Engineering Activities Resources Enrichment Program Summer School Contact Us


Heat Transfer


Heat is energy or more precisely transfer of thermal energy. As energy, heat is measured in watts (W) whilst temperature is measured in degrees Celsius (°C) or Kelvin (K). The words “hot” and “cold” only make sense on a relative basis. Thermal energy travels from hot material to cold material. Hot material heats up cold material, and cold material cools down hot material. It is really that simple. When you feel heat, what you are sensing is a transfer of thermal energy from something that's hot to something that is cold.

The discipline of heat transfer is concerned with only two things: temperature, and the flow of heat. Temperature represents the amount of thermal energy available, whereas heat flow represents the movement of thermal energy from place to place. On a microscopic scale, thermal energy is related to the kinetic energy of molecules. The greater a material’s temperature, the greater the thermal agitation of its constituent molecules (manifested both in linear motion and vibrational modes).



The most efficient method of heat transfer is conduction. This mode of heat transfer occurs when there is a temperature gradient across a body. In this case, the energy is transferred from a high temperature region to low temperature region due to random molecular motion (diffusion). Conduction occurs similarly in liquids and gases. Regions with greater molecular kinetic energy will pass their thermal energy to regions with less molecular energy through direct molecular collisions. In metals, a significant portion of the transported thermal energy is also carried by conduction-band electrons. Different materials have varying abilities to conduct heat. Materials that conduct heat poorly (wood, styrofoam) are often called insulators. However, materials that conduct heat well (metals, glass, some plastics) have no special name.

The simplest conduction heat transfer can be described as “one-dimensional heat flow” as shown in the following figure. The rate of heat flow from one side of an object to the other, or between objects that touch, depends on the cross-sectional area of flow, the conductivity of the material and the temperature difference between the two surfaces or objects.

Mathematically, it can be expressed as





where q is the heat transfer rate in watts (W), k is the thermal conductivity of the material (W/m.K), A is the cross sectional area of heat path, and  is the temperature gradient in the direction of the flow (K/m).

The above equation is known as Fourier’s law of heat conduction. Therefore, the heat transfer rate by conduction through the object in the above figure can be expressed as





Where L is the conductor thickness (or length), DT is the temperature difference between one side and the other (for example, DT = T1T2 is the temperature difference between side 1 and side 2).

The quantity (DT/L) in Equation (16.5) is called the temperature gradient: it tells how many 0C or K the temperature changes per unit of distance moved along the path of heat flow. The quantity L/kA is called the thermal resistance 





Thermal resistance has SI units of kelvins per watt (K/W). Notice from Equation (16.6) that the thermal resistance depends on the nature of the material (thermal conductivity k and geometry of the body d/A). We realize from the above equations, we realize the heat transfer rate as a flow, and the combination of thermal conductivity, thickness of material and area as a resistance to this flow.

Considering the temperature as a potential function of the heat flow, the Fourier law can be written as 





If we define the resistance as the ratio of potential to the corresponding transfer rate, the thermal resistance for conduction can be expressed as 





It is clear from the above equation that decreasing the thickness or increasing the cross-sectional area or thermal conductivity of an object will decrease its thermal resistance and increase its heat transfer rate.



 A slower method of heat transfer is convection, which involves fluid currents that carry heat from one place to another. In conduction, energy flows through a material but the material itself does not move. In convection, the material itself moves from one place to another. The convection heat transfer is comprised of two mechanisms: random molecular motion (diffusion) and energy transferred by bulk or macroscopic motion of the fluid. Heat transfer from a solid to a fluid (liquid or gaseous) is more complex than solid-solid transfer as heat differentials within the fluid generally cause internal movement known as convection currents. As volume increases with temperature, warmer areas of a fluid have less mass than colder areas. Air is poor conductor of heat, but it can easily flow and carry heat by convection. The use of sealed, double-paned windows replaces the larger air gap between a storm window and regular window with a much smaller gap. The smaller air gap minimizes circulating convection currents between the two panes.

The magnitude of convective heat flow within the fluid depends upon the area of contact with the solid, its viscosity, velocity past the solid, flow characteristics and the overall temperature difference between the two.  The term convection has also been used historically to describe the transport of heat from one solid to another separated by a fluid medium.


Newton’s law of cooling expresses the overall effect of convection:





Where h is the convection heat transfer coefficient (W/m2K), A is the surface area, DTTsTf is  the temperature difference between the surface temperature Ts,  and the fluid temperature Tf . As in the case of conduction, thermal resistance is also associated with the convection heat transfer and can be expressed as





The convection heat transfer may be classified according to the nature of fluid flow.

Forced convection occurs when the flow is caused by external means, such as a fan, a pump, etc.



 The least efficient method of heat transfer is radiation. Radiant heat is simply heat energy in transit as electromagnetic radiation.  All materials radiate thermal energy in amounts determined by their temperature, where the energy is carried by photons of light in the infrared and visible portions of the electromagnetic spectrum. In this case, heat moves through space as an electromagnetic radiation without the assistance of a physical substance. All objects that contain heat emit some level of radiant energy.  The amount of radiation is inversely proportional to its wavelength (the shorter the wavelength the greater the energy content) which is, in turn, inversely proportional to its temperature (in °K).

The Sun’s heat is an example of thermal radiation that reaches the Earth. Radiative heat is transferred directly into the surface of any solid object it hits (unless it is highly reflective), but passes readily through transparent materials such as air and glass. An ideal thermal radiator or a blackbody, will emit energy at a rate proportional to the forth power of its absolute temperature and its surface area. Mathematically, that is





where s is a proportionality constant (Stefan-Boltzmann constant = 5.669 ´ 10-8 W/m2.K4). The above equation is called the Stefan-Boltzmann law of thermal radiation and it applies only to the blackbodies. The fourth-power temperature dependence implies that the power emitted is very sensitive to temperature changes. If the absolute temperature of a body doubles, the energy emitted increases by a factor of 24 = 16.

For bodies not behaving as a blackbody a factor known as emissivity e, which relates the radiation of a surface to that of an ideal black surface is introduced. The equation becomes





  The emissivity ranges from 0 to 1; e = 1 for a perfect radiator and absorber ( a blackbody) and e = 0 for a perfect radiator. Human skin, for example, no matter what the pigmentation, has an emissivity of about 0.97 in the infrared part of the spectrum. While a polished aluminum has an emissivity of about 0.05.

Thermal radiation from a body is used as a diagnostic tool in medicine. A thermogram shows whether one area is radiating more heat than it should, indicating a higher temperature due to abnormal cellular activity. Thermography or thermovision in medicine is based on the natural thermal radiation of the skin. Most advantage is the radiance free of the measuring principle.

Certain body regions have different temperature levels. If one exposes the body e.g. to a cooling attraction, then the body zones of the skin react, in order to repair the heat balance of the body. Thereby the thermal regulation of diseased body regions and organs is different to healthy one. The so-called "regulation thermography" is based on this principle.



Picture: University of Wisconsin


Greenhouse Effect


Multiple-Choice Question

Consider the following cooking pan.

Which of the following is important while selecting a material for the pan's handle?

1. High thermal expansion. 2. Low thermal conductivity. 3. High elasticity. 4. High hardness.


Open-Ended Question


Consider a house with a basement, first floor, and second floor. Design and sketch a water heating system for the house. Give an example of where heat convection and heat radiation occur in the heating system. Show the location of the pipes carrying the hot water. Do ceiling fans help in heating the house?