Persamaan distribusi panas paa batang homogen dengan panjang tak hingga

Abstract

Dalam skripsi ini dibahas temperatur dari batang uniform yang tipis dan panjang tak hingga yang mengalami konduksi dengan persamaan panas berbentuk homogen daft non homogen. Pada persamaan panas ini tidak meiniliki syarat Batas tetapi hanya ada syarat awal. Pada persamaan panas homogen dalam mencari solusinya digunakan transformasi fourier sehingga didapatkan persamaan diferensial kemudian dieari solusinya dan digunakan theorema konvolusi maka didapatkan solusi persamaan panas homogen, pada persamaan panas non homogen digunakan asumsi bahwa solusinya berupa fungsi Green dan fungsi Green tersebut di transformasi Fourier kan sehingga didapatkan sebuah Gaussian dan menerapakn identitas Lagrange untuk mendapatkan solusi persamaan panas non homogen. Pada persamaan panas dengan panjang talc hingga dapat digunakan pada persamaan panas yang mempunyai daerah asal berhingga dimana temperatur yang didapatkan diskontinu dan akan mengetahui apa yang terjadi waktu yang singkat. The paper analyzed temperature from very long uniform tin rod that had conduction with homogenous and non homogeneous the heat equation. Boundaries condition shouldn't be important and initial condition used to predict the future temperature. Fourier Transformation used to solve homogenous heat equation so obtained ordinary differential equation, applied the initial condition, determined the initial Fourier transform and than used the convolution theorem. The Green's function defined as solution of non homogenous heat equation. To solved the problem used the Fourier transform of the Green's function, so obtained a Gaussian, applied Lagrange's identity to get solution non homogeneous heat equation. If have a temperature discontinuity for the heat equation in a finite domain, and wish to understand what happens for the short time, the boundaries shouldn't be important so used infinite domain heat equation with discontinuity initial temperature which a simpler problem. The paper analyzed temperature from very long uniform tin rod that had conduction with homogenous and non homogeneous the heat equation. Boundaries condition shouldn't be important and initial condition used to predict the future temperature. Fourier Transformation used to solve homogenous heat equation so obtained ordinary differential equation, applied the initial condition, determined the initial Fourier transform and than used the convolution theorem. The Green's function defined as solution of non homogenous heat equation. To solved the problem used the Fourier