A closed form approximate solution has been obtained for the transient temperature distribution in a hollow cylinder with a linear variation in thermal conductivity with temperature. The boundary conditions considered are convective heating (Newton’s law) at the exposed inner surface and adiabatic outer surface. The solution is obtained using the method of optimal linearization, with the initial solution given by the integral method. The nonlinear analytical solution is shown to compare well with the finite difference solution.
1.
Yang
, K. T.
, 1958, “Transient Conduction in a Semi-infinite Solid With Variable Thermal Conductivity
,” ASME J. Appl. Mech.
0021-8936, 89
, pp. 146
–147
.2.
Ozisik
, M. N.
, 1989, Boundary Value Problems of Heat Conduction
, Dover
, New York
.3.
Mastanaiah
, K.
, and Muthunayagam
, A. E.
, 1975, “Transient Conduction in a Finite Slab With Variable Thermal Conductivity
,” AIAA J.
0001-1452, 13
(7
), pp. 954
–956
.4.
Vujanovic
, B.
, 1973, “Application of Optimal Linearization Method to the Heat Transfer Problem
,” Int. J. Heat Mass Transfer
0017-9310, 16
, pp. 1111
–1117
.5.
Goodman
, T. R.
, 1961, “The Heat Balance Integral—Further Considerations and Refinements
,” ASME J. Heat Transfer
0022-1481, 83
, pp. 83
–86
.6.
Lin
, S. H.
, 1978, “Transient Heat Conduction With Temperature-Dependent Thermal Conductivity by the Orthogonal Collocation Method
,” Lett. Heat Mass Transfer
0094-4548, 5
, pp. 29
–39
.7.
Meyer
, E.
, 1952, “Heat Flow in Composite Slabs
,” J. Am. Rocket Soc.
0095-9073, 22
, pp. 150
–158
.8.
Mishra
, S. C.
, and Pavan Kumar
, T. B.
, 2009, “Analysis of a Hyperbolic Heat Conduction-Radiation Problem With Temperature Dependent Thermal Conductivity
,” ASME J. Heat Transfer
0022-1481, 131
, p. 111302
.9.
Agbezuge
, L.
, 2009, “Transient Heat Transfer in a Partially Cooled Cylindrical Rod
,” ASME J. Heat Transfer
0022-1481, 131
, p. 074504
.10.
Lin
, J. -Y.
, and Chen
, H. -T.
, 1992, “Radial Axisymmetric Transient Conduction in Composite Hollow Cylinders With Variable Thermal Conductivity
,” Eng. Anal. Boundary Elem.
0955-7997, 10
, pp. 27
–33
.11.
Chen
, C. J.
, and Ozisik
, M. N.
, 1994, “Optimal Convective Heating in a Hollow Cylinder With Temperature Dependent Thermal Conductivity
,” Appl. Sci. Res.
0003-6994, 52
, pp. 67
–79
.12.
Mastanaiah
, K.
, 1975, “Transient Heat Conduction in a Hollow Cylinder With Variable Thermal Conductivity
,” Proceedings of the Third National Heat and Mass Transfer Conference
, Indian Institute of Technology, Bombay, Dec. 11–13, Paper No. HMT-02-75.13.
Lardner
, T. J.
, and Pohle
, F. B.
, 1961, “Application of Heat Balance Integral to the Problems of Cylindrical Geometry
,” ASME J. Appl. Mech.
0021-8936, 92
, pp. 310
–312
.14.
West
, J. C.
, 1960, Analytical Techniques for Nonlinear Control Systems
, English Universities
, London
.15.
Eckert
, E. R. G.
, and Drake
, R. M.
, 1987, Analysis of Heat and Mass Transfer
, Hemisphere
, New York
, p. 191
.16.
Mastanaiah
, K.
, 1976, “On the Numerical Solution of Phase Change Problems in Transient Nonlinear Heat Conduction
,” Int. J. Numer. Methods Eng.
0029-5981, 10
, pp. 833
–844
.Copyright © 2010
by American Society of Mechanical Engineers
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