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HEAT TRANSFER
By Nasif Nahle

WHAT’S HEAT?

Heat is energy in transit from warmer systems to colder systems.

Heat is associated with the internal potential and kinetic energy (an apparently disorganized molecular motion) of a system.

If heat is a form of energy associated to the particles’ rotational, translational and vibratory movements, how does the heat move through the space between the Sun and the Earth, which density is extremely low? The answer is: heat could be transferred from warmed systems by radiation. The thermal radiation is electromagnetic radiation that consists of particles and waves, i.e. photons and waves, the same as visible light. Thus, the radiative heat transfer can take place through vacuum.

The energy always moves from a warmer system to a colder system. The energy which is moving from one system to another is known as heat. The transfer or dispersion of heat can occur by means of three main mechanisms, conduction, convection and radiation:

CONDUCTION: It is the flow of heat through solids and liquids by vibration and collision of molecules and free electrons. The molecules of a given point of a system which are at higher temperature vibrate faster than the molecules of other points of the same system -or of other systems- which are at lower temperature. The molecules with a higher movement collide with the less energized molecules and transfer part of their energy to the less energized molecules of the colder regions of the structure. For example, the heat transfer by conduction through the bodywork of a car.

Metals are the best thermal conductors; while non-metals are poor thermal conductors. For comparison, the thermal conductivity (k) of the copper is 401 W/m*K, while the thermal conductivity (k) of the air is 0.0263 W/m*K. The thermal conductivity of the carbon dioxide (CO2) is 0.01672 W/m*K, almost the thermal conductivity of an isolator.

Formula to calculate the conductivity gradient for a given system:

q = - kA (Δ T/Δ n)

Where Δ T/Δ n is the temperature gradient in the direction of area A, and k is the thermal conductivity constant obtained by experimentation in W/m.K.


CONVECTION: Flow of heat through currents within a fluid (liquid or gas). Convection is the displacement of volumes of a substance in a liquid or gaseous phase. When a mass of a fluid is heated up, for example when it is in contact with a warmer surface, its molecules are carried away and scattered causing that the mass of that fluid becomes less dense. For this reason, the warmed mass will be displaced vertically and/or horizontally, while the colder and denser mass of fluid goes down (the low-kinetic-energy molecules displace the molecules in high-kinetic-energy states). Through this process, the molecules of the hot fluid transfer heat continuously toward the volumes of the colder fluid.

For example, when heating up water on a stove, the volume of water at the bottom of the pot will be warmed up by conduction from the metallic bottom of the pot and its density decreases. Given that it gets lesser dense, it shifts upwards up to the surface of the volume of water and displaces the upper -colder and denser- mass of water downwards, to the bottom of the pot.

Formula of Convection:

q = hA (Ts - T ∞)

Where h is for convective heat transfer coefficient, A is the area implied in the heat transfer process, Ts is for the temperature of the system and T ∞ is a reference temperature.


RADIATION: It is heat transfer by electromagnetic waves or photons. It does not need a propagating medium. The energy transferred by radiation moves at the speed of light. The heat radiated by the Sun can be exchanged between the solar surface and the Earth's surface without heating the transitional space.

For example, if I place an object (such as a coin, a car, or myself) under the direct sunbeams, I will note in a little while that the object will be heated. The exchange of heat between the Sun and the object occurs by radiation.

The formula to know the amount of heat transferred by radiation is:

q = e σ A [(ΔT)^4]

Where q is the heat transferred by radiation, E is the emissivity of the system, σ is the constant of Stephan-Boltzmann (5.6697 x 10^-8 W/m^2.K^4), A is the area involved in the heat transfer by radiation, and (ΔT)^4 is the difference of temperature between two systems to the fourth or higher power.

A Heat Sink is a system capable of absorbing heat from an object with which it is in thermal contact without a phase change or a significant variation in temperature.

At Earth's location, the outer space, the gravity field (Guth. 1999. Pp. 29-31) and the false void are heat sinks.

Water has a specific Heat of 4.190 kJ/Kg.K, while air has a specific heat of 1.0057 kJ/Kg.K, and soil have a Specific Heat of 0.725 kJ/Kg.K.

