**1. Modes of Heat Transfer**

Conduction, convection and radiation are the three mechanisms by which thermal energy may be transferred from one point in space (and time) to another.

• Conduction: diffusion of heat due to temperature gradients. A measure of the amount of conduction for a given gradient is the heat conductivity.

• Convection: when heat is carried away by moving fluid. The flow can either be caused by external influences, forced convection; or by buoyancy forces, natural convection. Convective heat transfer is tightly coupled to the fluid flow solution.

• Radiation: transfer of energy by electromagnetic waves between surfaces with different temperatures, separated by a medium that is at least partially transparent to the (infrared) radiation. Radiation is especially important at high temperatures, e.g. during combustion processes, but can also have a measurable effect at room temperatures.

**2. Overview of Dimensionless Numbers**

**Nusselt Number**

The Nusselt number (*Nu*) represents the relative magnitude of “real” heat flux to conduction heat flux and is essentially a dimensionless heat transfer coefficient.

The Nusselt number is derived through equating the heat conducted from the wall to the same heat transfer in convective terms:

(92)

where *k* is the thermal conductivity and *h* is the convective heat transfer coefficient.

Then by defining the following dimensionless quantities:

The definition of Nusselt number is obtained through:

Therefore, the Nusselt number is a dimensionless ratio of convective to conductive heat transfer.

**Prandtl Number**

Prandtl number is the ratio between momentum diffusivity and thermal diffusivity and is defined as:

Typical values are *Pr *= 0.01 for liquid metals; *Pr *= 0.7 for most gases; *Pr *= 6 for water at room temperature.

**Grashof Number**

Grashof number (*Gr*) is the ratio between buoyancy forces and viscous forces:

**Rayleigh Number**

Natural convection problems are characterized using the Rayleigh number. The Rayleigh number governs natural convection phenomena (*Ra* = *Gr.Pr*):

**Reynolds Number**

The Reynolds Number (*Re*) is the ratio between inertial and viscous forces and is defined as:

**Froude Number**

In most industrial applications, free and forced convection occur simultaneously. The relative magnitude of these effects can be determined by using a modified Froude number, *Fr.*

In the definition of the above dimensionless numbers:

*b* is the thermal expansion coefficient, *g* is the acceleration to gravity, *ν* is the kinematic viscosity (=*μ*/*ρ*), *α* is the thermal diffusivity (=*k*/*ρcp*),* L* is the length-scale and *T* is temperature.

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