0
Research Papers: Conduction

Transient Conduction From Parallel Isothermal Cylinders

[+] Author and Article Information
Rajai S. Alassar

Department of Mathematics and Statistics,
King Fahd University of Petroleum & Minerals,
Box No. 1620,
Dhahran 31261, Saudi Arabia
e-mail: alassar@kfupm.edu.sa

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 3, 2011; final manuscript received July 23, 2012; published online October 10, 2012. Assoc. Editor: Patrick E. Phelan.

J. Heat Transfer 134(12), 121301 (Oct 10, 2012) (5 pages) doi:10.1115/1.4007312 History: Received September 03, 2011; Revised July 23, 2012

The transient heat conduction from two parallel isothermal cylinders is studied using the naturally fit bipolar cylindrical coordinates system. The energy equation is expanded in a Fourier series using appropriate basis functions to eliminate one of the physical coordinates. The resulting modes of the expansion are solved using a finite difference scheme. It is shown that, as is the case with a single isothermal cylinder in an infinite medium, steady states for two isothermal cylinders are not possible and heat transfer changes indefinitely with time.

FIGURES IN THIS ARTICLE
<>
Copyright © 2012 by ASME
Your Session has timed out. Please sign back in to continue.

References

Abdulhadi, R. S., and Chato, J. C., 1977, “Combined Natural and Forced Convective Cooling of Underground Electric Cables,” IEEE Trans. Power Appar. Syst. (PAS), 96, pp. 1–8. [CrossRef]
El-Shaarawi, M. A. I., and Mokheimer, E., 1995, “Transient Conduction in Eccentrically Hollow Cylinders,” Int. J. Heat Mass Transfer, 38(11), pp. 2001–2010. [CrossRef]
Trombetta, M. L., 1971, “Laminar Forced Convection in Eccentric Annuli,” Int. J. Heat Mass Transfer, 14, pp. 1161–1173. [CrossRef]
DiFelice, R. F., and Bau, H. H., 1983, “Conductive Heat Transfer Between Eccentric Cylinders With Boundary Conditions of the Third Kind,” ASME J. Heat Transfer, 105, pp. 678–680. [CrossRef]
Ioffe, I. A., 1972, “A Problem of Transient Heat Conduction in a Semibounded Body With an Internal Cylindrical Heat Source,” J. Eng. Phys., 23, pp. 1051–1054. [CrossRef]
Thiyagarajan, R., and Yovanovich, M. M., 1974, “Thermal Resistance of a Buried Cylinder With Constant Flux Boundary Condition,” ASME J. Heat Transfer, 96, pp. 249–250. [CrossRef]
Bau, H. H., and Sadhai, S. S., 1982, “Heat Losses From a Fluid Flowing in a Buried Pipe,” Int. J. Heat Mass Transfer, 25, pp. 1621–1629. [CrossRef]
Martin, W. W., and Sadhal, S. S., 1978, “Bounds on Transient Temperature Distribution Due to a Buried Cylindrical Heat Source,” Int. J. Heat Mass Transfer, 21, pp. 783–789. [CrossRef]
Mahfouz, F. M., and Badr, H. M., 2002, “Mixed Convection From a Cylinder Oscillating Vertically in a Quiescent Fluid,” Heat Mass Transfer, 38(6), pp. 477–486. [CrossRef]
Ozisik, M. N., 1980, Heat Conduction, Wiley, New York.
El-Saden, M. R., 1961, “Heat Conduction in an Eccentrically Hollow, Infinitely Long Cylinder With Internal Heat Generation,” ASME J. Heat Transfer, 83, pp. 510–512. [CrossRef]
Arfken, G., 1970, Mathematical Methods for Physicists, Academic Press, London.
Moon, P., and Spencer, D. E., 1988, Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions, 2nd ed., Springer-Verlag, New York.

Figures

Grahic Jump Location
Fig. 3

Rectangular map of the region

Grahic Jump Location
Fig. 2

The coordinates system

Grahic Jump Location
Fig. 1

Two parallel cylinders in an infinite medium

Grahic Jump Location
Fig. 4

Time development of isotherms, r1=1,r2=3, H=6, ϕ1=1, ϕ2=2 (a) τ=1, (b) τ=2, (c) τ=5, (d) τ=10, (e) τ=50, and (f) τ=100

Grahic Jump Location
Fig. 5

Time development of heat transfer, r1=1,r2=3, H=6, ϕ1=1, ϕ2=2 (a) Nu and (b) Nu¯

Grahic Jump Location
Fig. 6

Isotherms, r1=1,r2=1, H=4, ϕ1=1, τ=100 (a) ϕ2=2, (b) ϕ2=1, (c) ϕ2=1/2, (d) ϕ2=0, (e) ϕ2=-1/2, (f) ϕ2=-1, and (g) ϕ2=-2

Grahic Jump Location
Fig. 7

Time development of Nu¯, r1=1,r2=1, H=4, ϕ1=1

Grahic Jump Location
Fig. 8

Time development of Nu¯, r1=1,r2=1/4, ϕ1=1, ϕ2=4

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