CHAPTER-I

This paper highlights some work of Fluid Dynamics using two very important methods, i.e., Perturbation method and the method of Laplace Transform.

Before getting into the insights of this paper, here are the quick look at the types of continuum mechanics, forces and the governing equations of fluid flow. The importance of the approach of macroscopic study is used in the study of concept of continuum and not the approach of microscopic study.

CONTINUUM MECHANICS

Fluid Mechanics Solid Mechanics

Ideal fluid Real fluid

Newtonian Non- Newtonian

• Ideal fluid- (i) no viscosity

(ii) incompressible

(iii) zero surface tension

(iv) irrotational

(v) example : water, honey, milk etc.

• Real fluid- (i) existence of viscosity

(ii) compressible

(iii) existence of surface tension

(iv) example: gases , air etc.

• Newtonian fluid- (i) Linear relationship between stress and strain-rate.

(ii) obeys Newton’s law of viscosity.

(iii) example: Glycerine, air, water etc.

• Non-newtonian fluid- (i) Do not obey Newton’s law of viscosity(Newton’s law of viscosity states that the shear stress that has been applied is linearly proportional with the rate of deformation.)

(ii) example: Ketchup.

GOVERNING EQUATIONS OF FLUID FLOW

Equation of continuity Equation of Momentum Energy Equation

(Volume flow in= Volume flow out) (Rate of momentum change= Pressure energy+ Potential

total forces that are acting on the body) Energy+ Kinetic energy=

Constant

• Equation of continuity: The basic principle of this equation is that- conservation of mass is observed. The equation is given by

• Equation of Momentum: Conservation of momentum is the basic principle of this equation.

• Energy Equation: Its basic principle is that energy is conserved.

• Navier-Stokes Equation: This equation is also very important in the study of continuum mechanics. The equation is given by-

Where the 1st term in the L.H.S is the Local Acceleration

the 2nd term in the L.H.S is the Convective acceleration

the 1st , 2nd and 3rd term in the R.H.S is the Pressure Gradient, Body force and Viscous term respectively.

TYPES OF FORCES

Surface Forces Body Forces

• Surface forces: These forces lead to the contact of one fluid with another fluid.

Example- Pressure force, forces due to electric firldet.

• Body Forces: These kind of forces acts throughout the body volume.

Example- Gravity force, centrifugal force etc.

Now, let us have a look at some of the dimensionless numbers:

Buoyant forces

• Grashof number,

Viscous forces

Convective mass transfer

• Sherwood number,

Mass diffusion rate

Viscous diffusion rate

• Prandtl number,

Thermal diffusion rate

Heat transfer (convective)

• Nusselt number,

Heat transfer (conductive)

Advective mass transfer

• Eckert number,

Heat dissipation

Diffusion rate (viscous)

• Schmidt number,

Diffusion rate (mass)

Electromagnetic forces

• Hartmann number,

Viscous forces

Here are some important terms that are used in this paper. Let us have a look at them:

• Magnetohydrodynamics: Some fluids such as plasma, electrolytes having the properties of a magnet and behaves as conducting fluids

are known as magnetohydrodynamics.

• Heat transfer: The phenomenon of exchanging heat among those objects that are in physical touch is known as heat transfer. Heat

flows from a body having higher temperature to the body having lower temperature.

• Mass transfer: Some processes such as absorption, evaporation etc., in which there is a total transfer of mass from one phase to

another is termed as mass transfer.

• Skin friction: Skin friction is that friction or that drag force that is observed between the surface of a solid and the fluid through which

it is running.

• Free convective flow: The flow through a surface which is solid in nature and whose temperature can be higher or lower than the

temperature of the surroundings is termed as free convective flow. It can be both laminar and turbulent.

Heat and mass transfer has blowing effects in the industrial use. It varies due to many effects such as the effect in time, effect in velocity, effect in temperature etc. various numbers is also related to it such as the Prandtl number, Grashof number, Schmidt number and so on which is being described in a very brief way above. in the following chapter various methods have been used to study the effects of mass and heat transfer.