Water has a Specific Heat higher than soil and air; then, the Thermal Capacity of water is higher than the Thermal Capacity of the air and the soil. To a greater Thermal Capacity, a slower rate of dissipation of heat.

The atmosphere and the soil don't maintain a load of heat for longer periods than water because they have a specific heat capacity lower than water, so water absorbs more heat for inreasing its temperature for a determined interval. For equal volumes (1Kg, for example), water absorbs more heat than air or soil. The absorbed heat will be transformed into kinetic and potential energy. A body with a high energy density will lose its inner energy slower than a body with a lower energy density. For example, if you have ten dollars and your friend has five dollars, and each one is obliged to spend one dollar per day, you will delay ten days to spend your money, while your friend will delay only five days to consume his money.

In general, the soil and the air have independently 1/4 of the specific heat of water. For example, the Specific Heat of Carbon Dioxide is 850 J/Kg °C; to be precise, 4.92 times less than the Specific Heat of water; then, its Thermal Capacity will be less than the Thermal Capacity of water. For equal masses of the evaluated substances, at controlled temperatures and pressure, the Carbon Dioxide will release its internal heat five times faster than the water. If one Kilogram of water at 30 °C is cooled by 10 °C in 10 minutes, one Kilogram of Carbon Dioxide at 30 °C would be cooled by 10 °C in two minutes. The rule is: If you get it fast, you will lose it fast. As an interesting datum, the Hydrogen has a Specific Heat of 14200 J/Kg -°C; while Methane, another of the famous "Greenhouse" gases, has 2200 J/Kg °C. Steam water has a Specific Heat of 2100 J/Kg-°C (Data on Specific Heat of the substances obtained from MONACHOS ENGINEERING and from Wittemann).

Water absorbs the incoming solar Infrared Radiation because the frequency of the internal vibration of the water molecules is the same frequency of the waves of the solar Infrared Radiation. This form of Radiative Heat transfer is known as Resonance Absorption.

We humans feel the heat radiated by the Sun and other systems with a higher temperature because our bodies contain 55-75% of water. The radiative energy inciding on our skin is absorbed by the molecules of water in our bodies by Resonance Absorption. Just then, the Infrared Radiation absorbed by our bodies leads to a more intense internal vibration of the water molecules in our bodies and our bodies get warmer. However, in general, living beings possess thermoregulatory systems that permit us to eliminate the excess of heat from our bodies, maintaining a quasi-stable internal temperature (it is one of the homeostatic processes of biosystems).

If the Earth did not have water, nights would be extremely cold.

For example, if the atmospheres of Mars and Earth had the same density, Mars would have an atmospheric CO2 concentration of 11998.5 ppmv. However, due to the lower density of Mars' atmosphere, the concentration of CO2 in that planet's atmosphere is equivalent to 0.95% on Earth; nevertheless, Mars is a frozen planet because Mars has only vestiges of water (0.03%) and it has not ponds, lakes and oceans, as Earth has.

Have you read that “the main explanation of the blazing Venus surface and the frosty Martian surface has been quite clear and straightforward: the "greenhouse effect”? This assertion is ambiguous because the real cause is the distance of Venus (nearly) and Mars (distant) from the Sun, and because Mars and Venus do not have water as Earth has. If the greenhouse effect was the responsible, then Mars, a planet with 95% of Carbon Dioxide in its atmosphere, would not be an iced, but a tepid planet. Besides, Mars only receives 589.2 W/m+e2 of solar irradiance, while Earth receives 1367.6 W/m+e2 of solar irradiance (2.32 times higher than Mars). Mars’ core has a temperature of 1727 °C (Fei and Bertka, Science; 2005), while the temperature of the Earth's core is 7,200 °C, ¡This is a core temperature four times higher than Mars' core temperature!

Despite the low density of the Martian atmosphere, it has a concentration of carbon dioxide (CO2) of 0.95%, which is 29.5 times higher than the concentration of CO2 in Earth’s atmosphere. If the global temperature was determined by CO2, Mars would be comfortably warm. On the other hand, NASA has reported a Climate Change on Mars -i.e. a Martian Global Warming due to the "shrunk" of frozen deposits of CO2 on Mars means that its atmosphere's temperature has increased far from normal. The report on the Martian Global Warming from NASA says, “New impact craters formed since the 1970s suggest changes to age-estimating models. And for three Mars summers in a row, deposits of frozen carbon dioxide near Mars' South Pole have shrunk from the previous year's size, suggesting a climate change in progress.” (cursives are mine). Scientists have also observed that Venus, Jupiter, Saturn and its satellite Titan are experiencing Climate Changes, which indicates that the Climate Change and the Global Warming are phenomena which are taking place in the whole Solar System, which denotes a cosmic origin.

