Convective Heat Exchange

the process of heat transfer that takes place in moving fluid mediums (liquids or gases) as a result of the combined action of two heat transfer mechanisms—convective transfer proper and thermal conductivity.

In convective heat exchange, the heat is spatially distributed by the movement of the fluid medium from a region of higher temperature to a region of lower temperature and by the thermal motion of microparticles and the exchange of kinetic energy between them. In view of the fact that for dielectric mediums the rate of convective transfer is very great in comparison to its thermal conductivity, the latter, during laminar flow, acts only to transfer heat crosswise to the flow of the medium. The role played by thermal conductivity in convective heat exchange is much more important during the movement of electrically conducting mediums, such as liquid metals, where thermal conductivity has a major influence on heat transfer in the direction of the fluid’s movement. In turbulent flow, the pulsating displacement of turbulent eddies across the fluid flow plays a fundamental role in the crosswise heat transfer process. The participation of thermal conductivity in the processes of convective heat exchange causes these processes to be affected considerably by the thermophysical properties of the medium, such as its coefficient of thermal conductivity, its specific heat, and its density.

Inasmuch as convective transfer plays an important part in the processes of convective heat exchange, these processes must to a considerable degree be dependent on the nature of the fluid’s movement, that is, on the magnitude and direction of the medium’s velocity, on the velocity distribution in the flow, and on the mode of the fluid’s movement (laminar or turbulent flow). When a gas flows at high (supersonic) velocities, the pressure distribution in the flow begins to affect the processes of convective heat exchange. If the movement of the fluid is due to the action of some external stimulus (a pump, fan, compressor), then this movement is known as forced motion and the overall process is called forced convection. If the movement of the fluid is produced by the presence of a nonuniform temperature field and, therefore, of nonuniform density in the medium, then this movement is known as free, or natural, motion and the overall process is called free, or natural, convection. Cases are also encountered in which both forced and free convection must be taken into account.

For practical application, the type of convective heat exchange of most interest is the convective heat emission at the interface between two phases (solid and liquid, solid and gas, liquid and gas). The problem in this case is to determine the density of the heat flow at the interface, that is, the value that indicates the amount of heat received or given up per unit of interface surface per unit time. In addition to the factors affecting the convective heat exchange process, heat flow density is also a function of the size and shape of the body, the degree of surface roughness, the surface temperature, and the temperature of the medium giving up or receiving the heat.

The following formula is used to describe convective heat emission:

q_s = ɑ(T_o ˗ T_s)

where q_s is the density of the heat flow at the surface in watts per sq m, ɑ is the thermal emission coefficient in W/(m² ˗ °C), and T_o and T_s are the temperatures of the medium (liquid or gas) and of the surface, respectively. The quantity (T_o ˗ T_s) is often represented by ΔT and is called the thermal head. The thermal emission coefficient ɑ characterizes the rate of the thermal emission process; it increases with the velocity of the medium’s movement and when the mode of the flow changes from laminar to turbulent in connection with the intensification of convective transfer. In addition, the coefficient is always larger for mediums with a higher coefficient of thermal conductivity. The thermal emission coefficient increases substantially if a phase transition (for example, evaporation or condensation) takes place on the surface, since such a transition is always accompanied by either release or absorption of latent heat. The mass exchange at the surface has an important influence on the value of the thermal emission coefficient.

The principal and most difficult problem in calculations of the convective heat emission processes is in determining the thermal emission coefficient ɑ. Modern methods of describing the process, based on boundary-layer theory, make it possible to obtain theoretical (precise and approximate) solutions for certain simple situations. In the majority of the cases encountered in practice, thermal emission coefficients are determined experimentally. In addition, both the experimental data and the theoretical solutions are treated by the theory of similitude and are presented generally in the dimensionless form Nu = f (Re, Pr) for forced convection and Nu = f (Gr, Pr) for free convection, where Nu = ɑ · L/λ is the Nusselt number, a dimensionless thermal emission coefficient (L is the characteristic dimension of flow, λ is the coefficient of thermal conductivity); Re = uL/v is the Reynolds number, which characterizes the ratio of the inertial forces to the forces of internal friction in the flow (u is the characteristic speed of motion of the medium, v is the kinematic modulus of viscosity);Pr = v/a is the Prandtl number, which defines the relation of the rates of the thermodynamic processes (a is the thermal diffusivity coefficient); and Gr = gL³ΔβT/v² is the Grashof number, which characterizes the relationship between the buoyancy forces, the inertial forces, and the forces of internal friction in the flow (g is the acceleration of gravity, β is the coefficient of thermal volume expansion).

Convective heat exchange processes are extremely common both in technology (in power engineering, refrigeration engineering, rocket engineering, metallurgy, and chemical engineering) and in nature (heat transfer in the atmosphere and in the seas and oceans).