Analytical solution for the transient temperature distribution in a moving rod or plate of finite length with surface heat transfer

S. Roy Choudhury, Y. Jaluria

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17 Citations (Scopus)

Abstract

An analytical solution for the transient temperature distribution in a wide flat plate and in a cylindrical rod of finite length moving at a constant speed and subjected to convective heat transfer at the surface is obtained. The analytical solution is obtained as an infinite series. However, inclusion of the first 25 terms of the series was found to be sufficient to obtain a converged solution in most cases. The analytical solutions are compared with previously obtained numerical solutions for this moving boundary problem. Excellent agreement between the analytical and numerical results is obtained, indicating the importance of the analytical solution for the validation of numerical schemes. The variation of the temperature field within the material with time is investigated. Even though this is one of the first attempts to solve, analytically, the problem of a finite-length moving material subjected to surface heat transfer, the analytical solutions are found to be of limited use at moderate or large times. However, at very small times, following the start of the process, numerical solutions are often quiet inaccurate. Then the analytical results are particularly useful. The versatility and ease of application of the numerical method are discussed.

Original languageEnglish (US)
Pages (from-to)1193-1205
Number of pages13
JournalInternational Journal of Heat and Mass Transfer
Volume37
Issue number8
DOIs
StatePublished - May 1994

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Temperature distribution
temperature distribution
rods
heat transfer
Heat transfer
Numerical methods
convective heat transfer
versatility
flat plates
inclusions

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Cite this

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abstract = "An analytical solution for the transient temperature distribution in a wide flat plate and in a cylindrical rod of finite length moving at a constant speed and subjected to convective heat transfer at the surface is obtained. The analytical solution is obtained as an infinite series. However, inclusion of the first 25 terms of the series was found to be sufficient to obtain a converged solution in most cases. The analytical solutions are compared with previously obtained numerical solutions for this moving boundary problem. Excellent agreement between the analytical and numerical results is obtained, indicating the importance of the analytical solution for the validation of numerical schemes. The variation of the temperature field within the material with time is investigated. Even though this is one of the first attempts to solve, analytically, the problem of a finite-length moving material subjected to surface heat transfer, the analytical solutions are found to be of limited use at moderate or large times. However, at very small times, following the start of the process, numerical solutions are often quiet inaccurate. Then the analytical results are particularly useful. The versatility and ease of application of the numerical method are discussed.",
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N2 - An analytical solution for the transient temperature distribution in a wide flat plate and in a cylindrical rod of finite length moving at a constant speed and subjected to convective heat transfer at the surface is obtained. The analytical solution is obtained as an infinite series. However, inclusion of the first 25 terms of the series was found to be sufficient to obtain a converged solution in most cases. The analytical solutions are compared with previously obtained numerical solutions for this moving boundary problem. Excellent agreement between the analytical and numerical results is obtained, indicating the importance of the analytical solution for the validation of numerical schemes. The variation of the temperature field within the material with time is investigated. Even though this is one of the first attempts to solve, analytically, the problem of a finite-length moving material subjected to surface heat transfer, the analytical solutions are found to be of limited use at moderate or large times. However, at very small times, following the start of the process, numerical solutions are often quiet inaccurate. Then the analytical results are particularly useful. The versatility and ease of application of the numerical method are discussed.

AB - An analytical solution for the transient temperature distribution in a wide flat plate and in a cylindrical rod of finite length moving at a constant speed and subjected to convective heat transfer at the surface is obtained. The analytical solution is obtained as an infinite series. However, inclusion of the first 25 terms of the series was found to be sufficient to obtain a converged solution in most cases. The analytical solutions are compared with previously obtained numerical solutions for this moving boundary problem. Excellent agreement between the analytical and numerical results is obtained, indicating the importance of the analytical solution for the validation of numerical schemes. The variation of the temperature field within the material with time is investigated. Even though this is one of the first attempts to solve, analytically, the problem of a finite-length moving material subjected to surface heat transfer, the analytical solutions are found to be of limited use at moderate or large times. However, at very small times, following the start of the process, numerical solutions are often quiet inaccurate. Then the analytical results are particularly useful. The versatility and ease of application of the numerical method are discussed.

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