Many authors say that “Greenhouse” gases act as a “blanket” which reflects the heat back to Earth -i.e. “Some re-radiated heat reflected back to Earth” (Ultimate Visual Dictionary – The Atmosphere. DK publishing, Inc. p. 301. 1998) and “The reason is that the atmosphere functions like the crystals of a glasshouse. This is, the properties of absorption and conduction of glass are similar to those of the atmospheric greenhouse gases …” (Wilson, Jerry D. College Physics-2nd Edition; p. 382. Prentice Hall Inc. 1994).

There are other authors who discuss thermal events similarly as the writers I have quoted in the previous paragraph; I have found the same mistakes written on reports from NASA, NOA, EPA, etc. Those unintentional faults have been inflated by some pseudo-environmentalists and politicians that enforce the erroneous concept of "Greenhouse Gases", “Anthropogenic Global Warming” and “Manmade Climate Change”, closing their eyes to the Laws of Thermodynamics, Heat Transfer, Thermal Expansion, Physics Laws, etc.

The atmosphere is not a “glass”, nor acts like a glass. It either is a blanket that “reradiates” heat to the surface, or that obstructs convection. Far from impeding convective heat transfer, gases allow convection.

CO2 is able to absorb the energy emitted by the ground and the oceans and transforms it into kinetic and potential energy. By these transformations from one class of energy into another, the CO2 emits radiant energy (energy in transit or heat), which is transferred by convection to the upper atmosphere layers. After it has been transferred to the upper layers of the atmosphere, the heat is released to the outer space (Heat Sink). However, we have understood that the current concentration of Carbon Dioxide cannot be a source of “Global Warming”. We would need about 560 ppmv for increasing the Earth’s surface temperature up to 0.7 °C.

The terrestrial atmosphere is a stratum composed by a mixture of gases (air) that wraps the Earth and is retained by Earth’s gravity.

The atmosphere stratifies according to differences of density and temperature. Nitrogen and Oxygen are the predominant constituents in all layers, but each layer is less dense than the previous layer, starting up from the troposphere which is the denser layer (density = magnitude of mass per unit of volume; for example, the density of liquid water is 1 Kg per liter).

The quantity of mass of air per unit of volume decreases as height increases. At sea level and 288.2 K (15.2 °C or 59.36 °F), the density of air is 1.225 Kg/m+e3 and its thermal conductivity is 0.02596 W/m K.

However, like all materials, when gases warm up their density decreases because their molecules vibrate faster and are scattered (expansion). Thus, the volume of air is enlarged to a maximum value, but its density decreases because its molecules distribute in a greater volume. If the gas expansion were not feasible, then the pressure exerted by the gas would increase; for example, inside a closed container or into the cylinders of a modern engine.

At my childhood, I performed a very dangerous experiment with an empty glass container (a flask of instantaneous coffee) that I placed into an empty wood box (after all, I took a few precautions). I placed the box on a firewood stove and kept waiting. I do not remember how long it delayed, but the flask was cracked out and, after few minutes, it exploded (DO NOT TRY IT AT HOME!). The expansion of the glass cracked the flask, and the expansion of the air trapped inside the flask blew it up. Obviously, thermal energy was the driver.

Vertical convection does not occur in the stratosphere because in this layer of the atmosphere the gases move only horizontally; consequently, the main modes of heat transfer in the stratosphere are radiation and conduction; however there is horizontal convection in the stratosphere known like advection, which is a horizontal heat transfer due to the horizontal displacement of air masses. The advection in the stratosphere is chaotic  (cat’s eyes).

QUESTION FROM A STUDENT: If air has a density of 1.29 Kg/cubic meter and the water's density is 1.00 Kg/cubic meter, why the air does not submerge into liquid water?

