1. Fundamentals of Convection

2. Introduction
Convection is the mechanism of heat transfer through a fluid in the presence of bulk fluid motion.
It is classified as natural (or free) and forced convection depending on how the fluid motion is initiated.
In forced convection, fluid is forced to flow by external means such as pump or fan.
Natural convection is caused by natural means such as buoyancy effects.

3. Forced and Natural Convection

4. Newton’s law of cooling
All types of convection are governed by Newton’s law of cooling:

5. The convection heat transfer coefficient h can be defined as the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature difference.
No-slip condition
No-temperature-jump

6. The convection heat transfer coefficient varies along the flow direction.
The average or mean convection heat transfer coefficient is determined by averaging the local coefficients over the entire surface.
A large number of parameters are needed to describe heat transfer.
Parameters may be grouped together to form a small number of dimensionless numbers.
These give simpler and more general equations by which heat transfer coefficients may be calculated.

7. Nusselt Number
The larger the Nusselt number, the more effective the convection

11. The part of the flow where the velocity is influenced by the surface is called the boundary layer.
Near the front edge of the plate the thickness of the boundary layer is thin and it then grows successively thicker.
As long as the boundary layer is thin, there is no mixing between layers at different distances from the plate. The flow is then said to be laminar.
At some distance from the leading edge, the laminar layer will become unstable, and eddies will develop, mixing the different layers. The flow is then becoming turbulent.

12. Because of the mixing, the difference in velocity between layers is much smaller in turbulent flow than in laminar, and the velocity profile thus much flatter.
Even in the turbulent region there is a laminar sub-layer closest to the surface. In this sub-layer, the temperature profile is nearly linear.
The type of flow, laminar or turbulent, can be determined from the Reynolds number calculated with the distance from the leading edge as the characteristic length. Transition will occur at Re ≈ 5⋅105.

14. Film temperature

15. The average Nusselt number over the entire plate is:
When the laminar region is not small

16. The average heat transfer coefficient is:

18. Example
Engine oil at 60 ºC flows over the upper surface of a 5-m-long flat plate whose temperature is 20 ºC with a velocity of 2 m/s. Determine the rate of heat transfer per unit width of the entire plate.

24. The average Nusselt number for cylindrical and non-cylindrical pipes is expressed as:
C, m, and n are constants evaluated from the following table. All fluid properties are evaluated at film temperature.