Skip to main content
SpringerLink
Log in
Book cover

Thermal Stresses—Advanced Theory and Applications pp 133–224Cite as

Heat Conduction Problems

  • Chapter
  • First Online:

  • 1731 Accesses

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 158))

Abstract

The ability of obtaining the temperature distribution in an elastic continuum through the solutions of the heat conduction equation is an essential tool for the analysis of thermal stress problems. The analytical methods of solution of heat conduction problems may be classified as the differential, the lumped, and the integral formulations. This chapter presents the analytical methods of solution of heat conduction problems based on the differential and lumped formulations. Similar to the analysis given in Chap. 3, this chapter presents the method of analysis of heat conduction in three main classical coordinate systems, namely the rectangular Cartesian coordinates, the cylindrical coordinates, and the spherical coordinates. The temperature distributions in each coordinate system for one-, two-, and three-dimensional problems for steady-state and transient conditions are obtained. The temperature distributions in a number of structures of functionally graded materials are also presented. The basic mathematical techniques of solution are discussed. The extent of the heat conduction analysis given in this chapter should be adequate for further applications to various thermal stress problems.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Arpaci VS (1966) Conduction Heat Transfer. Addison-Wesley, Reading, Massachusets

    MATH  Google Scholar 

  2. Carslaw HS, Jaeger JC (1959) Conduction of Heat in Solids. Clarendon, Oxford

    MATH  Google Scholar 

  3. Holman JP (1963) Heat Transfer. McGraw-Hill, New York

    Google Scholar 

  4. Kreith F (1973) Principles of Heat Transfer. Intext Educational, New York

    Google Scholar 

  5. Noda N, Hetnarski RB, Tanigawa Y (2003) Thermal Stresses, 2nd edn. Taylor and Francis, New York

    Google Scholar 

  6. Koniorczyk P, Zmywaczyk J (2014) Two-dimensional steady-state conduction. In: Hetnarski RB (ed) Encyclopedia of thermal stresses, vol 11. Springer, Dordrecht, pp 6260–6277

    Chapter  Google Scholar 

  7. Frąckowiak A, Ciałkowski M (2014) Green’s functions in steady-state conduction. In: Hetnarski RB (ed) Encyclopedia of thermal stresses, vol 4. Springer, Dordrecht, pp 2053–2061

    Google Scholar 

  8. Seremet V (2014) Green’s functions in three-dimensional thermoelastostatic. In: Hetnarski RB (ed) Encyclopedia of thermal stresses, vol 2061–2070. Springer, Dordrecht, pp 2061–2070

    Chapter  Google Scholar 

  9. Pipes LA, Harvill LR (1970) Applied mathematics for engineers and physicists. McGraw-Hill, New York

    Google Scholar 

  10. Bowman F (1958) Introduction to Bessel functions. Dover, New York

    Google Scholar 

  11. McLachlan NW (1955) Bessel functions for engineers. Clarendon, Oxford

    MATH  Google Scholar 

  12. Johnson DG, Johnson JR (1965) Mathematical methods in engineering and physics. Ronald, New York

    Book  Google Scholar 

  13. Korn GA, Korn TM (1968) Mathematical handbook for scientists and engineers. McGraw-Hill, New York

    MATH  Google Scholar 

  14. Sabbaghian M, Eslami MR (1974) Creep relaxation of nonaxisymmetric thermal stresses in thick walled cylinders. AIAA J 12(12):1652–1658

    Article  Google Scholar 

  15. Kantorovich LV, Krylov VI (1964) Approximate methods of higher analysis, Interscience, New York. P. Noordhoff Groningen, The Netherlands

    Google Scholar 

  16. Hetnarski RB, Ignaczak J (2011) The mathematical theory of elasticity, 2nd edn. CRC Press, Boca Raton

    MATH  Google Scholar 

  17. Takeuti Y, Noda N (1980) Three-dimensional transient thermal stresses in a finite circular cylinder under nonaxisymmetric temperature distribution. J Therm Stress 3(2):159–183

    Article  Google Scholar 

  18. Takeuti Y, Noda N (1979) Thermal stress problems in industry, 2: transient thermal stresses in Disk Brake. J Therm Stress 2(1):61–72

    Article  Google Scholar 

  19. Hetnarski RB (1969) Stresses in long cylinder due to rotating line source of heat. AIAA J 7(3):419–423

    Article  Google Scholar 

  20. Abramowitz M, Stegun J (1965) Handbook of mathematical functions. Dover, New York

    MATH  Google Scholar 

  21. Cheung JB, Chen TS, Thirumalai K (1974) Transient thermal stresses in a sphere by local heating. J Appl Mech 41(4):930–934

    Article  Google Scholar 

  22. Olecer NY (1965) On the theory of conductive heat transfer in finite regions with boundary conditions of the second kind. Int J Heat Mass Tran 8:529–556

    Article  Google Scholar 

  23. Takeuti Y, Tanigawa Y (1982) Transient thermal stresses of a hollow sphere due to rotating heat source. J Therm Stress 5(3–4):283–298

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. 7117 Pelican Bay Blvd., Apt.1209, Naples, FL, 34108, USA

    Richard B. Hetnarski

  2. Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran

    M. Reza Eslami

Authors
  1. Richard B. Hetnarski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Reza Eslami
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Richard B. Hetnarski .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Hetnarski, R.B., Eslami, M.R. (2019). Heat Conduction Problems. In: Thermal Stresses—Advanced Theory and Applications. Solid Mechanics and Its Applications, vol 158. Springer, Cham. https://doi.org/10.1007/978-3-030-10436-8_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-10436-8_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10435-1

  • Online ISBN: 978-3-030-10436-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation