Thermal stresses associated with a thermosensitive multilayered disc analysed due to point heating

• Autorzy: Srinivas, V. B. , Manthena, V. R. , Warbhe, S. D. , Kedar, G. D. , Lamba, Navneet Kumar
• Języki publikacji: EN

Abstrakty

EN

In this paper, analytical solutions are presented for temperature and thermal behavior of a thermosensitive multilayered annular disc due to point heat source. Convective heating is applied to both the innermost and outermost layers. The nonlinearity of the thermal diffusivity equation is dealt using Kirchhoff’s transformation technique. A finite integral transform in the form of Bessel’s function is used to deal with the radial variable r. Fourier transform and angular eigen functions are also used to solve the thermal diffusivity equation. Deflection, resultant forces, shearing forces, resultant moments and thermal stresses are obtained. A mathematical representation is formulated for a 3-layered disc, with the inner, middle and outer layers composed of copper, zinc and aluminum respectively. The results are depicted graphically.

Słowa kluczowe

PL

przepływ ciepła; odchylenie; naprężenie

EN

multilayered annular disc; thermosensitive; heat conduction; instantaneous point heat source; deflection; stresses

• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2024
• Tom: Vol. 29, no. 2
• Strony: 118--137
• Opis fizyczny: Bibliogr. 35 poz., rys., wykr.

Twórcy

autor

Srinivas, V. B.

• Department of Mathematics, Anurag University, Venkatapur, Ghatkesar, Medchal-Malkajgiri District, Telangana, INDIA

autor

Manthena, V. R.

• Department of Mathematics, Priyadarshini J. L. College of Engineering, Nagpur, INDIA,

autor

Warbhe, S. D.

• Department of Mathematics, Laxminarayan Innovation Technological University, Nagpur, INDIA

autor

Kedar, G. D.

