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Solving protoplanetary structure equations using Adomian decomposition method.

Gour Chandra Paul1, Shahinur Khatun1, Md Nuruzzaman2

  • 1Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh.

Heliyon
|November 11, 2021
PubMed
Summary
This summary is machine-generated.

This study investigates thermodynamic variables in protoplanets using the Adomian decomposition method. Results show good agreement between the semi-analytical solution and numerical data for convective heat transfer.

Keywords:
Adomian decomposition methodDisk instabilityProtoplanetThermodynamic variables

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Area of Science:

  • Planetary Science
  • Astrophysics
  • Computational Physics

Background:

  • Protoplanets form through gravitational instability.
  • Understanding their initial thermodynamic state is crucial for planet formation theories.
  • Convective heat transfer plays a significant role in protoplanetary evolution.

Purpose of the Study:

  • To investigate the distribution of thermodynamic variables in protoplanets.
  • To analyze the initial state of protoplanets formed via gravitational instability.
  • To assess the accuracy of the Adomian decomposition method for solving protoplanetary structure equations.

Main Methods:

  • Solving protoplanetary structure equations using the Adomian decomposition method.
  • Incorporating convective heat transfer into the models.
  • Comparing semi-analytical solutions with numerical results.

Main Results:

  • The Adomian decomposition method provides a reasonably accurate semi-analytical solution for protoplanetary thermodynamic variables.
  • The first 8 terms of the Adomian solution show good agreement with numerical results.
  • The distribution of thermodynamic variables in the initial state of protoplanets was successfully modeled.

Conclusions:

  • The Adomian decomposition method is a viable and efficient tool for studying protoplanetary structure.
  • Accurate modeling of thermodynamic variables, including convection, is essential for understanding planet formation.
  • This approach offers a promising alternative to purely numerical simulations for initial protoplanet states.