The present work deals with the determination of unknown temperature and thermal stresses in a solid sphere. A solid sphere is subjected to arbitrary known interior temperature under steady state. The Legendre's transform are used for heat transfer analysis to determine temperature change within solid sphere. The solution of Navier's equation in terms of Goodier's thermoelastic displacement potential and the Boussinesq's harmonic function for spherical co-ordinate system have been used for thermal stress analysis. The results for temperature change, displacement and stresses have been computed numerically and illustrated graphically.
Cialkowski N.J., Grysa K.W., “On a certain Inverse problem of temperature and thermal Stresses fields”, Acta Mechanica, 36, 169-185, 1981.
Haghighi G., Eghtesad M., Malekzadeh P., Necsulescu D.S., “Two dimensional inverse heat transfer analysis of functionally graded materials in estimating time dependent surface heat flux”, Numerical heat transfer, Part A: Applications, 54, 744-762, 2008.
Huang C H., Cheng S.C., “Three dimensional inverse problem of estimating the volumetric heat generation for a composite material”, Numerical heat transfer, Part A: Applications, 39, 383-403, 2001.
Choulli M., Zeghal A., “Laplace transform approach for an inverse problem”, Transport Theory and Statistical Physics, 24, 1353-1367, 1995.
Taler J., “Theory of transient experimental technique for surface heat transfer”, Int. J. Heat Mass Transfer, 42, 1123-1140, 1999.
Noda N., Hetnarski R. ,Tanigawa Y., “Thermal Stresses in spherical bodies”, in Thermal Stresses, 2nd edition, New York, Taylor & Francis, 2003, Chp.7, p.295-341.
Mohammadium M., Rahimi A.B., “Estimation of heat flux using temperature distribution at a point by conjugate gradient method”, Int. J. Thermal Sciences, 50, 2443-2450, 2011.
Kulkarni V.S., Deshmukh K.C., “An inverse quasi- static steady state thermal stresses in a thick circular plate”, J. Franklin Institute, 345, 29-38, 2008.
Ozisik M.N., “Heat conduction in spherical coordinate system” in Boundary value problems of heat conduction, Scranton, Pennsylvania, International Company, 1968, pp.194-236.
Year 2015,
Volume: 18 Issue: 3, 206 - 211, 01.04.2015
Cialkowski N.J., Grysa K.W., “On a certain Inverse problem of temperature and thermal Stresses fields”, Acta Mechanica, 36, 169-185, 1981.
Haghighi G., Eghtesad M., Malekzadeh P., Necsulescu D.S., “Two dimensional inverse heat transfer analysis of functionally graded materials in estimating time dependent surface heat flux”, Numerical heat transfer, Part A: Applications, 54, 744-762, 2008.
Huang C H., Cheng S.C., “Three dimensional inverse problem of estimating the volumetric heat generation for a composite material”, Numerical heat transfer, Part A: Applications, 39, 383-403, 2001.
Choulli M., Zeghal A., “Laplace transform approach for an inverse problem”, Transport Theory and Statistical Physics, 24, 1353-1367, 1995.
Taler J., “Theory of transient experimental technique for surface heat transfer”, Int. J. Heat Mass Transfer, 42, 1123-1140, 1999.
Noda N., Hetnarski R. ,Tanigawa Y., “Thermal Stresses in spherical bodies”, in Thermal Stresses, 2nd edition, New York, Taylor & Francis, 2003, Chp.7, p.295-341.
Mohammadium M., Rahimi A.B., “Estimation of heat flux using temperature distribution at a point by conjugate gradient method”, Int. J. Thermal Sciences, 50, 2443-2450, 2011.
Kulkarni V.S., Deshmukh K.C., “An inverse quasi- static steady state thermal stresses in a thick circular plate”, J. Franklin Institute, 345, 29-38, 2008.
Ozisik M.N., “Heat conduction in spherical coordinate system” in Boundary value problems of heat conduction, Scranton, Pennsylvania, International Company, 1968, pp.194-236.
Kulkarni, V., Deshmukh, K., & Bhave, A. (2015). AN INVERSE MATHEMATICAL APPROACH FOR THERMAL STRESSES IN A SOLID SPHERE. International Journal of Thermodynamics, 18(3), 206-211. https://doi.org/10.5541/ijot.5000109638
AMA
Kulkarni V, Deshmukh K, Bhave A. AN INVERSE MATHEMATICAL APPROACH FOR THERMAL STRESSES IN A SOLID SPHERE. International Journal of Thermodynamics. August 2015;18(3):206-211. doi:10.5541/ijot.5000109638
Chicago
Kulkarni, Vinayak, K. Deshmukh, and Asha Bhave. “AN INVERSE MATHEMATICAL APPROACH FOR THERMAL STRESSES IN A SOLID SPHERE”. International Journal of Thermodynamics 18, no. 3 (August 2015): 206-11. https://doi.org/10.5541/ijot.5000109638.
EndNote
Kulkarni V, Deshmukh K, Bhave A (August 1, 2015) AN INVERSE MATHEMATICAL APPROACH FOR THERMAL STRESSES IN A SOLID SPHERE. International Journal of Thermodynamics 18 3 206–211.
IEEE
V. Kulkarni, K. Deshmukh, and A. Bhave, “AN INVERSE MATHEMATICAL APPROACH FOR THERMAL STRESSES IN A SOLID SPHERE”, International Journal of Thermodynamics, vol. 18, no. 3, pp. 206–211, 2015, doi: 10.5541/ijot.5000109638.
ISNAD
Kulkarni, Vinayak et al. “AN INVERSE MATHEMATICAL APPROACH FOR THERMAL STRESSES IN A SOLID SPHERE”. International Journal of Thermodynamics 18/3 (August 2015), 206-211. https://doi.org/10.5541/ijot.5000109638.
JAMA
Kulkarni V, Deshmukh K, Bhave A. AN INVERSE MATHEMATICAL APPROACH FOR THERMAL STRESSES IN A SOLID SPHERE. International Journal of Thermodynamics. 2015;18:206–211.
MLA
Kulkarni, Vinayak et al. “AN INVERSE MATHEMATICAL APPROACH FOR THERMAL STRESSES IN A SOLID SPHERE”. International Journal of Thermodynamics, vol. 18, no. 3, 2015, pp. 206-11, doi:10.5541/ijot.5000109638.
Vancouver
Kulkarni V, Deshmukh K, Bhave A. AN INVERSE MATHEMATICAL APPROACH FOR THERMAL STRESSES IN A SOLID SPHERE. International Journal of Thermodynamics. 2015;18(3):206-11.