Simulation of Heat Conduction by Smoothed Particle Hydrodynamics: Application for Two Dimensional Skew Symmetric Bodies

ABSTRACT

Two dimensional skew symmetric bodies are bounded by isothermal and adiabatic boundaries having a specific temperature glide across it. For such type bodies there exists a thermal line of symmetry along which adiabatic boundaries replicate over the isothermal boundaries. Geometric line of symmetry may or may not coincide with thermal line of symmetry depending on the distribution of boundary conditions. In 1995 Kuyper [1] proposed that the two dimensional heat conduction through skew symmetric bodies are very unique and does not depend on the geometry or the size of the body. The shape factor reduces to 1 for this class of specially symmetric geometry. But due to the inherent complicacy associated with common numerical methodologies in handling irregular shape and arbitrary distribution of two different types of boundary conditions this conjecture has not been verified.

In the present paper we have employed Lagrangian smoothed particle hydrodynamics (SPH) method for solving conduction problem in irregular skewsymmetric bodies. Organization and locations for virtual particles are also discussed for both Dirichlet and Neumann boundary conditions. Three different problems having typical geometries that pose numerical complicacies in grid based technique, are tackled by SPH efficiently. To substantiate the proposition of Kuyper [1] conduction shape factor has been calculated from numerical simulations. It shows that calculation of heat flux from any arbitrary geometry depends only on the temperature glide between the two constant temperature boundaries and the material thermal conductivity as proposed by Kuyper [1].

Keywords: Skew symmetric, Shape factor, Smoothed particle hydrodynamics, Irregular geometry.

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