qx=−kdTdxq sub x equals negative k the fraction with numerator d cap T and denominator d x end-fraction is thermal conductivity (
q=ϵσ(Ts4−Tsur4)q equals epsilon sigma open paren cap T sub s to the fourth power minus cap T sub s u r end-sub to the fourth power close paren is emissivity. is the Stefan-Boltzmann constant ( MATLAB Example 1: 1D Steady-State Heat Conduction qx=−kdTdxq sub x equals negative k the fraction
We use the Finite Difference Method (FDM) to break down the continuous partial differential equation into discrete steps that MATLAB can calculate iteratively. qx=−kdTdxq sub x equals negative k the fraction
We first define our physical constants and grid points in MATLAB. Step 2: Solve System qx=−kdTdxq sub x equals negative k the fraction
The plot above visualizes the strictly linear temperature drop across the material.