Analytical Solution of Transient Heat Conduction through a Hollow Spherical Thermal Insulation Material of a Temperature Dependant Thermal Conductivity
Main Article Content
Abstract
The one-dimensional, spherical coordinate, non-linear partial differential equation of transient heat conduction through a hollow spherical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant thermal conductivity. It is found that the characteristics of the thermal insulation material and the pressure value between its particles have a major effect on the rate of heat transfer and temperature profile.
Article Details
How to Cite
Publication Dates
References
Exact analytical solution of unsteady axi-symmetric conductive heat transfer in cylindrical orthotropic composite laminates, International journal of heat and mass transfer, ELSEVIER, 55, 4427-4436, 2012.
Carslaw H.S. and Jaeger J.C., Conduction of Heat in Solids, 2nd ed., Oxford University Press, New York, 1959.
Christiansen R.M. and Hollingworth Jr.M., The performance of glass fiber insulation under high vacuum, Adv. Cryogen Eng., 1958(4):S141.
Christiansen R.M., Hollingworth Jr.M. and Marsh Jr.H.N., Low temperature insulation systems, Adv. Cryogen Eng., 1959(5).
Corruccini R.J. and Gniewek J.J., Specific Heats and Enthalpies of Technical Solids at Low Temperatures, NBS Monograph, 21, 1960.
Gerald C.F. and Wheatley P.O., Applied Numerical Analysis, 4th ed., Addison-Wesley, New York, 1989.
Hofmann A., The thermal conductivity of cryogenic insulation materials and its temperature dependence, Elsevier, Cryogenics, 46, 815-824, 2006.
Jain P.K., Singh S. and Rizwan-uddin, An exact analytical solution for two-dimensional, unsteady, multilayer heat conduction in spherical coordinates, International journal of heat and mass transfer, ELSEVIER, 53, 2133-2142, 2010.
Kaganer, Thermal Insulation in Cryogenic Engineering, Israel Program for Scientific Translations, 1969.
Kropschot R.H. and Burges R.W., Perlite for cryogenic insulation, Adv. Cryogen Eng., 1962(8):S425.
Perlite Institute New York, Thermal Data Sheet No. 2-4, 1970.
Singh S., Jain P.K., Rizwan-Uddin, Analytical solution to transient heat conduction in polar coordinates with multiple layers in radial direction, International journal of thermal sciences, ELSEVIER, 47, 261-273, 2008.
Verschoor and Greebler, Heat transfer by gas conduction and radiation in fibrous insulations, Transactions of ASME Paper No. 51-A54, 1952.
Zivkovic M.M., Nikolic A.V., Slavkovic R.B. and Zivic F.T., Non-Linear transient heat conduction analysis of insulation wall of tank for transportation of liquid Aluminum, Thermal Science, Vol. 14, Suppl., S299-S312, 2010.