• Department of Mathematics, RTM Nagpur University, Nagpur, INDIA

autor

Lamba, Navneet Kumar

• Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Mandhal, Nagpur, INDIA

Bibliografia

• [1] Noda N. (1986): Thermal stresses in materials with temperature dependent properties.– Applied MechanicsReviews, vol.44, pp.383-397, https://api.semanticscholar.org/CorpusID:120719142.
• [2] Olcer N.Y. (1968): A general unsteady heat flow problem in a finite composite hollow circular cylinder underboundary conditions of second kind.– Nuclear Engineering and Design, vol.7, No.2, pp.97-112.https://doi.org/10.1016/0029-5493(68)90052-6.
• [3] Gorman D.G. (1985): Thermal gradient effects upon the vibrations of certain composite circular plates Part I: PlaneOrthotropic.– Journal of Sound and Vibration, vol.101, No.3, pp.337-345, https://doi.org/10.1016/S0022-460X(85)80134-6.
• [4] Popovich V.S. and Fedai B.N. (1997): The axisymmetric problem of thermoelasticity of a multilayer thermosensitivetube.– Journal of Mathematical Sciences, vol.86, pp.2605-2610, https://doi.org/10.1007/BF02356105.
• [5] Popovych V.S. and Makhorkin I.M. (1998): On the solution of heat conduction problems for thermosensitivebodies.– Journal of Mathematical Sciences, vol.88, No.3, pp.352-359, https://doi.org/10.1007/BF02365251.
• [6] Malzbender J. and Jülich F. (2004): Mechanical and thermal stresses in multilayered materials.– Journal of AppliedPhysics, vol.95, No.4, pp.1780-1782. DOI: 10.1063/1.1642289.
• [7] Kayhani M., Nourouzi M. and Delooei A.A. (2010): An exact solution of axi-symmetric conductive heat transfer incylindrical composite laminate under the general boundary condition.– International Journal of Mechanical,Aerospace, Industrial, Mechatronic and Manufacturing Engineering, vol.4, pp.776-783.
• [8] Singh S., Jain P.K. and Rizwan-uddin (2010): Analytical solution of time-dependent multilayer heat conductionproblems for nuclear applications.– Proceedings of the 1st International Nuclear and Renewable Energy Conference(INREC10), Amman, Jordan, March 21-24, https://doi.org/10.1109/INREC.2010.5462601.
• [9] Singh S., Jain P.K. and Rizwan-uddin (2011): Finite integral transform method to solve asymmetric heat conductionin a multilayer annulus with time-dependent boundary conditions.– Nuclear Engineering and Design, vol.241, No.1,pp.144-154. https://doi.org/10.1016/j.nucengdes.2010.10.010.
• [10] Kayhani M., Nourouzi M. and Delooei A.A. (2012): A general analytical solution for heat conduction in cylindricalmultilayer composite laminates.– International Journal of Thermal Sciences, vol.52, No.1, pp.73-82,10.1016/j.ijthermalsci.2011.09.002.
• [11] Norouzi M., Delouei A.A. and Seilsepour M. (2013): A general exact solution for heat conduction in multilayer sphericalcomposite laminates.– Composite Structures, vol.106, pp.288-295, http://dx.doi.org/10.1016/j.compstruct.2013.06.005.
• [12] Dalir N. and Nourazar S.S. (2014): Analytical solution of the problem on the three-dimensional transient heatconduction in a multilayer cylinder.– Journal of Engineering Physics and Thermophysics, vol.87, No.1, pp.89-97,DOI: 10.1007/s10891-014-0988-2.
• [13] Popovych V.S. and Kalynyak B.M. (2016): Mathematical modelling and methods for the determination of the staticthermoelastic state of multilayer thermally sensitive cylinders.– Journal of Mathematical Sciences, vol.215, pp.218-242, https://doi.org/10.1007/s10958-016-2833-y.
• [14] Torabi M. and Zhang K. (2016): Analytical solution for transient temperature and thermal stresses within convectivemultilayer discs with time-dependent internal heat generation, Part I: Methodology.– Journal of Thermal Stresses,vol.39, No.4, pp.398-413, DOI: 10.1080/01495739.2016.1152132.
• [15] Manthena V.R., Lamba N.K., Kedar G.D. and Deshmukh K.C. (2016): Effects of stress resultants on thermal stressesin a functionally graded rectangular plate due to temperature dependent material properties.– International Journalof Thermodynamics, vol.19, No.4, pp.235-242, DOI: 10.5541/ijot.5000201356.
• [16] Bhad P., Varghese V. and Khalsa L. (2017): Heat production in a simply supported multilayer elliptic annuluscomposite plate and its associated thermal stresses.– Journal of Stress Analysis, vol.2, issue 2,DOI: 10.22084/jrstan.2018.15081.1034.
• [17] Manthena V.R., Lamba N.K. and Kedar G.D. (2018): Estimation of thermoelastic state of a thermally sensitivefunctionally graded thick hollow cylinder: a mathematical model.– Journal of Solid Mechanics, vol.10, No.4,pp.766-778, doi: 20.1001.1.20083505.2018.10.4.6.4.
