rerender pdf.

fire. but the pic page is pmo

proj/proj.md

@@ -1,4 +1,8 @@
-# Project: 1D Heat Transfer Simulation Report
+---
+title: |
+   Project: 1D Heat Transfer Simulation Report
+author: Luong Duc Anh
+---
 
 This report summarizes the solution to the 1D Heat Transfer Project, focusing on the numerical solution of the Heat Equation using the Explicit Finite Difference Method.
 
@@ -114,9 +118,9 @@ The algorithm to solve the 1D Heat Equation using the Explicit Finite Difference
 
 1. **Define Parameters and Material Properties:** Set `L`, `dx`, `dt`, `Tg`, `Td`, `T0`, `rho`, `Cp`, `lambda`, and `t_final_s_sim`.
 
-2. **Calculate Thermal Diffusivity (**$\alpha$**):** Compute `α = λ / (ρ * cp)`.
+2. **Calculate Thermal Diffusivity (**$\alpha$**):** Compute `alpha = lambda / (rho * Cp)`.
 
-3. **Calculate Fourier Number (**$r$**) and Check Stability:** Compute `r = α * Δt / (Δx)^2`. For stability, `r` must be $\le 0.5$. A warning is issued if this condition is violated.
+3. **Calculate Fourier Number (**$r$**) and Check Stability:** Compute `r = alpha * dt / (dx)^2`. For stability, `r` must be $\le 0.5$. A warning is issued if this condition is violated.
 
 4. **Discretize Spatial Domain:** Create a vector `x` representing the spatial nodes from `0` to `L` with step `dx`. Determine `Nx`, the total number of nodes.
 
@@ -172,4 +176,4 @@ The MATLAB code implements the algorithm described in Question 6 using the speci
 
 An example of the generated figure (`Figure_1.png`) would be:
 
-![Temperature Profile Evolution](./Figure_1.png)
+![Temperature Profile Evolution](./Figure_1.pdf)