### Application of Jacobi Polynomial and Multivariable Aleph- Function in Heat Conduction in Non-Homogeneous Moving Rectangular Parallelepiped

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**Authors:**D. KUMAR AND F. AYANT

**DOI:**10.46793/KgJMat2103.439K

**Abstract:**

The present paper deals with an application of Jacobi polynomial and multivariable Aleph-function to solve the diﬀerential equation of heat conduction in non-homogeneous moving rectangular parallelepiped. The temperature distribution in the parallelepiped, moving in a direction of the length (x-axis) between the limits x = −1 and x = 1 has been considered. The conductivity and the velocity have been assumed to be variables. We shall see two particular cases and the cases concerning Aleph-function of two variables and the I-function of two variables.

**Keywords:**

Jacobi polynomial, heat conduction, Aleph-function of several variables, aleph-function of two variables, I-function of two variables.

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