Heat Transfer Conduction, Convection, and Radiation

Heat Transfer Conduction, Convection, and Radiation

Heat Transfer is the study of the rates of thermal energy motion. There are three modes of Heat Transfer: Conduction, Convection, and Radiation. Conduction is concerned with the transfer of thermal energy through a material without bulk motion of the material. This phenomenon is fundamentally a diffusion process that occurs at the microscopic level. Convection is concerned with the transfer of thermal energy in a moving fluid (liquid or gas). Convection is characterized by two physical principles, conduction (diffusion) and bulk fluid motion (advection). The bulk fluid motion can be caused by an external force, for example, a fan, or may be due to buoyancy effects. Finally, Radiation is the transfer of thermal energy through electro-magnetic waves (or photons). It is interesting to note that Radiation requires no medium.

Conduction

Conduction is the diffusion of thermal energy, i.e., the movement of thermal energy from regions of higher temperature to regions of lower temperature. On a microscopic level, this occurs due to the passing energy through molecularvibrations.

Heat flux is denoted as . The units of heat flux are watts. It should be noted that heat flux is a vector quantity. It is often convenient to describe heat flux in terms of the geometry being studied. Thus we define , , and as the heat flux per unit length, area, and volume, respectively.

The governing rate equation for conduction is given by Fourier's Law. For one dimension, Fourier's law is expressed as:

Where x is the direction of interest, k is a proportionality constant known as thermal conductivity and is the temperature gradient at the location of interest. The negative sign indicates that heat is transferred in the direction of decreasing temperature.

The thermal conductivity is a measure of how readily a material conducts heat. Materials with high conductivity, such as metals, will readily conduct heat even at low temperature gradients. Materials with low conductivity, such as asbestos, will resist heat transfer and are often referred to as insulators.

Convection

Convection is the transfer of thermal energy between a solid and a moving fluid. If the fluid is not in motion, the problem can be classified as Conduction. Convection is governed by two phenomenon. The movement of energy due to molecular vibrations and bulk fluid motion. In general, Convection is of two types, Forced Convection and Free Convection.

Forced Convection occurs when a fluid is forced to flow. For example, a fan blowing air over a heat exchanger is an example of Forced Convection. In Free Convection, the bulk fluid motion is due to buoyancy effects. For example, a vertical heated plate surrounded by quiescent air causes the air surrounding it to be heated. Because hot air has a lower density than cold air, the hot air rises. The void is filled by cold air and the cycle continues.

The governing rate equation for Convection is given by Newton's Law of Cooling:

where h is the heat transfer coefficient, T is the temperature of the solid surface, and is the temperature of the fluid far from the surface. This expression, in spite of its name, is not law. Rather, it is an empirical expression of proportionality of the heat flux and the temperature difference between the solid and the fluid. The heat transfer coefficient is typically determined by experiment. Correlations for heat transfer coefficient for various kinds of flows are have been determined and are documented in literature.

Radiation

Radiation is the transfer of thermal energy between two objects through electro-magnetic waves. Unlike conduction and convection, radiation does not require a medium. In general, gasses do not take part in radiation heat transfer.

Radiation is based on the fact that all objects of finite temperature, i.e. not absolute zero, emit radiation in the form of electro-magnetic waves. These waves travel until they impinge another object. The second object in turn either absorbs or reflects the energy. It should be noted that if the second object is of a finite temperature, it is also emitting radiation.

Conduction

The Plane Wall

Heat transfer through a wall is a one dimensional conduction problem where temperature is a function of the distance from one of the wall surfaces. It is assumed that the rest of the surfaces of the walls are at a constant temperature. Heat transfer from the surfaces of the wall takes place through convection by the surrounding air, which causes them to have steady state temperatures of T1 and T2 on their surfaces. Let us assume that the fluid on the side of the wall with temperature T1 is at and has a heat transfer coefficient h1, and that on the side of the wall with temperature T2 is at with heat transfer coefficient h2, and that . The assumption implies that . Since the wall does not store any heat energy, all the heat from the hotter surface is conducted to the cooler surface. Conservation of energy dictates that

for a body which generates no heat nor stores any heat. Applying the same to the 1-D case with the direction of the x-axis normal to the wall surface, we get

On solving and putting the appropriate boundary conditions, (At x=0, T = T1 and at x=L, T = T2) we get a linear variation for T within the wall thickness.

It is evident from the equation that the temperature profile within the wall varies linearly with the distance from the surfaces. Since we have the temperature variation, the conduction rate can be calculated from Fourier's Law.

It can be seen from the above equation that the heat flux is independent of x and are constants. This example shows the standard method of solving a conduction problem. First, the temperature profile within the body is found using the equation for conservation of energy and the temperature equation is used to solve for the heat flux by plugging it into the Fourier's Law equation.

In general, we would like to have a material with very low conductivity which is able to withstand great temperatures to build furnaces. In practice, we find that high temperature materials have relatively high thermal conductivity. Thus, furnaces are constructed from several layers, each of a different material. We can use the thermal breakdown temperatures of each material to find the optimum thickness so that the heat loss is minimal. It is easy to see that each material should receive heat at its thermal breakdown temperature and reject heat at the thermal breakdown temperature of the adjacent material.