildiz

Department of Mathematics and Statistics,
Al-Imam University,
Riyadh, Saudi Arabia

Mhamed Boutaous

Université de Lyon,
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 140(10), 101701 (Jun 18, 2018) (7 pages) Paper No: HT-18-1120; doi: 10.1115/1.4040153 History: Received March 01, 2018; Revised April 29, 2018

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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References

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Figures

Grahic Jump Location
Fig. 3

Newtonian fluid: fully developed velocity profile and developing temperature profiles at three locations in the axial direction :εα=1.49,ΛN=7.454,andBr = 0; ΛN is the root of Eq. (2.11)

Grahic Jump Location
Fig. 4

Newtonian fluid: fully developed velocity and developing temperature profiles at three locations in the axial direction: εα=0.1,ΛN=1.002,and Br=0.1; ΛN is the root of Eq. (2.11)

Grahic Jump Location
Fig. 5

Newtonian fluid: fully developed velocity and developing temperature profiles at three locations in the axial direction: εα=1.49andBr=0.0001; ΛN is the root of Eq. (2.11)

Grahic Jump Location
Fig. 6

Newtonian fluid: combined effects of the pressure coefficient εα and the Brinkman number Br on the local Nusselt number Nu; ΛN is the root of Eq. (2.11)

Grahic Jump Location
Fig. 1

Newtonian fluid: effect of the pressure coefficient εα on the local Nusselt number Nu when Br=0; ΛN is the root of Eq. (2.11)

Grahic Jump Location
Fig. 2

Newtonian fluid: fully developed velocity profile and developing temperature profiles at three locations in the axial direction :εα=0.1,ΛN=1.002,andBr=0;ΛN is the root of Eq. (2.11)

Grahic Jump Location
Fig. 9

Viscoelastic fluid: deviation of the velocity profile of the Maxwell fluid from the parabolic velocity profile of the Newtonian fluid: εα =0.4, Wi = 0.13, andΛvis=3.245; Λvis is the root of Eq. (2.10)

Grahic Jump Location
Fig. 10

Viscoelastic fluid: deviation of the temperature profile of the Maxwell fluid from the temperature profile of the Newtonian fluid: εα = 0.4, Wi = 0.13, andΛvis=3.245; Λvis is the root of Eq. (2.10)

Grahic Jump Location
Fig. 11

Viscoelastic fluid: effect of the elasticity (Wi ≠ 0) on the local Nusselt number Nu: εα = 0.4, full line Wi = 0 and dashed line Wi = 0.13, andΛvis=3.245; Λvis is the root of Eq. (2.10)

Grahic Jump Location
Fig. 7

Newtonian fluid: effect of the Brinkman number Br on the local Nusselt number Nu: εα=0.1andΛN=1.002; ΛN is the root of Eq. (2.11)

Grahic Jump Location
Fig. 8

Newtonian fluid: effect of the Brinkman number Br on the local Nusselt number Nu: εα=1.49andΛN=7.454; ΛN is the root of Eq. (2.11)

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