**2.1 Introduction**

· Differential formulation of basic laws:

· Conservation of mass

· Conservation of momentum

· Conservation of energy

**2.2 Flow Generation**

**(i) ****Forced convection. **Motion is driven by mechanical means.

**(ii) ****Free (natural) convection. **Motion is driven by natural forces.

**2.3 Laminar vs. Turbulent Flow**

· **Laminar flow: **no fluctuations in velocity, pressure, temperature, …

· **Turbulent flow: **random fluctuations in velocity, pressure, temperature, …

· **Transition from laminar to turbulent flow: **Determined by the Reynolds number:

Flow over a flat plate:

Flow through tubes:

**2.4 Conservation of Mass: The Continuity Equation**

**2.4.1 Cartesian Coordinates**

The principle of conservation of mass is applied to an element *dxdydz*

*Rate of mass added to element – Rate of mass removed from element =*

*Rate of mass change within element*

(2.1)

Expressing each term in terms of velocity components gives continuity equation

This equation can be expressed in different forms:

**2.4.2 Cylindrical Coordinates**

**2.4.3 Spherical Coordinates**

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