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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.

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Figures

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Fig. 1

Two parallel cylinders in an infinite medium

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Fig. 2

The coordinates system

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Fig. 3

Rectangular map of the region

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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

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Fig. 5

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

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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

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Fig. 7

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

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Fig. 8

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

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