• [18] Manthena V.R. and Kedar G.D. (2018): Mathematical modeling of thermoelastic state of a functionally gradedthermally sensitive thick hollow cylinder with internal heat generation.– International Journal of Thermodynamics,vol.21, No.4, pp.202-212, https://doi.org/10.5541/ijot.434180.
• [19] Manthena V.R. and Kedar G.D. (2018): Transient thermal stress analysis of a functionally graded thick hollowcylinder with temperature dependent material properties.– Journal of Thermal Stresses, vol.41, No.5, pp.568-582,DOI: 10.1080/01495739.2017.1402669.
• [20] Manthena V.R. and Kedar G.D. (2019): On thermoelastic problem of a thermosensitive functionally gradedrectangular plate with instantaneous point heat source.– Journal of Thermal Stresses, vol.42, No.7, pp.849-862,https://doi.org/10.1080/01495739.2019.1587327.
• [21] Manthena V.R. (2019): Uncoupled thermoelastic problem of a functionally graded thermosensitive rectangularplate with convective heating.– Archive of Applied Mechanics, vol.89, No.8, pp.1627-1639, DOI: 10.1007/s00419-019-01532-1.
• [22] Manthena V.R., Srinivas V.B. and Kedar G.D. (2020): Analytical solution of heat conduction of a multilayeredannular disc and associated thermal deflection and thermal stresses.– Journal of Thermal Stresses, vol.43, No.5,pp.563-578, https://doi.org/10.1080/01495739.2020.1735975.
• [23] Jangid K. and Mukhopadhyay S. (2020): Variational and reciprocal principles on the temperature-rate dependenttwo-temperature thermoelasticity theory.– Journal of Thermal Stresses, vol.43, issue 7, pp.816-828,DOI: 10.1080/01495739.2020.1753607.
• [24] Etkin V. (2021): Solving the problem of thermodynamic inequalities.– International Journal of Thermodynamics,vol.24, No.1, pp.54-60, https://doi.org/10.5541/ijot.874737.
• [25] Srinivas V.B., Manthena V.R., Bikram J. and Kedar G.D. (2021): Fractional order heat conduction andthermoelastic response of a thermally sensitive rectangular parallelepiped.– International Journal ofThermodynamics, vol.24, issue 1, pp.62-73, https://doi.org/10.5541/ijot.849663.
• [26] Razavi S.E., Adibi T. and Hassanpour H. (2021): Thermo-flow analysis of cylinder with crossed splitter plates witha characteristics-based scheme.– International Journal of Thermodynamics, vol.24, No.2, pp.83-91.https://doi.org/10.5541/ijot.783614.
• [27] Balci E. and Akpinar S. (2021): Quaternary element incorporation effects on thermal properties and crystal-microstructure of Cu-Al-Fe high temperature shape memory alloys.– International Journal of Thermodynamics, vol.24,No.2, pp.119-126, https://doi.org/10.5541/ijot.805275.
• [28] Bikram J. and Kedar G.D. (2021): Study of thermoelastic behaviour, efficiency and effectiveness of rectangular finwith fractional order energy balance equation.– International Journal of Thermodynamics, vol.24, No.3, pp.216-225, https://doi.org/10.5541/ijot.879603.
• [29] Etkin V. (2021): Synthesis of equilibrium and non-equilibrium thermodynamics.– International Journal ofThermodynamics, vol.24, No.4, pp.91-101, https://doi.org/10.5541/ijot.912365.
• [30] Su C.H., Hwu C. and Nguyen V.T. (2021): Transient thermal stress analysis of temperature-dependent anisotropicviscoelastic solids.– Journal of Thermal Stresses, vol.44, No.12, pp.1495-1513.https://doi.org/10.1080/01495739.2021.2000344.
• [31] Lamba N.K. (2022): Thermosensitive response of a functionally graded cylinder with fractional order derivative.–International Journal of Applied Mechanics and Engineering, vol.27, No.1, pp.107-124.https://doi.org/10.2478/ijame-2022-0008.
• [32] Yadav A.K., Singh A. and Jurczak P. (2023): Memory dependent triple-phase-lag thermo-elasticity in thermo-diffusive medium.– International Journal of Applied Mechanics and Engineering, vol.28, No.4, pp.137-162,DOI: https://doi.org/10.59441/ijame/172631.
• [33] Roy S. and Lahiri A. (2020): A study on fractional order thermoelastic half space.– International Journal of AppliedMechanics and Engineering, vol.25, No.4, pp.191-202, doi:10.2478/ijame-2020-0058.
• [34] Lamba N. (2023): Impact of memory-dependent response of a thermoelastic thick solid cylinder.– Journal of Appliedand Computational Mechanics, vol.9, No.4, pp.1135-1143, doi: 10.22055/jacm.2023.43952.4149.
• [35] Noda N., Hetnarski R.B. and Tanigawa Y. (2003): Thermal Stresses, second edition.– Taylor & Francis, New York.

Identyfikatory

DOI

10.59441/ijame/187051