# Convection Study Guide

## Heat Transfer Type: Convection

The second type of heat transfer is convecvtion. **Convection** is a heat transfer mode that uses the movement of a fluid (liquid or gas) across a boundry surface. This movement can either be forced or natural. The general equation for this is Netwon’s Law of Convection which is shown in equation 1

Equation 1

Generally you will know the area and the two different temperatures. The only variable you will not usually know is the film coefficient (*h*). Solving for the film transfer coefficient can be done depending on how the convection is taking place.

### Forced Convection

Forced convection is when the fluid is moved by an external source. Like when you blow on your soup to cool it down because the soup is to hot. Sometimes this flow will be inside a pipe. Other times the flow will be around an object. In order to determine the film transfer coefficient you will need to decide on which equation to use, which is dependent on how the fluid is flowing.

### Turbulent Flow In Pipes

When the fluid is flowing inside a pipe, we can use the Nusselt Number (equation 2) to solve for the film coefficient. The **Nusselt Number** (*Nu*) is the ratio of convective heat transfer to conductive heat transfer. When solving for fluid inside a pipe use the diameter of the pipe instead of the characteristic length (*L*)

Equation 2

If the temperatures across the fluid is not too great the Dittus-Boelter equation (equation 3) can be used to solve for the film coefficient. You will also need to use equations 4 and 5 to find some missing information, the Reynolds Number (*Re*) and the Prandtl Number (*Pr*).

Equation 3

Equation 4

Equation 5

The last variable that is not defined in equation 3 is *n*. This variable depends on if the heat flow is out of the pipe (*n = 0.3*) or if the flow of heat is into the pipe (*n = 0.4*)

In order to use equation 3 there is still some rules that need to be followed:

The Prandtl Number (*Pr*) must be between 0.7 and 16,700

The Reynolds Number (*Re*) must be greater than 10,000

And you must have more than 10 times the diameter of the pipe in length (Length/Diameter > 10)

### Reynolds Number

The **Reynolds Number** (*Re*) is a dimensionless number that is the ratio of inertia forces to viscous forces. Building upon equation 4, we can rewrite the Reynolds Number equation in 3 different ways as shown in equation 6

Equation 6

Where v is the velocity, *Q* is the volumetric flow rate, *A* is the area, ρ is the density, D_{h} is the hydraulic diameter , μ is the dynamic viscosity, and *v* is the kinematic viscosity.

### Hydraulic diameter

For a circular pipe the diameter equals the hydraulic diameter, for a channel the hydraulic diameter is 4 times the cross section area that is wetted divided by the perimeter. This is shown in equation 7

Equation 7

### Prandtl Number

The **Prandtl Number** (*Pr*) is the ratio of kinematic viscosity to thermal diffusivity. Equation 8 shows how the Prandtl Number is calculated

Equation 8

Where *C _{p}* is the specific heat,

*k*is the thermal conductivity, and α is the thermal diffusivity.