Current issue
Archive
About the Journal
About
Editorial Board
Abstract & Indexing
Contact
Editorial Policies
Authorship & COI
Ethical principles
Principles of Transparent Checklist
Open access
For Authors
Instructions to Authors
Detailing Guidelines for Authors
Review process
Review sheet
How to submit
Open Access license
ORIGINAL PAPER
Thermal stresses associated with a thermosensitive multilayered disc analysed due to point heating
1
Department of Mathematics, Anurag University, Venkatapur, Ghatkesar, Medchal-Malkajgiri District, Telangana, INDIA, India
2
Department of Mathematics, Priyadarshini J. L. College of Engineering, Nagpur, INDIA., India
3
Department of Mathematics, Laxminarayan Innovation Technological University, Nagpur, INDIA, India
4
Department of Mathematics, RTM Nagpur University, Nagpur, INDIA, India
5
Mathematics, Shri Lemdeo Patil Mahavidyalaya, Mandhal, India
Submission date: 2024-01-29
Final revision date: 2024-02-29
Acceptance date: 2024-04-11
Online publication date: 2024-06-19
Publication date: 2024-06-27
Corresponding author
International Journal of Applied Mechanics and Engineering 2024;29(2):118-137
KEYWORDS
TOPICS
elasticityplasticitymechanics of structuresplates & shellsthermodynamicsmaterial sciencematerials engineering
ABSTRACT
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.
REFERENCES (35)
1.
Noda N. (1986): Thermal stresses in materials with temperature dependent properties.– Applied Mechanics Reviews, vol.44, pp.383-397, https://api.semanticscholar.or....
2.
Olcer N.Y. (1968): A general unsteady heat flow problem in a finite composite hollow circular cylinder under boundary conditions of second kind.– Nuclear Engineering and Design, vol.7, No.2, pp.97-112. https://doi.org/10.1016/0029-5....
3.
Gorman D.G. (1985): Thermal gradient effects upon the vibrations of certain composite circular plates Part I: Plane Orthotropic.– Journal of Sound and Vibration, vol.101, No.3, pp.337-345, https://doi.org/10.1016/S0022-....
4.
Popovich V.S. and Fedai B.N. (1997): The axisymmetric problem of thermoelasticity of a multilayer thermosensitive tube.– Journal of Mathematical Sciences, vol.86, pp.2605-2610, https://doi.org/10.1007/BF0235....
5.
Popovych V.S. and Makhorkin I.M. (1998): On the solution of heat conduction problems for thermosensitive bodies.– Journal of Mathematical Sciences, vol.88, No.3, pp.352-359, https://doi.org/10.1007/BF0236....
6.
Malzbender J. and Jülich F. (2004): Mechanical and thermal stresses in multilayered materials.– Journal of Applied Physics, 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 in cylindrical 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 conduction problems 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.....
9.
Singh S., Jain P.K. and Rizwan-uddin (2011): Finite integral transform method to solve asymmetric heat conduction in 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.nuce....
10.
Kayhani M., Nourouzi M. and Delooei A.A. (2012): A general analytical solution for heat conduction in cylindrical multilayer 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 spherical composite laminates.– Composite Structures, vol.106, pp.288-295, http://dx.doi.org/10.1016/j.co....
12.
Dalir N. and Nourazar S.S. (2014): Analytical solution of the problem on the three-dimensional transient heat conduction 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 static thermoelastic state of multilayer thermally sensitive cylinders.– Journal of Mathematical Sciences, vol.215, pp.218-242, https://doi.org/10.1007/s10958....
14.
Torabi M. and Zhang K. (2016): Analytical solution for transient temperature and thermal stresses within convective multilayer 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 stresses in a functionally graded rectangular plate due to temperature dependent material properties.– International Journal of 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 annulus composite 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 sensitive functionally 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 graded thermally 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.4....
19.
Manthena V.R. and Kedar G.D. (2018): Transient thermal stress analysis of a functionally graded thick hollow cylinder 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 graded rectangular plate with instantaneous point heat source.– Journal of Thermal Stresses, vol.42, No.7, pp.849-862, https://doi.org/10.1080/014957....
21.
Manthena V.R. (2019): Uncoupled thermoelastic problem of a functionally graded thermosensitive rectangular plate 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 multilayered annular disc and associated thermal deflection and thermal stresses.– Journal of Thermal Stresses, vol.43, No.5, pp.563-578, https://doi.org/10.1080/014957....
23.
Jangid K. and Mukhopadhyay S. (2020): Variational and reciprocal principles on the temperature-rate dependent two-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.8....
25.
Srinivas V.B., Manthena V.R., Bikram J. and Kedar G.D. (2021): Fractional order heat conduction and thermoelastic response of a thermally sensitive rectangular parallelepiped.– International Journal of Thermodynamics, vol.24, issue 1, pp.62-73, https://doi.org/10.5541/ijot.8....
26.
Razavi S.E., Adibi T. and Hassanpour H. (2021): Thermo-flow analysis of cylinder with crossed splitter plates with a characteristics-based scheme.– International Journal of Thermodynamics, vol.24, No.2, pp.83-91. https://doi.org/10.5541/ijot.7....
27.
Balci E. and Akpinar S. (2021): Quaternary element incorporation effects on thermal properties and crystal-micro structure 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.8....
28.
Bikram J. and Kedar G.D. (2021): Study of thermoelastic behaviour, efficiency and effectiveness of rectangular fin with fractional order energy balance equation.– International Journal of Thermodynamics, vol.24, No.3, pp.216-225, https://doi.org/10.5541/ijot.8....
29.
Etkin V. (2021): Synthesis of equilibrium and non-equilibrium thermodynamics.– International Journal of Thermodynamics, vol.24, No.4, pp.91-101, https://doi.org/10.5541/ijot.9....
30.
Su C.H., Hwu C. and Nguyen V.T. (2021): Transient thermal stress analysis of temperature-dependent anisotropic viscoelastic solids.– Journal of Thermal Stresses, vol.44, No.12, pp.1495-1513. https://doi.org/10.1080/014957....
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-....
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....
33.
Roy S. and Lahiri A. (2020): A study on fractional order thermoelastic half space.– International Journal of Applied Mechanics 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 Applied and 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.
Share
RELATED ARTICLE
| eISSN: | 2353-9003 |
| ISSN: | 1734-4492 |
Task: edition of a scientific journal, its internationalization and ensuring open access to the journal via the Internet
© 2006-2024 Journal hosting platform by Bentus
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
