# Heat Transfer/Convection

Convection

## Contents

#### Laminar and Turbulent Flow

Laminar Flow: Smooth uninterrupted flow determined by a low Reynolds number. The Reynolds number for a Newtonian fluid is defined as:

$N_{Re} = \frac{Dv\rho}{\mu}$

where D is a characteristic diameter (such as the diameter of a cylindrical pipe), v is the fluid velocity, $\rho$ is the density, and $\mu$ is the (dynamic) viscosity. There are several other ways of writing it as well (based on volumetric flow rate, mass flow rate, and the like) depending on what is known. Flow in a cylindrical pipe is laminar if the Reynolds number is less than 2100.

In laminar flow in a pipe, the velocity profile is parabolic; the maximum velocity occurs at the center and the velocity is zero at the wall of the pipe.

Turbulent flow: This is flow characterized by movement in random directions, so that the net result is that all the flows cancel and the velocity on average is approximately constant everywhere in the pipe. Turbulent flow occurs when the Reynolds number is greater than 4000.

Transition regime: In the region between Turbulent and Laminar flow ($2100 < N_{Re} < 4000$), we cannot say much about the flow, except by emprical experimentation. The pattern is not linear in general but carries no distinct pattern in this region.

#### Dimensionless Parameters

In addition to the Reynolds number, $N_{Re}$, there are several other dimensionless parameters that are important in correlations involving convection. These include the Prandtl number, the Nusselt number, and the Grashof number. The Prandtl number is a dimensionless combination of three properties of a material: heat capacity, viscosity, and thermal conductivity:

$N_{Pr} = \frac{C_p\mu}{k}$

Since it is a material property, the Prandtl number depends only on the conditions (temperature and pressure) that a material is held at, not the system in which it is placed.

The Nusselt number tells us how important convection is compared to conduction. It is defined as:

$N_{Nu} = \frac{hD}{k}$

In contrast to the Prandtl number, the Nusselt number involves a heat transfer coefficient and a characteristic length, both of which depend on the type of system one is using, so this number must be individually evaluated for each system for maximum accuracy (or an estimate for similar systems can be used).

Finally, the Grashof number is a dimensionless parameter generally used to model natural convection (in which the surrounding fluid is relatively still except very close to the object receiving or losing heat by convection). This number is defined as:

$N_{Gr} = \frac{L^3{\rho}^2g{\beta}{\Delta}T}{\mu^2}$

It is used instead of the Reynolds number in natural convection modelling, since the surrounding environment is not at a high velocity, unlike in forced convection.

#### External Flow

External Flow, means flow over a surface.

#### Internal Flow

flow inside a closed,hollow,body.The cross section may be of circular,rectangular, or may be of any shape.

#### Free Convection

Also called natural convection. Results from a temperature difference between two media in contact.