## F Elements of Heat Transfer

63 One of the relations which we will need is the one which relates temperature to heat flux. This constitutive realtion will be discussed in the next chapter under Fourrier's law.

64 However to place the reader in the right frame of reference to understand Fourrier's law, this section will provide some elementary concepts of heat transfer.

65 There are three fundamental modes of heat transfer:

Conduction: takes place when a temperature gradient exists within a material and is governed by Fourier's Law, Fig. 6.3 on :

Figure 6.3: Flux vector

where T = T(x, y) is the temperature field in the medium, qx and qy are the componenets of the heat flux (W/m2 or Btu/h-ft2), k is the thermal conductivity (W/m.°C or Btu/h-ft-°F) and dx, dry are the temperature gradients along the x and y respectively. Note that heat flows from "hot" to "cool" zones, hence the negative sign.

Convection: heat transfer takes place when a material is exposed to a moving fluid which is at different temperature. It is governed by the Newton's Law of Cooling q = h(T - Tro) on rc (6.69)

where q is the convective heat flux, h is the convection heat transfer coefficient or film coefficient (W/m2.oC or Btu/h-ft2.oF). It depends on various factors, such as whether convection is natural or forced, laminar or turbulent flow, type of fluid, and geometry of the body; T and Tare the surface and fluid temperature, respectively. This mode is considered as part of the boundary condition.

Radiation: is the energy transferred between two separated bodies at different temperatures by means of electromagnetic waves. The fundamental law is the Stefan-Boltman's Law of Thermal Radiation for black bodies in which the flux is proportional to the fourth power of the absolute temperature., which causes the problem to be nonlinear. This mode will not be covered.

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