## Combined Forced and Natural Convection

As was written, convection takes place through advection, diffusion or both. In preceding chapters we considered convection transfer in fluid flows that originate from an external forcing condition – **forced convection**. In this chapter, we consider **natural convection**, where any fluid motion occurs by natural means such as buoyancy. In fact, there are flow regimes, in which we have to consider **both forcing mechanisms**. When flow velocities are low, natural convection will also contribute in addition to forced convection. Whether or not free convection is significant for heat transfer, it can be checked using the following criteria:

- If Gr/Re
^{2}>> 1 free convection prevails - If Gr/Re
^{2}<< 1 forced convection prevails - If Gr/Re
^{2}≈ 1 both should be considered

The effect of buoyancy on heat transfer in a forced flow is strongly influenced by the direction of the buoyancy force relative to that of the flow. **Natural convection** may **help **or** hurt** forced convection heat transfer, depending on the relative directions of buoyancy-induced and the forced convection motions. Three special cases that have been studied extensively correspond to buoyancy-induced and forced motions:

**Assisting flow**. The buoyant motion is in the same direction as the forced motion.**Opposing flow**. The buoyant motion is in the opposite direction to the forced motion.**Transverse flow**. The buoyant motion is perpendicular to the forced motion.

It is obvious, in assisting and transverse flows, buoyancy enhances the rate of heat transfer associated with pure forced convection. On the other hand, in opposing flows, it decreases the rate of heat transfer. When determining the **Nusselt number** under combined natural and forced convection conditions, it is tempting to add the contributions of natural and forced convection in assisting flows and to subtract them in opposing flows:

**Combined Forced and Natural Convection**

For the specific geometry of interest, the Nusselt numbers **Nu _{forced}** and

**Nu**are determined from existing correlations for pure forced and natural (free) convection, respectively. The best correlation of data to experiments is often obtained for

_{natural}**exponent n = 3**, but it may vary between 3 and 4, depending on the geometry of the problem.

## Natural Convection – Correlations

As was written, most **heat transfer correlations** in **natural convection** are based on experimental measurements and engineers often use proper characteristic numbers to describe natural convection heat transfer. The characteristic number that describes convective heat transfer (i.e. the heat transfer coefficient) is the **Nusselt number**, which is defined as the ratio of the **thermal energy convected** to the fluid to the **thermal energy conducted** within the fluid. The **Nusselt number** represents the enhancement of heat transfer through a fluid layer as a result of **convection relative to conduction **across the same fluid layer. But in case of free convection, heat transfer correlations (for the Nusselt number) are usually expressed in terms of the **Rayleigh number.**

The **Rayleigh number** is used to express heat transfer in natural convection. The magnitude of the Rayleigh number is a good indication as to whether the natural convection boundary layer is laminar or turbulent. The simple empirical correlations for the average Nusselt number, Nu, in natural convection are of the form:

**Nu _{x} = C. Ra_{x}^{n}**

The values of the **constants C** and** n** depend on the geometry of the surface and the flow regime, which is characterized by the range of the **Rayleigh number**. The value of n is usually **n = 1/4** for **laminar flow** and **n = 1/3** for **turbulent flow**.

For example:

See also: Nusselt Number

See also: Rayleigh Number

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