Heat transfer is an important concept in the world of physics and engineering. It is also at the same time both one of the most difficult and easiest subjects in these fields. It is one of the most difficult subjects because of the complex mathematics involved in modeling and predicting heat transfer in even the simplest systems. It is also one of the easiest because once you get past the math, it is a very conceptually intuitive subject.
Everyone knows from their middle science classes that heat is transferred in three different ways, conduction, convection, and radiation. But what do these really mean, and how can they be described in terms of mathematics so that useful calculations can be done? This article will attempt to describe the ideas of heat transfer more thoroughly than the fifth grade, but yet in a way that a fifth grader would understand.
So what exactly is heat? Heat is a form of energy called thermal energy that is primarily due to the motion, or vibrations, of molecules and atoms within the medium. The temperature of an object is actually a measurement of the intensity of molecular vibrations, or a measure of its thermal energy. Heat transfer then is the transfer of thermal energy through a physical space due to a temperature difference. All heat transfer is driven by temperature differences. Scientists and engineers who are interested in heat transfer are often interested in the heat transfer rate, the total amount of thermal energy transferred, or the temperature distribution during heat transfer processes.
Conduction is the most familiar and easy to understand mode of heat transfer. In middle school we learned that conduction is heat transfer due to contact between two objects. This is true, but usually we are more interested in the conduction heat transfer within an object. This too is due to contact, contact between molecules. As hot, energetic molecules vibrate, they collide with nearby molecules, transferring some of their energy to the next molecules. These molecules are now more energetic and transfer some energy to molecules near them. This happens on a large scale and thermal energy is effectively transferred from a higher temperature (high energy) region to a low temperature (low energy) region. This transfer due to random molecular motion is also called the diffusion of energy. Using the concept of conservation of energy a formula can be derived to describe this. This equation is known as Fourier’s Law and is as follows:
q = -k*dT/dx. In this equation q is the heat transfer rate, which is the amount of thermal energy transferred per unit time, k is a material property known as the thermal conductivity, and dT/dx is the temperature gradient. For non-calculus people, this can be approximated as the difference in temperature at two points divided by the distance between the points.
Convection is the next mode of heat transfer and is less intuitive at first. Convection is similar to conduction; in fact I like to think of it as “enhanced” conduction. Convection is heat transfer in fluids, i.e. gasses and liquids. We usually think about the transfer of heat from a solid to a moving fluid or vice versa. Heat is transferred in two ways in conduction. The first is through the diffusion of energy, exactly like in conduction. The other way that enhances the heat transfer is through the bulk movement of the fluid. This means that large numbers of molecules are moving past carrying additional thermal energy away. This is also known as advection. Convection is the combination of diffusion and advection. There are two kinds of convection, forced convection and free convection. Forced convection happens when the fluid is moving due to some outside force, like a pump or a fan. Free convection happens when heat is transferred to a still fluid, and the heating of part of a fluid causes motion in a fluid; like hot air rising, bringing cooler air to move in its place. In forced convection, the fluid movement causes the heat transfer, in free convection, heat transfer causes fluid motion. Convection can also be described by an equation, known as Newton’s Law of Cooling: q = h(Ts-Tinf). In this equation q is again the heat transfer rate, and h is the heat transfer coefficient. Ts is the surface temperature and Tinf is the temperature of the fluid. The heat transfer coefficient h is not easily derived mathematically and has to be determined through experiments.
Radiation, the final mode of heat transfer, is completely different from either conduction or convection. Conduction and convection require a medium for heat transfer to occur, radiation does not. Radiation is the transfer of energy through space in the form of electromagnetic waves. In all objects, molecules are not only vibrating, but they can also change electrical energy states. This means that an object can absorb some energy and an electron will move into a higher energy state. When the electron moves back into a lower energy state, it releases energy in the form of a photon. Photons are another way of thinking about electromagnetic waves. It is in this way that a surface will radiate energy. It turns out that the amount of energy emitted by an object in this way doesn’t depend on the material, only the temperature. This is known as the Stefan-Boltzmann Law: E = σT4. In this equation, E is the amount of energy emitted, and σ is a constant know as the Stefan-Boltzmann constant. In equilibrium, surfaces emit the same amount of energy as they emit. A net heat transfer between two objects is then dependent again on the temperature difference and is shown here: q = σ(T14-T24), with energy flowing from the higher temperature object to the lower temperature object. Not only is radiation important in the field of heat transfer, but the discoveries related to radiation at the beginning of the twentieth century were the first discoveries that launched physics into the world of quantum mechanics, but that is another story.
Heat transfer in a system may consist of one, two, or all three of these modes. This is only a brief introduction to the field. In real life applications, the rate equations mentioned here are used and, especially in conduction, compose differential equations that have to be solved to determine the temperature and heat transfer. These equations can quickly become intractable with complex geometries and boundary conditions, but luckily there are now computer programs that can solve these equations numerically. But without a basic understanding of heat transfer, these programs are useless. Hopefully, this article provided an insight into a better understanding of heat transfer and the basic laws that govern how it occurs.
