Convective Heat Transfer

Convective heat transfer is the transfer of thermal energy by the movement of a fluid. In engineering practice, it is used to provide specific temperature changes. Examples include heat exchangers, electronic device cooling, and cooling of turbine blades.

Convective heat transfer comprises two mechanisms: energy transfer due to random molecular motion (diffusion), and energy transfer due to the larger-scale bulk motion of the fluid (advection - the collective movement of groups of molecules).

Convective heat transfer to or from a solid requires the transfer of heat by the bulk motion of the fluid and the transfer of heat by diffusion. The contribution due to random molecular motion dominates near the surface where the fluid velocity is low. At the interface between the surface and the fluid, the fluid velocity is zero (that is, there is no relative motion between the fluid and surface) and heat transfer is transferred by diffusion only.

Convection is usually described as being either natural (”free”) or forced, although other mechanisms also exist (for example, gravitational, granular, thermomagnetic, capillary action-driven, or Marangoni and Weissenberg driven effects).

Convective heat transfer at a surface is governed by Newton’s law of cooling:

Figure 1. EQUATION_DISPLAY

q_{s} ″ = h (T_{s} - T_{r e f})

(196)

where:

$q_{s} ″$ is the local surface heat flux (that is, power per unit area).
$h$ is the local convective heat transfer coefficient.
$T_{s}$ is the surface temperature.
$T_{r e f}$ is a characteristic temperature of the fluid moving over the surface.

Newton’s law of cooling expresses a linear relationship between the local surface heat flux and the difference between the local surface and fluid temperatures. This linear relationship is only an approximation: in reality the relationship can be strongly nonlinear. Because flow conditions can vary from point to point on the surface, both $q_{s} ″$ and $h$ can vary as a function of space and time.

Natural Convection

In a gravitational field, natural convection occurs due to temperature differences which affect the density, and thus the relative buoyancy, of the fluid. Denser components fall, while lighter (less dense) components rise, leading to bulk fluid movement.

Natural convection is more likely and more rapid when any of the following conditions apply:

a greater variation in density between two mixing fluids
a larger acceleration due to gravity that drives the convection
a larger distance through the convecting medium.

Natural convection is less likely and/or less rapid when any of the following conditions apply:

a more rapid diffusion (which acts to diffuse away the thermal gradient that causes the convection)
a more viscous (sticky) fluid.

To quantify when natural convection is possible, the dimensionless Rayleigh number is defined and can be viewed as the ratio of buoyant and viscous forces times the ratio of momentum and thermal diffusivities. Natural convection becomes possible when the Rayleigh number exceeds $10^{5}$ .

Forced Convection

In forced convection, fluid movement results from external sources (for example, a fan, pump, or the action of a propeller), and is typically used to increase the rate of heat transfer at a surface in cooling or heating applications.

In cases of mixed convection (that is, natural convection and forced convection occurring together) you can determine how much is due to forced convection and how much is due to natural convection. The relative magnitudes of the Rayleigh (Ra), Prandtl (Pr), and Reynolds (Re) numbers indicate which form of convection dominates:

If $\frac{R a}{P r {Re}^{2}} » 1$ , natural convection dominates, forced convection is neglected.

If $\frac{R a}{P r {Re}^{2}} « 1$ , forced convection dominates, natural convection is neglected.

If $\frac{R a}{P r {Re}^{2}} ≃ 1$ , mixed convection occurs, neither forced or free convection dominate, so both are taken into account.