0
Technical Brief

# Cooling of a Hot Torus

[+] Author and Article Information
Rajai S. Alassar

Department of Mathematics and Statistics,
King Fahd University of Petroleum and Minerals,
Dhahran 31261, Saudi Arabia
e-mail: alassar@kfupm.edu.sa

Mohammed A. Abushoshah

Department of Mathematics and Statistics,
King Fahd University of Petroleum and Minerals,
Dhahran 31261, Saudi Arabia

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 22, 2015; final manuscript received November 26, 2015; published online December 29, 2015. Assoc. Editor: Wilson K. S. Chiu.

J. Heat Transfer 138(4), 044501 (Dec 29, 2015) (5 pages) Paper No: HT-15-1062; doi: 10.1115/1.4032149 History: Received January 22, 2015; Revised November 26, 2015

## Abstract

The problem of a hot torus left to cool in a medium of known temperature is studied. We write the governing equation in toroidal coordinates and expand the temperature in terms of a series in the angular direction. The resulting modes in the radial direction are numerically obtained. We consider both isothermal and convective boundary conditions and study the effect of Biot number and aspect ratio on the heat transfer rate.

<>

## Figures

Fig. 3

Variation of φ at the center point for different aspect ratios

Fig. 8

Variation of φ on the surface for the case R/r=1.5 and τ=10−6

Fig. 9

Time variation of φ for the case R/r=1.5 in (a) the center and (b) the focal point

Fig. 1

Problem configuration

Fig. 2

Variation of Nu¯ on the surface for different aspect ratios

Fig. 4

Variation of Nu¯ on the surface for tori with equal volume

Fig. 5

Variation of φ at the center point for tori with equal volume

Fig. 6

Time development (τ=0.0001, 0.01, 0.2, 0.5) of isotherms for R/r=1.5 and Bi=10

Fig. 7

Time development of φ on the surface for the case R/r=1.5 and Bi=5

## 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 Proceedings Articles
Related eBook Content
Topic Collections