# Write a 11 pages paper on mathematical models. In solving the above equation, the prevailing boundary conditions must be considered so as to ensure the accuracy of the results is maintained. Due to th

Write a 11 pages paper on mathematical models.

In solving the above equation, the prevailing boundary conditions must be considered so as to ensure the accuracy of the results is maintained. Due to the fact that this equation is held in a closed system, only the prevailing wall boundary conditions are of utmost importance and need to be considered for a complete simulation (Ferziger and Peric, 1999). This equation states that the acceleration, convection and pressure gradient of a fire in motion is equal to the force of gravity acting on it, body forces, and viscous forces.

This equation is based on Newton’s Second law of motion which holds that acceleration is directly proportional to the force exerted and the force acts in the direction of acceleration. (Wesseling, 2000) With regard to this, it is therefore important to note that when solving this equation, both the prevailing inlet and outlet boundary conditions must be put into consideration. This ensures that these can be used to compute the acceleration as well as the momentum. This equation states that the temperature rise of a flame coupled with the convective heat transfer is equal to the change in pressure over the same time plus heat released per unit volume from reaction less energy transferred to evaporating droplets and diffusion energy in addition to any other heat source3.

The basis for this equation is the first law of thermodynamics which is itself an application of the principle of conservation of energy for thermodynamic and heat systems. The law holds that energy can neither be created nor destroyed. Thus, the energy flowing within a CFD is maintained throughout the simulation. All the boundary conditions, therefore, need to be considered when solving CFD problems using this equation so as to link the surroundings and the simulation model and also define the net interchange of energy from the surroundings to the model and vice versa.

Dirichlet – This is a boundary condition that is enforced on an ordinary or partial differential equation. It specifies the values that a solution to a problem should take on along the limits of the area. In CFD analysis the no-slip condition for viscous fluids posits that at a solid boundary a fluid will have zero velocity relative to the limit.

• Neumann – This is a boundary condition that when enforced on an ordinary or a partial differential equation, stipulates the values that the derivative of a solution is to take on the limits of the area affected. 