Heat transfer Introduction

Modes of Heat Transfer

1. Conduction
2. Convection
3. Radiation

Conduction

In the solids heat is conducted via molecular lattice vibration and free electron transfer. Thermal energy transfers from higher temperature to lower temperature. In gases and liquids, conduction is due to the collisions and diffusion of the molecules during their random motion.
Conduction process depends on the geometry of medium, temperature gradient, its thickness and physical material properties.

Fourier’s Law

The heat flux(q, W/m^2), heat transfer rate in the x direction per unit area perpendicular to the direction x, is proportional to the temperature gradient dT/dx.
\[q = -k \frac{dT}{dx}\]

k is the proportionality constant and is known as thermal conductivity of the material.  

Thermal conductivity(k) of different materials:

1. Diamond - 2300 W/m-K
2. Silver  -     406 W/m-K
3. Copper  -  385 W/m-K
4. Aluminium -  200 W/m-K
5. Steels -  15 to 35 W/m-K
6. Mercury -  8 W/m-K
7. Ice    -   2.25 W/m-K
8. Water at 20° C    -  0.6 W/m-K
9. Air at 0° C    -  0.024 W/m-K

• Note that pure crystals and metals have the highest thermal conductivity, and gases and insulating materials the lowest
• Thermal conductivity of gases increases with increasing temperature and decreasing molecular weight.
• Thermal conductivity of metal decreases with increasing temperature
• Thermal conductivity is independent of pressure.
• Thermal conductivity of a substance is highest in solid phase and lowest in gas phase.

Convection

Convection is mode of heat transfer which occur between a hot solid plate and the surrounding cold fluid due to temperature difference associated with the macroscopic bulk displacement at the fluid over the solid surface which is provided by density difference and resulting buoyancy forces in case of free convection or which is provided by an external source like fan in case of forces convection.

Newton's Law of Cooling

\[q = h(T_s - T_f)\]

or
\[Q = hA(T_s - T_f) \]

where, q - heat flux and Q is rate of heat transfer

$T_s$ is surface temperature

$T_f$ is fluid temperature

h is coefficient of convective heat transfer (W/m^2-K)

Radiation

Radiation is the mode of heat transfer which does not require any medium and occurs by electromagnetic waves travelling with speed of light.

The maximum flux, E (W / m2), at which radiation may be emitted from a blackbody surface is given by Stefan-Boltzmann law: