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Elementary Thermodynamics - Heat Transfer

Heat transfer

Heat spontaneously flows from higher-temperature substances to lower-temperature substances. This is the phenomenon you experience standing next to a fire on a cold day. Your body is cold (low temperature), but the fire is much hotter (high temperature), and your proximity to the fire aids in heat transfer from the fire to you.

Three principal methods exist for heat to transfer from one substance to another:

  • Radiation1 (by light waves)

  • Conduction (by direct contact)

  • Convection (by intermediate contact with a moving fluid)



If you have ever experienced the immediate sensation of heat from a large fire or explosion some distance away, you know how radiation works to transfer thermal energy. Radiation is also the method of heat transfer experienced in the Earth’s receiving of heat from the Sun (and also the mechanism of heat loss from Earth to outer space). Radiation is the least efficient of the three heat transfer mechanisms. It may be quantified by the Stefan-Boltzmann Law, which states the rate of heat lost by an object ( ) is proportional to the fourth power of its absolute temperature, and directly proportional to its radiating area:



  = Radiant heat loss rate (watts)

  e = Emissivity factor (unitless)

  σ = Stefan-Boltzmann constant (5.67 × 10-8 W / m2 K4)

  A = Surface area (square meters)

  T = Absolute temperature (Kelvin)

The emissivity factor varies with surface finish and color, ranging from one (ideal) to zero (no radiation possible). Dark-colored, rough surfaces offer the best emissivity factors, which is why heater elements and radiators are usually painted black.



If you have ever accidently touched a hot iron or stove heating element, you possess a very vivid recollection of heat transfer through conduction. In conduction, fast-moving molecules in the hot substance transfer some of their kinetic energy to slower-moving molecules in the cold substance. Since this transfer of energy requires collisions between molecules, it only applies when the hot and cold substances directly contact each other.

Perhaps the most common application of heat conduction in industrial processes is heat conduction through the walls of a furnace or some other enclosure. In such applications, the desire is usually to minimize heat loss through the walls, so those walls will be “insulated” with a substance having poor thermal conductivity.

Conductive heat transfer rate is proportional to the difference in temperature between the hot and cold points, the area of contact, the distance of heat travel from hot to cold, and the thermal conductivity of the substance:


  = Conductive heat transfer rate

  k = Thermal conductivity

  A = Surface area

  ΔT = Difference of temperature between “hot” and “cold” sides

  l = Length of heat flow path from “hot” to “cold” side


In the United States, a common measure of insulating ability used for the calculation of conductive heat loss in shelters is the R-value. The greater the R-value of a thermally insulating material, the less conductive it is to heat (lower k value). “R-value” mathematically relates to k and l by the following equation:

Rearranging this equation, we see that l = kR, and this allows us to substitute kR for l in the conduction heat equation, then cancel the k terms:


R is always expressed in the compound unit of square feet hours degrees Fahrenheit per BTU. This way, with a value for area expressed in square feet and a temperature difference expressed in degrees Fahrenheit, the resulting heat transfer rate () will naturally be in units of BTU per hour, which is the standard unit in the United States for expressing heat output for combustion-type heaters.

The usefulness of R-value ratings may be shown by a short example. Consider a contractor trailer, raised up off the ground on a mobile platform, with a total skin surface area of 2400 square feet (walls, floor, and roof) and a uniform R-value of 4 for all surfaces. If the trailer’s internal temperature must be maintained at 70 degrees Fahrenheit while the outside temperature averages 40 degrees Fahrenheit, the required output of the trailer’s heater will be:


If the trailer’s heater is powered by propane and rated at 80% efficiency (requiring 22,500 BTU per hour of fuel heating value to produce 18,000 BTU per hour of heat transfer into the trailer), the propane usage will be just over one pound per hour, since propane fuel has a heating value of 21,700 BTU per pound.



Most industrial heat-transfer processes occur through convection, where a moving fluid acts as an intermediary substance to transfer heat from a hot substance (heat source) to a cold substance (heat sink). Convection may be thought of as two-stage heat conduction on a molecular scale: fluid molecules come into contact with a hot object and pick up heat from that object through conduction, then later come into contact with a cold(er) object and release that heat energy to it through conduction. If the fluid is recycled in a piping loop, the two-stage conduction process repeats indefinitely, individual molecules heating up as they absorb heat from the heat source and then cooling down as they release heat to the heat sink.

