Transient Heat Conduction in Nonuniform Hollow Cylinders with Time Dependent Boundary Condition at One Surface
A solution methodology without using integral
transformation is proposed to develop analytical solutions for
transient heat conduction in nonuniform hollow cylinders with
time-dependent boundary condition at the outer surface. It is shown
that if the thermal conductivity and the specific heat of the medium
are in arbitrary polynomial function forms, the closed solutions of the
system can be developed. The influence of physical properties on the
temperature distribution of the system is studied. A numerical
example is given to illustrate the efficiency and the accuracy of the
solution methodology.
[1] Őzisik, M.N., Boundary value problems of heat conduction, first ed.,
International Textbook Company, Scranton, 1968, pp. 125-163.
[2] Obata, Y. and Noda, N., “Steady Thermal Stresses in a Hollow Circular
Cylinder and a Hollow Sphere of a Functionally Gradient Material”,
Journal of Thermal stresses, vol. 17, 1994, pp. 471– 487.
[3] Awaji, H. and Sivakumar, R., “Temperature and Stress Distributions in a
Hollow Cylinder of Functionally Graded Material: The Case of
Temperature- Dependent Material Properties”, Journal of the American
Ceramic Society, vol. 84, 2001, pp. 1059 – 1065.
[4] Praveen, G.N. and Reddy, J.N., “Nonlinear Transient Thermoelastic
Analysis of Functionally Graded Ceramic-Metal Plates”, International
Journal of Solids and Structures, vol. 35, pp. 4457– 4476, 1998.
[5] Jabbari, M., Sohrabpour, S. and Eslami, M.R., “Mechanical and Thermal
Stresses in a Functionally Graded Hollow Cylinder due to Radially
Symmetric Loads”, International Journal of Pressure Vessels and Piping,
vol. 79, 2002, pp. 493 – 497.
[6] Jabbari, M., Sohrabpour, S. and Eslami, M.R., “General Solution for
Mechanical and Thermal Stresses in a Functionally Graded Hollow
Cylinder due to Nonaxisymmetric Steady-State Loads”, ASME Journal
of Applied Mechanics, vol. 70, 2003, pp. 111 – 118.
[7] Ootao, Y. and Tanigawa, Y., “Transient Thermoelastic Analysis for a
Functionally Graded Hollow Cylinder”, Journal of Thermal Stresses, vol.
29, 2006, pp. 1031 – 1046.
[8] Zhao, J., Ai, X., Li, Y.Z. and Zhou, Y.H., “Thermal Shock Resistance of
Functionally Gradient Solid Cylinders”, Materials Science and
Engineering, vol. 418, 2006, pp. 99 – 110.
[9] Hosseini, S.M., Akhlaghi, M. and Shakeri, M., “Transient Heat
Conduction in Functionally Graded Thick Hollow Cylinders by
Analytical Method”, Heat Mass Transfer, vol. 43, 2007, pp. 669 – 675.
[10] Shao, Z.S. and Ma, G.W., “Thermo-Mechanical Stresses in Functionally
Graded Circular Hollow Cylinder with Linearly Increasing Boundary
Temperature”, Composite Structures, vol. 83, 2008, pp. 259 – 265.
[11] Wang, H.M. and Liu, C.B., “Analytical solution of two-dimensional
transient heat conduction in fiber-reinforced cylindrical composites”,
International Journal of Thermal Sciences, vol. 69, 2013, pp. 43-52.
[12] Lee, S.Y. and Huang, C.C., “Exact solutions for Heat Conduction in
Functionally Graded Circular Hollow Cylinders with Time Dependent Boundary Conditions”, Mathematical Problems in Engineering, vol.
2013, Article ID 816385, 8 pages.
[13] Lee, S.Y. and Huang, T.W., “Exact solutions for Heat Conduction in
Non-uniform Mediums with General Time-Dependent Boundary
Conditions”, J. Chinese Society of Mechanical Engineering, vol.34, no.6,
2013, pp.475-485.
[14] Lee, S.Y. and Lin, S.M., “Dynamic analysis of nonuniform beams with
time-dependent elastic boundary conditions”, ASME Journal of Applied
Mechanics, vol. 63, 1996, pp. 474-478.
[1] Őzisik, M.N., Boundary value problems of heat conduction, first ed.,
International Textbook Company, Scranton, 1968, pp. 125-163.
