Convection

Convection is the heat transfer mode in which heat transfers between a solid face and an adjacent moving fluid (or gas). Convection has two elements:
  • Energy transfer due to random molecular motion (diffusion), and
  • Energy transfer by bulk or macroscopic motion of the fluid (advection).
The mechanism of convection can be explained as follows: as the layer of the fluid adjacent to the hot surface becomes warmer, its density decreases (at constant pressure, density is inversely proportional to the temperature) and becomes buoyant. A cooler (heavier) fluid near the surface replaces the warmer fluid and a pattern of circulation forms.

The rate of heat exchange between a fluid of temperature Tf and a face of a solid of area A at temperature Ts obeys the Newton's law of cooling which can be written as:

Qconvection = h A (Ts - Tf)

where h is the convection heat transfer coefficient. The units of h are W/m2.K or Btu/s.in2.F. The convection heat transfer coefficient (h) depends on fluid motion, geometry, and thermodynamic and physical properties.

Generally, there are two modes convection heat transfer:

Natural (Free) Convection

The motion of the fluid adjacent to a solid face is caused by buoyancy forces induced by changes in the density of the fluid due to differences in temperature between the solid and the fluid. When a hot plate is left to cool down in the air the particles of air adjacent to the face of the plate get warmer, their density decreases, and hence they move upward.

Forced Convection

An external means such as a fan or a pump is used to accelerate the flow of the fluid over the face of the solid. The rapid motion of the fluid particles over the face of the solid maximizes the temperature gradient and increases the rate of heat exchange. In the following image, air is forced over a hot plate.

Convection Heat Coefficient

Newton's law of cooling states that the heat transfer rate leaving a surface at temperature Ts into a surrounding fluid at temperature Tf is given by the equation:

Qconvection = h A (Ts - Tf)

where the heat transfer coefficient h has the units of W/m2.K or Btu/s.in2.F. The coefficient h is not a thermodynamic property. It is a simplified correlation to the fluid state and the flow conditions and hence it is often called a flow property.

Convection is tied to the concept of a boundary layer which is a thin layer of transition between a surface that is assumed adjacent to stationary molecules and the flow of fluid in the surroundings. This is illustrated in the next figure for a flow over a flat plate.

Where u(x,y) is the x-direction velocity. The region up to the outer edge of the fluid layer, defined as 99% of the free stream velocity, is called the fluid boundary layer thickness δ(x).

A similar sketch could be made of the temperature transition from the temperature of the surface to the temperature of the surroundings. A schematic of the temperature variation is shown in the next figure. Notice that the thermal boundary layer thickness is not necessarily the same as that of the fluid. Fluid properties that make up the Prandtl Number govern the relative magnitude of the two types of boundary layers. A Prandtl Number (Pr) of 1 would imply the same behavior for both boundary layers.

The actual mechanism of heat transfer through the boundary layer is taken to be conduction, in the y-direction, through the stationary fluid next to the wall being equal to the convection rate from the boundary layer to the fluid. This can be written as:

h A (Ts - Tf) = - k A (dT/dy)s

Thus the convection coefficient for a given situation can be evaluated by measuring the heat transfer rate and the temperature difference or by measuring the temperature gradient adjacent to the surface and the temperature difference.

Measuring a temperature gradient across a boundary layer requires high precision and is generally accomplished in a research laboratory. Many handbooks contain tabulated values of the convection heat transfer coefficients for different configurations.

The following table shows some typical values for the convective heat transfer coefficient:

Medium Heat Transfer Coefficient h (W/m2.K)
Air (natural convection) 5-25
Air/superheated steam (forced convection) 20-300
Oil (forced convection) 60-1800
Water (forced convection) 300-6000
Water (boiling) 3000-60,000
Steam (condensing) 6000-120,000

Prandtl Number

The Prandtl number is a parameter that relates the thicknesses of the velocity and thermal boundary layers and is given by:

where ν is the kinematic viscosity, α is the thermal diffusivity, ρ is the fluid density, κ is the fluid thermal conductivity, and cp is the fluid heat capacity at constant pressure.

The kinematic viscosity ν of a fluid reveals information about the rate at which momentum may diffuse through the fluid because of molecular motion. Thermal diffusivity α reveals information about the diffusion of heat in the fluid. Thus the ratio of these two quantities expresses the relative magnitudes of diffusion of momentum and heat in the fluid.