 |
| Heat Transfer Mechanisms |
|
| We know that there is a transfer of energy, as heat, between a system and its environment. Here we discuss how this transfer takes place. There are three mechanisms of heat transfer. They are conduction, convection and radiation. |
| |
|
| If you leave the end of a metal poker in the fire for some time, its handle will get hot. Energy is transferred from the fire to the handle by (thermal) conduction along the length of the poker. The amplitude of vibration of the atoms and electrons of the poker near the fire becomes relatively large because of the high temperature of their environment. The increase in the amplitude of vibration and the associated energy, are passed along the poker from atom to atom during collisions between adjacent atoms. In this way, the region of rising temperature extends itself all along the length of the poker till its handle. |
| |
 |
| |
| Consider a slab of surface area A and thickness L, whose faces are maintained at temperature TH and Tc by a hot reservoir and a cold reservoir, as in the above figure. Let Q be the energy transferred as heat through the slab, from its hot face to its cold face, in time t. Experiment shows that the conduction rate pcond (the amount of energy transferred per unit time) is |
| |
 -----(i) |
| |
| In which k, the thermal conductivity, is a constant that depends on the material of the slab. A material that readily transfers energy by conduction is a good thermal conductor and has a high value of k. The table below, gives the thermal conductivities of some common metals, gases and building materials. |
| |
| Thermal Conductivities of Some Common Metals, Gases and Building materials |
| |
 |
| |
 |
| |
 |
| |
 |
| |
|
| When you look at the flame from a candle or a matchstick, you are watching thermal energy being transported upward by convection. Such energy transfer occurs when a fluid, such as air or water, comes in contact with an object whose temperature is higher than that of the fluid. The temperature of the part of the fluid that is in contact with a hot object increases and (in most cases) the fluid expands and thus, becomes less dense. Since, the expanded fluid is lighter than the surrounding cooler fluid, buoyant forces cause it to rise. Some of the surrounding cooler fluid flows in order to take the place of the rising, warmer fluid, and this process continues. |
| |
|
| The third mode of energy transfer between an object and its environment is via electromagnetic waves (visible light is a kind of electromagnetic wave). |
| |
| Energy transferred in this way is often called thermal radiation, to distinguish it from electromagnetic signals (as in, say, television broadcast) and from nuclear radiation (energy and particles emitted by nuclei). To 'radiate' generally means to emit. When you stand in front of a big fire, absorbing thermal radiation, the fire warms you; that is, your thermal energy increases as the thermal energy of the fire decreases. No medium is required for heat transfer by radiation; the radiation can travel through vacuum. For example, the heat is transferred from the sun to you by this method. |
| |
| |
| The rate Prad at which an object emits energy in form of electromagnetic radiation depends on the object's surface area A and the temperature T of that area in Kelvin, and is given by |
| |
 ------(ii) |
| |
| Here s=5.6703X10-8W/m2K4 is called the Stefan-Boltzmann constant after Josef Stefan (who discovered equation (ii) experimentally in 1879) and Ludwig Boltzmann (who derived it theoretically, later). The symbol e represents the emissivity of the object's surface, which has a value between 0 and 1, depending on the composition of the surface. A surface with the maximum emissivity of 1.0 is said to be a black body radiator, but such a surface is an ideal one and does not occur in nature. Note again that the temperature in equation (ii) must be in Kelvin, so that, a temperature of absolute zero corresponds to no radiation. Also note that every object whose temperature is above 0 K, including you, emits thermal radiation. |
| |
|
| If one end of a metal rod is placed in a stove, the temperature of the other end increases gradually. Heat is transferred from one end of the rod to the other end. This transfer takes place due to molecular collisions and the process is called heat conduction. The molecules at one end of the rod gain heat from the stove and their average kinetic energy increases. As these molecules collide with the neighbouring molecules having less kinetic energy, the energy is shared between these two groups. The kinetic energy of the neighbouring molecules increases, as they collide with their neighbours on the colder side. They transfer energy to them. This way, heat is passed along the rod from molecule to molecule. The average position of a molecule does not change and hence, there is no mass movement of matter. |
| |
|
| The ability of a material to conduct heat is measured by thermal conductivity (defined below) of the material. |
| |
 |
| |
Consider a slab of uniform cross-section A and length x. Let one face of the slab be maintained at temperature T1 and the other at T2. Also let us assume the remaining surface is covered with a non-conducting material so that no heat is transferred through the sides. After some time, a steady state is reached and the temperature at any point remains unchanged, with the passage of time. In such a case, the amount of heat crossing per unit time through any cross-section of the slab is equal. If an amount of heat DQ, passes through any cross-section
in time Dt,  is
called the heat current. It is found that in |
| |
| steady state, the heat current is proportional to the area of cross-section A and the temperature difference (T1 - T2) between the ends and is inversely proportional to the length x. Thus, |
| |
 |
| |
| where k is a constant for the material of the slab and is called the thermal conductivity of the material. |
| |
| If the area of cross-section is not uniform or if the steady state conditions are not reached, the equation can only be applied to a thin layer of material perpendicular to the heat flow. If A be the area of cross-section at a place, dx be a thin section along the direction of heat flow, and dT be the temperature difference across the layer of thickness dx, the heat current through this cross-section is |
| |
 |
| |
| The quantity dT/dx, is called the temperature gradient. The minus sign indicates that dT/dx is negative along the direction of the heat flow. |
| |
| The unit of thermal conductivity can be easily worked out using equation (1) or equation (2). The SI unit is
Js-1 m-1 K-1 or W m-1
k-1. As a change of 1K and a change of 1o C are the same, the unit may also be written as
W m-1oC-1. |
| |