[2] Obata, Y. and Noda, N., “Steady Thermal Stresses in a Hollow Circular
Cylinder and a Hollow Sphere of a Functionally Gradient Material”,
Journal of Thermal stresses, vol. 17, 1994, pp. 471– 487.
[3] Awaji, H. and Sivakumar, R., “Temperature and Stress Distributions in a
Hollow Cylinder of Functionally Graded Material: The Case of
Temperature- Dependent Material Properties”, Journal of the American
Ceramic Society, vol. 84, 2001, pp. 1059 – 1065.
[4] Praveen, G.N. and Reddy, J.N., “Nonlinear Transient Thermoelastic
Analysis of Functionally Graded Ceramic-Metal Plates”, International
Journal of Solids and Structures, vol. 35, pp. 4457– 4476, 1998.
[5] Jabbari, M., Sohrabpour, S. and Eslami, M.R., “Mechanical and Thermal
Stresses in a Functionally Graded Hollow Cylinder due to Radially
Symmetric Loads”, International Journal of Pressure Vessels and Piping,
vol. 79, 2002, pp. 493 – 497.
[6] Jabbari, M., Sohrabpour, S. and Eslami, M.R., “General Solution for
Mechanical and Thermal Stresses in a Functionally Graded Hollow
Cylinder due to Nonaxisymmetric Steady-State Loads”, ASME Journal
of Applied Mechanics, vol. 70, 2003, pp. 111 – 118.
[7] Ootao, Y. and Tanigawa, Y., “Transient Thermoelastic Analysis for a
Functionally Graded Hollow Cylinder”, Journal of Thermal Stresses, vol.
29, 2006, pp. 1031 – 1046.
[8] Zhao, J., Ai, X., Li, Y.Z. and Zhou, Y.H., “Thermal Shock Resistance of
Functionally Gradient Solid Cylinders”, Materials Science and
Engineering, vol. 418, 2006, pp. 99 – 110.
[9] Hosseini, S.M., Akhlaghi, M. and Shakeri, M., “Transient Heat
Conduction in Functionally Graded Thick Hollow Cylinders by
Analytical Method”, Heat Mass Transfer, vol. 43, 2007, pp. 669 – 675.
[10] Shao, Z.S. and Ma, G.W., “Thermo-Mechanical Stresses in Functionally
Graded Circular Hollow Cylinder with Linearly Increasing Boundary
Temperature”, Composite Structures, vol. 83, 2008, pp. 259 – 265.
[11] Wang, H.M. and Liu, C.B., “Analytical solution of two-dimensional
transient heat conduction in fiber-reinforced cylindrical composites”,
International Journal of Thermal Sciences, vol. 69, 2013, pp. 43-52.
[12] Lee, S.Y. and Huang, C.C., “Exact solutions for Heat Conduction in
Functionally Graded Circular Hollow Cylinders with Time Dependent Boundary Conditions”, Mathematical Problems in Engineering, vol.
2013, Article ID 816385, 8 pages.
[13] Lee, S.Y. and Huang, T.W., “Exact solutions for Heat Conduction in
Non-uniform Mediums with General Time-Dependent Boundary
Conditions”, J. Chinese Society of Mechanical Engineering, vol.34, no.6,
2013, pp.475-485.
[14] Lee, S.Y. and Lin, S.M., “Dynamic analysis of nonuniform beams with
time-dependent elastic boundary conditions”, ASME Journal of Applied
Mechanics, vol. 63, 1996, pp. 474-478.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:70668", author = "Sen Yung Lee and Chih Cheng Huang and Te Wen Tu", title = "Transient Heat Conduction in Nonuniform Hollow Cylinders with Time Dependent Boundary Condition at One Surface", abstract = "A solution methodology without using integral
transformation is proposed to develop analytical solutions for
transient heat conduction in nonuniform hollow cylinders with
time-dependent boundary condition at the outer surface. It is shown
that if the thermal conductivity and the specific heat of the medium
are in arbitrary polynomial function forms, the closed solutions of the
system can be developed. The influence of physical properties on the
temperature distribution of the system is studied. A numerical
example is given to illustrate the efficiency and the accuracy of the
solution methodology.", keywords = "Analytical solution, nonuniform hollow cylinder,
time-dependent boundary condition, transient heat conduction.", volume = "9", number = "7", pages = "1321-6", }
