Some Examples of the Second Order Equations in One Dimension
-d/dx(adu/dx) = q for 0 < x < L
[Taken from J. N. Reddy's Book "Introduction to the Finite Element Method", J.N. Reddy, McGraw Hill Publishers, 2nd Edition, Page 71]
Field |
Primary Variable u |
Constant a |
Source term q |
Secondary Variable Qo |
Transverse Deflection of a Cable |
Transverse Deflection | Tension in Cable |
Heat Source Q |
Axial Force |
Axial Deformation of a bar |
Longitudiunal Dispalcement | EA (E= Young's Modulus, A = Cross Sectional Area) |
Distributed Transverse Load |
Axial Force |
Heat Transfer |
Temperature
|
Thermal Conductivity |
Friction or contact force on surface of bar |
Heat |
Flow Through Pipes |
Hydrostatic Pressure |
PD4/128m (D- Diameter, m - viscosity) |
Flow Source (Generally Zero) | Flow Rate |
| Laminar Incompressible Flow through a Channel under Constant Pressure Gradient | Velocity |
Viscosity | Pressure Gradient | Axial Stress |
Flow Through Porous Media |
Fluid Head |
Coefficient of Permeability | Fluid Flux | Flow (seepage) |
Electrostatics |
Electroststic Potential |
Dielectric Constant |
Charge Density |
Electric Flux |