Special process devices called heat exchangers perform this heat transfer function between two different fluids, the two fluids circulating past each other on different sides of tube walls. A simple example of a heat exchanger is the radiator connected to the engine of an automobile, being a water-to- air exchanger, the engine’s hot water transferring heat to cooling air entering the grille of the car as it moves.

Another example of a liquid-to-air heat exchanger is the condenser on a heat pump, refrigerator, or air conditioner, a photograph appearing here:


Another common style of heat exchanger works to transfer heat between two liquids. A small example of this design used to transfer heat from a boat engine is shown here:


This is an example of a shell-and-tube exchanger, where one fluid passes inside small tubes and a second fluid passes outside those same tubes, the tube bundle being contained in a shell. The interior of such an exchanger looks like this when cut away:


A common application of liquid-to-liquid heat exchangers is in exothermic (heat-releasing) chemical reaction processes where the reactants must be pre-heated before entering a reaction vessel (“reactor”). Since the chemical reaction is exothermic, the reaction itself may be used as the heat source for pre-heating the incoming feed. A simple P&ID shows how a heat exchanger accomplishes this transfer of heat:

Another industrial application of heat exchangers is in distillation processes, where mixed components are separated from each other by a continuous process of boiling and condensation. Alcohol purification is one example of distillation, where a mixture of alcohol and water are separated to yield a purer (higher-percentage) concentration of alcohol. Distillation (also called fractionation) is a very energy-intensive process, requiring great inputs of heat to perform the task of separation. Any method of energy conservation typically yields significant cost savings in a distillation process, and so we often find heat exchangers used to transfer heat from outgoing (distilled, or fractionated) products to the incoming feed mixture, pre-heating the feed so that less heat need be added to the distillation process from an external source.

The following P&ID shows a simple distillation process complete with heat exchangers for reboiling (adding heat to the bottom of the distillation column), condensing (extracting heat from the “overhead” product at the top of the column), and energy conservation (transferring heat from the hot products to the incoming feed):


Distillation “columns” (also called towers in the industry) are tall vessels containing sets of “trays” where rising vapors from the boiling process contact falling liquid from the condensing process. Temperatures increase toward the bottom of the column, while temperatures decrease toward the top. In this case, steam through a “reboiler” drives the boiling process at the bottom of the column (heat input), and cold water through a “condenser” drives the condensing process at the top of the column (heat extraction). Products coming off the column at intermediate points are hot enough to serve as pre-heating flows for the incoming feed. Note how the “economizing” heat exchangers expose the cold feed flow to the cooler Product A before exposing it to the warmer Product B, and then finally the warmest “Bottoms” product. This sequence of cooler-to-warmer maximizes the efficiency of the heat exchange process, with the incoming feed flowing past products of increasing temperature as it warms up to the necessary temperature for distillation entering the column.

Some heat exchangers transfer heat from hot gases to cool(er) liquids An example of this type of heat exchanger is the construction of a steam boiler, where hot combustion gases transfer heat to water flowing inside metal tubes:


Here, hot gases from the combustion burners travel past the metal “riser” tubes, transferring heat to the water within those tubes. This also serves to illustrate an important convection phenomenon: a thermal siphon (often written as thermosiphon). As water heats in the “riser” tubes, it becomes less dense, producing less hydrostatic pressure at the bottom of those tubes than the colder water in the “downcomer” tubes. This difference of pressure causes the colder water in the downcomer tubes to flow down to the mud drum, and hot water in the riser tubes to flow up to the steam drum. This natural convection current will continue as long as heat is applied to the riser tubes by the burners, and an unobstructed path exists for water to flow in a loop.

Natural convection also occurs in heated air, such as in the vicinity of a lit candle:


This thermally forced circulation of air helps convect heat from the candle to all other points within the room it is located, by carrying heated air molecules to colder objects.

Liquid-to-liquid heat exchangers are quite common in industry, where a set of tubes carry one process liquid while a second process liquid circulates on the outside of those same tubes. The metal walls of the tubes act as heat transfer areas for conduction to occur. Metals such as copper with very high k values (very low R values) encourage heat transfer, while long lengths of tube ensure ample surface area for heat exchange.


1In this context, we are using the word “radiation” in a very general sense, to mean thermal energy radiated away from the hot source via photons. This is quite different from nuclear radiation, which is what some may assume this term means upon first glance.

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Comments (1)Add Comment
written by mining recruitment, July 02, 2012
This is a good explanation of elementary thermodynamics or heat transfer.

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