---

Convection

---

Quick
Heat transfer that occurs between a surface and a moving fluid when they are at different temperatures.


Equation

(Eq1)     q" = h(Ts – T∞)

Newton's law of cooling

Nomenclature

q"	convective heat flux
h	convection heat transfer coefficient
Ts	temperature at surface
T∞	temperature of moving fluid

Visualization

The stationary medium may be a fluid or solid Ts is temperature at surface T∞ is temperature of moving fluid q" is the heat transfer from the solid surface to the moving fluid. The difference in temperatures result in the temperature gradient.

Details

The convection heat transfer mode is comprised of two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), energy is also transferred by the bulk (macroscopic) motion of the fluid. This fluid motion is associated with the fact that, at any instant, large numbers of molecules are moving collectively or as aggregates. Such motion, in the presence of a temperature gradient, contributes to heat transfer. Because the molecules in the aggregate retain their random motion, the total heat transfer is then due to a superposition of energy transport by the random motion of the molecules and by the bulk motion of the fluid. It is customary to use the term convection when referring to this cumulative transport and the term advection when referring to transport due to bulk fluid motion.

Convection is of special interest when it occurs between a fluid in motion and a bounding surface when the two are at different temperatures. Consider fluid flow over the heated suface in the figure shown below. A consequence of the fluid–surface interaction is the development of a region in the fluid through which the velocity varies from zero at the surface to a finite value u_∞ associated with the flow. This region of the fluid is known as the hydrodynamic, or velocity, boundary layer. Moreover, if the surface and flow temperatures differ, there will be a region of the fluid through which the temperature varies from T_s at y = 0 to T_∞ in the outer flow. This region, called the thermal boundary layer, may be smaller, larger, or the same size as that through which the velocity varies. In any case, if T_s > T_∞, convection heat transfer will occur from the surface to the outer flow.

The convection heat transfer mode is sustained by random molecular motion and by the bulk motion of the fluid within the boundary layer. The contribution due to random molecular motion (diffusion) dominates near the surface where the fluid velocity is low. In fact, as the interface between the surface and the fluid ( y = 0), the fluid velocity is zero and heat is transferred by this mechanism only. The contribution due to bulk fluid motion originates from the fact that the boundary layer grows as the flow progresses in the x direction. In effect, the heat that is conduced into this layer is swept downstream and is eventually transferred to the fluid outside the boundary layer. Appreciation of boundary layer phenomena is essential to understanding convection heat transfer. It is for this reason that the discipline of fluid mechanics will play a vital role in our later analysis of convection.

Convection heat transfer may be classified according to the nature of the flow. Forced convection is when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds. As an example, consider the use of a fan to provide forced convection air cooling of hot electrical components on a stack of printed circuit boards. In contrast, for free (or natural) convection the flow is induced by buoyancy forces, which are due to density differences caused by temperature variations in the fluid. An example is the free convection heat transfer that occurs from hot components on a vertical array of circuit boards in air. Air that makes contact with the components experiences an increase in temperature and hence a reduction in density. Since it is now lighter than the surrounding air, buoyancy forces induce a vertical motion for which warm air ascending from the boards is replace by an inflow of cooler ambient air.

While it has been presumed that pure forced convection in the following figure and pure natural convection in the next figure, conditions corresponding to mixed (combined) forced and natural convection may exist. For example, if velocities associated with the flow of the following figure are small and/or buoyancy forces are large, a secondary flow that is comparable to the imposed forced flow could be induced. In this case, the buoyancy-induced flow would be normal to the forced flow and could have a significant effect on convection heat transfer from the components. In the next figure, mixed convection would result if a fan were used to force air upward between the circuit boards, thereby assisting the buoyancy flow, or downward, thereby opposing the buoyancy flow.

The convection heat transfer mode has been described as energy transfer occurring within a fluid due to the combined effects of conduction and bulk fluid motion. Typically, the energy that is being transferred is the sensible, or internal thermal, energy of the fluid. However, there are convection processes for which there is, in addition, latent heat exchange. This latent heat exchange is generally associated with a phase change between the liquid and vapor states of the fluid. Two special cases of interest in this text are boiling and condensation. For example, convection heat transfer results from fluid motion induced by vapor bubbles generated at the bottom of a pan of boiling water or by the condensation of water vapor on the outer surface of a cold water pipe.

Regardless of the particular nature of the convection heat transfer process, the appropriate rate equation is of the form.

(Eq1)

q" = h(Ts – T∞)

where q", the convective heat flux (W/m²), is proportional to the difference between the surface and fluid temperatures, T_s and T_∞, respectively. This expression is known as Newton's law of cooling, and the parameter h (W/m²K) is termed the convection heat transfer coefficient. It depends on conditions in the boundary layer, which are influenced by surface geometry, the nature of the fluid motion, and an assortment of fluid thermodynamic and transport properties.

Any study of convection ultimately reduces to a study of the means by which h may be determined.

When Newton's law of cooling is used, the convection heat flux is presumed to be positive if heat is transferred from the surface (T_s > T_∞) and negative if heat is transferred to the surface (T_∞ > T_s). However, if T_∞ > T_s, there is nothing to preclude Newton's law of cooling from being expressed as:

q" = h(T_∞ – T_s)

in which case heat transfer is positive if it is to the surface.

Convective heat transfer takes place when a medium is flowing. In this mode the bulk motion of a substance moves matter with a certain energy level over or near a surface with a different temperature. Now the heat transfer by conduction is dominated by the manner in which the bulk motion brings the two substances in contact or close proximity. Examples of this are the wind blowing over a building or flow through heat exchangers, which can be air flowing over/through a radiator with water flowing inside the radiator piping. The overall heat transfer is typically correlated with Newton's law of cooling as:

q_x = AhΔT

where the transfer properties are lumped into the heat transfer coefficient h which then becomes a function of the media properties, the flow, and geometry. A more detailed study of fluid mechanics and heat transfer aspects of the overall process is necessary to evaluate the heat transfer coefficient for a given situation.

Typical values for the convection coefficient are:

	h [W/mK2]	h [W/mK2]
Natural convection	5 to 25 for gas	50 to 1000 for liquid
Forced convection	25 to 250 for gas	50 to 20000 for liquid
Boiling phase change	2500 to 100000