0
Research Papers: Forced Convection

Heat Transfer in Fully Developed Laminar Flow of Power Law Fluids

[+] Author and Article Information
A. Baptista

Departamento de Engenharia Mecânica,
Faculdade de Engenharia da
Universidade do Porto,
Rua Dr. Roberto Frias,
Porto 4200-465, Portugal
e-mail: em09123@fe.up.pt

M. A. Alves

CEFT,
Departamento de Engenharia Química,
Faculdade de Engenharia da
Universidade do Porto,
Rua Dr. Roberto Frias,
Porto 4200-465, Portugal
e-mail: mmalves@fe.up.pt

P. M. Coelho

CEFT, Departamento de Engenharia Mecânica,
Faculdade de Engenharia da
Universidade do Porto,
Rua Dr. Roberto Frias,
Porto 4200-465, Portugal
e-mail: pmc@fe.up.pt

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 19, 2013; final manuscript received September 17, 2013; published online January 9, 2014. Assoc. Editor: Giulio Lorenzini.

J. Heat Transfer 136(4), 041702 (Jan 09, 2014) (8 pages) Paper No: HT-13-1208; doi: 10.1115/1.4025662 History: Received April 19, 2013; Revised September 17, 2013

In this work, we present approximate and exact solutions for the temperature profile and Nusselt number under fully developed laminar flow of a power law fluid inside pipes and between parallel plates. Constant wall temperature and negligible axial heat conduction are considered, for both the cases with and without viscous dissipation. For completeness, the corresponding solutions for the related problem of constant heat flux at the wall are also presented. In the absence of viscous dissipation, the solutions obtained are semi-analytic, since they rely upon an iterative procedure. As a benchmark result, to allow comparison with the results obtained with the semi-analytical expressions, we also present highly accurate numerical solutions for the Nusselt number, Nu, based on numerical integration of the energy equation. Also based on these numerical results, simplified correlations for Nu are proposed, valid for a wide range of the power law index.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Grigull, U., 1956, “Wärmeübergang an nicht-Newtonsche flüssigkeiten bei laminarer rohrströmung,” Chem.-Ing.-Tech., 28, pp. 553–556. [CrossRef]
Barletta, A., 1997, “Fully Developed Laminar Forced Convection in Circular Ducts for Power-Law Fluids With Viscous Dissipation,” Int. J. Heat Mass Transfer, 40, pp. 15–26. [CrossRef]
Skelland, A. H. P., 1967, Non-Newtonian Flow and Heat Transfer, Wiley, New York.
Hartnett, J. P., and Cho, Y. I., 1998, “Non-Newtonian Fluids,” Handbook of Heat Transfer, 3rd ed., W.Rohsenow, J.Hartnett, and Y.Cho, eds., McGraw-Hill, New York, pp. 10.1–10.53.
Cruz, D. A., Coelho, P. M., and Alves, M. A., 2012, “A Simplified Method for Calculating Heat Transfer Coefficients and Friction Factors in Laminar Pipe Flow of Non-Newtonian Fluids,” ASME Trans. J. Heat Transfer, 134, p. 091703. [CrossRef]
Coelho, P. M., Pinho, F. T., and Oliveira, P. J., 2002, “Fully-Developed Forced Convection of the Phan-Thien-Tanner Fluid in Ducts With a Constant Wall Temperature,” Int. J. Heat Mass Transfer, 45(7), pp. 1413–1423. [CrossRef]
Eckert, E. R. G., and Drake, R. M.Jr., 1972, Analysis of Heat and Mass Transfer, 1st ed., McGraw-Hill, New York.
Silva, A. B., 2012, “Cálculo simplificado do número de Nusselt em escoamentos laminares de fluidos não-Newtonianos no interior de condutas com temperatura de parede constant,” University of Porto, Final project report (in Portuguese).
Coelho, P. M., and Pinho, F. T., 2009, “A Generalized Brinkman Number for Non Newtonian Duct Flows,” J. Non-Newtonian Fluid Mech., 156, pp. 202–206. [CrossRef]
Victor, S. A., and Shah, V. L., 1975, “Heat Transfer to Blood Flowing in a Tube,” Biorheology, 12, pp. 361–368. [PubMed]
Nóbrega, J. M., Pinho, F. T., Oliveira, P. J., and Carneiro, O. S., 2004, “Accounting for Temperature-Dependent Properties in Viscoelastic Duct Flows,” Int. J. Heat Mass Transfer, 47, pp. 1141–1158. [CrossRef]
Surana, K. S., Ma, Y. T., Reddy, J. N., and Romkes, A., 2012, “Computations of Evolutions for Isothermal Viscous and Viscoelastic Flows in Open Domains,” Int. J. Comput. Methods Eng. Sci. Mech., 13, pp. 408–429. [CrossRef]
Xiong, Q., Li, B., Xu, J., Wang, X., Wang, L., and Ge, W., 2012, “Efficient 3D DNS of Gas–Solid Flows on Fermi GPGPU,” Comput. Fluids, 70, pp. 86–94. [CrossRef]
Xiong, Q., Li, B., and Xu, J., 2013, “GPU-accelerated adaptive particle splitting and merging in SPH,” Comput. Phys. Commun., 184, pp. 1701–1707. [CrossRef]
Çengel, Y. A., and Turner, R. H., 2005, Fundamentals of Thermal-Fluid Sciences, 2nd ed., McGraw-Hill, New York.

Figures

Grahic Jump Location
Fig. 1

Schematic diagram of the problem under study and coordinate system: parallel plates (x, y); pipe (x, r)

Grahic Jump Location
Fig. 2

Difference between Nu values obtained by numerical integration with different numbers of grid points equally spaced along the ι* coordinate.: Mesh I—3000 points; Mesh II—6000 points; Mesh III—12,000 points; Mesh IV—24, 000 points. Lines: —— Flow between parallel plates; ········ Pipe flow

Grahic Jump Location
Fig. 3

Dimensionless temperature profile θ (cf. Eq. (7)) for flow between parallel plates for different values of n. × analytical solution (n = 0, Eq. (21)), ◇ numerical results. Lines (semi-analytical solutions): —— n = 0; – – – – n = 0.1; — · — n = 0.5; — — n = 1; ······· n → ∞.

Grahic Jump Location
Fig. 4

Dimensionless temperature profile θ (cf. Eq. (7)) for flow in a pipe for different values of n. × analytical solution (n = 0, Eq. (22)), ◇ numerical results. Lines (semi-analytical solutions): —— n → 0; – – – – n = 0.1; — · — n = 0.5; — — n = 1; ······· n → ∞.

Grahic Jump Location
Fig. 5

Influence of power law index in the Nusselt number for flow between parallel plates and inside a circular pipe. Comparison between the semi-analytical and numerical approaches: Lines – semi-analytical solutions; ○ numerical results for flow between parallel plates (Mesh IV); ◻ numerical results for pipe flow (Mesh IV).

Grahic Jump Location
Fig. 6

Dimensionless temperature profile (θ) in the presence of viscous dissipation for flow between parallel plates and for different values of n. ⋄ numerical results. Lines (analytical solutions, cf. Eq. (29)): —— n = 0; – – – – n = 0.1; — · — n = 0.5; — — n = 1; ······· n → ∞.

Grahic Jump Location
Fig. 7

Dimensionless temperature profile (θ) in the presence of viscous dissipation for flow in a pipe and for different values of n. ⋄ numerical results. Lines (analytical solutions, cf. Eq. (29)): ——n = 0; n = 0.1; ·n = 0.5; — —n = 1; ·······n → ∞.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In