Nesasio / Temperature-Distribution-FDM

Temperature Distribution in a Straight Fin using FDM

1-D Temperature Distribution in a Straight Fin using FDM

This repository contains the implementation of steady state temperature dirstribution in a finite straight fin problem in MATLAB. To determine the temperature distribution at the grid points Finite Difference Method (FDM) was used.

Parameters

• Length of the Fin: $L=4cm$
• Perimeter of the Fin: $P=40.4cm$
• Cross-section Area: $A_c=4cm^2$
• Base Temperature of the Fin: $T_b=225\degree C$
• Ambient Temperature: $T_\infty=25\degree C$
• Conductivity of the Fin Material: $k=45 W/m K$
• Convection Heat Transfer Coefficient: $h=15 W/m^2K$

Analytical Solution

It is assumed that the tip of the fin is insulated. The analytical solution of the problem is as follows: $$\frac{ T(x) - T_\infty }{ T_b - T_\infty } = \frac{ \cosh m(L - x) }{ \cosh mL }$$ where $\displaystyle m=\sqrt{ \frac{hP}{kA_c} }$

Finite Difference Method

The temperature distribution is calculated at every grid point using FDM. The distance between grid points $\Delta x$ is taken as $0.5cm$.