Page 219 - Geothermal Energy Renewable Energy and The Environment

Direct Use of Geothermal Resources 207

heaT Transfer by convecTion
Heat transfer by convection is a complex process that involves the movement of mass that contains a
quantity of heat. Previously this topic was discussed in terms of convective flow of hot rocks deep in
the mantle, where viscous forces strongly influence the behavior of materials. Convective heat trans-
fer also occurs at interfaces between materials, as when air is in contact with a warm pool of water
or is forced by a fan to flow at high velocity through a heat exchange unit. In such cases, buoyancy
effects, the character of the flow, the development of boundary layers, the effects of momentum and
viscosity, and the effects of the surface properties and shape of the geometry of the flow pathway
influence heat transfer.
Figure 11.4 schematically shows some of the influences on convective heat transfer for the sim-
plest possible case, namely fluid flowing over a flat surface. This geometry is grossly similar to that
which is typical of many situations in direct use applications. In this instance, airflow is depicted as
laminar (not turbulent) and the surface at the interface is assumed to be perfectly smooth. Cool air
at temperature T moves over a body of warm water that is at temperature T . Viscous and frictional
2
1
forces act to slow the movement of air near the surface of the body of water, forming a boundary
layer, which is a region where a velocity gradient develops between the interface and the main air
mass that has velocity v. At the interface the velocity approaches zero. The characteristics of the
boundary layer are dependent upon the fluid properties, velocity, temperature, and pressure. Heat
is transferred by diffusive processes from the water surface to the fluid at the near-zero velocity
boundary layer base, causing its temperature to approach that of the water, T . As a result, a tem-
1
perature gradient forms, in addition to the velocity gradient, between the main mass of moving fluid
and the water–air interface. This thermal gradient becomes the driving force behind thermal dif-
fusion that contributes to heat transfer through this boundary layer. Advective transport of heated
molecules provides an additional mechanism for heat to move through the boundary layer and into
the main air mass, resulting in an increase in the temperature of the air.
The rate at which convective heat transfer occurs follows Newton’s “law of cooling,” which is
expressed as
Q = h × A × dT, (11.2)
cv
where Q is the rate at which heat transfer occurs by convection, h is the convection heat transfer
cv
2
coefficient (J/s-m -K), A is the exposed surface area (m ), and dT is the temperature difference
2
between the warm boundary and the overlying cooler air mass, (T − T ).
2
1
Values for h are strongly dependent on the properties of the materials involved, the pressure
and temperature conditions, the flow velocity and whether flow is laminar or turbulent, surface
Air velocity, v

T 2
Cool air
Boundary layer

T 1
Warm water

FIGUre 11.4 Schematic representation of convective heat transfer at an air–water interface. The length of
the arrows are proportional to the air velocity at the distance from the interface. The boundary layer in the
air adjacent to the interface is that region for which the velocity is affected by the presence of the interface.
The temperature gradient in the air is indicated by the solid line labeled T 2 . The T 1 is the temperature of
the water.