Mumbai University > Mechanical Engineering > Sem 6 > Finite Element Analysis

Marks: 5M

Year: may 2016

i) 1-D steady state, heat transfer by conduction

Element matrix equation,

$\frac{KA}{he} \begin{bmatrix} \ 1 & -1 \\ \ -1 & 1 \\ \end{bmatrix} \begin{Bmatrix}\ \theta_1 \\ \ \theta_2 \\ \end{Bmatrix} = \begin{Bmatrix}\ Q_1^2 \\ \ Q_2^2 \\ \end{Bmatrix}$

Where, K = thermal conductivity

A = cross section area

he = length of an element

Q = Heat input

ii) 1 - D, steady state flow of fluid in a pipe.

$\frac{\pi d^4}{128 \mu he} \begin{bmatrix} \ 1 & -1 \\ \ -1 & 1 \\ \end{bmatrix} \begin{Bmatrix} \ \rho_1^e \\ \ \rho_2^e \\ \end{Bmatrix} = \begin{Bmatrix} \ Q_1^e \\ \ Q_2^e \\ \end{Bmatrix}$

Where, $\mu$ = viscosity of fluid

he = length of an element

Q = flow rate (Dischange)

P = pressure