Heat Transfer Methods: Basic Concepts

What is heat transfer and why does it occur?

Heat transfer occurs when thermal energy flows from a hotter surface to a colder one. Thermal energy is the summative effect of the energies that dictate atomic behaviour such as translational, rotational, vibrational etc. In fact the phenomenon that we call temperature is the result of atomic behaviour and it is a way of quantifying the internal energy of a substance.

The 3 ‘modes’ of heat transfer:

Conduction and Fourier’s law

Conduction occurs through a solid or a stationary fluid due to the random motion of its constituent atoms/particles.

Fourier’s Law: q'' = -k∇T

q’’ is the vector for local heat flux intensity (W/m2)

k is the material’s thermal conductivity (W/mK)

∇T is the temperature gradient (K/m)

*** The grad(T) operator, ∇T:

Heat conduction is a multidirectional procedure, which means heat is ‘leaving’ from a hot object from all directions (x,y,z).

Hence ∇T = (T/x)i + (T/y)j + (T/z)k where i, j and k are unit vectors.

For simplicity, we are going to consider one directional conduction only (at this stage at least).

Hence Fourier’s Law can be written as:

q''x = -k(T2 - T1L)

The picture above is the special case of the plane wall, where one dimensional conduction occurs from left to right, resulting in a linear temperature distribution.

Convection and Newton’s Law of cooling

Convection occurs between a surface and a moving fluid over that surface.

Newton’s Law of cooling: q'' = h(Ts - T∞)

q’’ is the vector for local heat flux intensity (W/m2)

h  is the convective heat transfer coefficient (W/m2K)

Ts is the temperature of the surface

T∞ is the temperature of the fluid sufficiently far from the surface

The picture above shows the process of convective heat transfer between a surface and a moving fluid.

Radiation

Every hot surface emits some infrared radiation.

Heat transfer between a surface and a flowing fluid involves both radiative and convective heat transfers as well as some radiation absorption from the surroundings.

Emissive heat flux from surface: q'' = ε σ Ts4

q’’ is the vector for local heat flux intensity (W/m2)

ε is the surface emissivity (0 ≤ ε ≤ 1)

σ is the Stefan-Boltzman constant (5.67E-08 W/m2K4)

Ts is the temperature of the surface (K)

Absorption from the surroundings: q'' = α σ Tsur4

q’’ is the vector for local heat flux intensity (W/m2)

α is the surface absorptivity (0 ≤ α ≤ 1)

σ is the Stefan-Boltzman constant (5.67E-08 W/m2K4)

Tsur is the temperature of the surroundings (K)

Net radiative heat flux for a surface if α=ε: q''rad = ε σ (Ts4-Tsur4)

*** All pictures and equations are taken directly from the lecture notes and the referenced textbook