ANSWER: First of all, you forgot to write "x 10+e3" after the density of liquid water. You should have written: "If air has a density of 1.29 Kg/cubic m and the water's density is 1.00 X 10+e3 Kg/cubic m..." If we express the quantities without the notations based on 10, we will read the phrase as follows: "If air has a density of 1.29 Kg/cubic m and the water's density is 1000 Kg/cubic m...", which clearly denotes that the air is less dense than the water. Regarding your question, if placed in denser mediums, the less dense materials would tend to float. As the air is less dense than water, it will move to the surface of water.

When we deal with ice (water in solid phase), given that the ice has a density of 920 Kg/cubic m, which is less dense than the water in liquid phase (1000 Kg/cubic m), the ice will tend to float in the mass of liquid water; however, only a portion will remain totally submerged in the water because the relation between the densities of ice and liquid water is 92%; this means that only the 8% of the ice will float above the surface of the water in the liquid phase. For an iceberg, we would only see an 11% of the complete block of ice above the level of water because seawater has a density of 1030 Kg/cubic m (920 ÷ 1030 = 0.89; 0.89 is equal to 89%).

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ALGORITHM AND EXAMPLE FROM REAL LIFE

If soil absorbs heat and its temperature in 31 March 2007 at 13:15 hrs is 348.15 K (75 °C) and the temperature of air is 300.15 K (27 °C), what would be the tropospheric ΔT if we consider the absorptivity-emissivity of CO2?

To know the answer, we have to know first the heat transfer from the soil to the mixed air. Primary, we have to obtain the Grashof Number and the Convective Heat Transfer Coefficient for those particular conditions:

Grashof Number:

Gr L = g β (TsT ∞) D^3 / v^2

Where,

g is the gravitational constant (9.8 m/s)
β is the volumetric expansion coefficient
T1-T2 is the difference of temperature between two adjacent systems expressed in Kelvin
D is the distance between the two systems
v is the velocity of heat transfer between two systems.

Gr L = (9.8 m/s^2) (2.857 x 10^-3 K^-1) (48 K) (1 m)^3 / (2.076 X 10^-3)^2 m^4 /s^2 = 0.699965 m^4/s^2 / (2.076 X 10^-3)^2 m^4 /s^2 = 3.12 x 10^5

Convective Heat Transfer Coefficient:

    k
Ћ =  ------- (C) [(Gr) (Pr)]^1/4
  D^3

Where,

k is the thermal conductivity
D is the distance between the two systems
C is a correction factor for heterogeneous systems
Gr is the Grashof Number
Pr is the Prandtl Number
a is the constant of proportionality for natural laminar systems.

     0.03003 W/m*K
Ћ =  ------------------------------ (0.60) [(3.12 x 10^5) (0.697)]^1/4 = 0.389 W/m^2*K
1 m^3

The heat transfer from soil to mixed air is:

q = Ћ A (TsT ∞) = 0.389 W/m^2*K (1 m)^2 (48 K) = 18.7 W

18.7 W = 4.47 cal/s

If m of mixed air = 1.18 Kg/m  and the Cp of mixed air at 300.15 K = 1005.7 J/kg*K (240.37 cal), then:

Δ T = q / m (Cp) = 4.47 cal/s / (1.18 Kg/m^3 ) (240.37 cal) = 4.47 cal / 283.64 = = 0.016 °C/s

If 0.016 °C is the ΔT caused by the thermal transfer by conduction-convection from the ground to the total mixture of air each second, then we must first warm up the soil and the oceans for the next reason:

The energy absorbed by dry air from incoming Solar radiation is 697.04 W/m^2 X 0.14 (absorptivity of dry air at T = 300.15 K, and P = 1 atm) = 18.7 W/m^2 = 4.47 |cal/s| / m^2.

Considering the same conditions but including water vapor (relative humidity of 50%), the temperature caused by the heat absorbed by water vapor and carbon dioxide, taken independently, is:

Heat absorbed by water vapor: 278 W = 278 J/s (absorptivity = 0.75)
Heat absorbed by carbon dioxide: 0.4 W = 0.4 J/s (absorptivity = 0.001 at its current partial pressure)

Change of temperature by the load of heat absorbed by water vapor:

ΔT = 278 J / 0.013 Kg (1864 J/Kg °C) = 11.5 °C

Change of temperature by the load of heat absorbed by carbon dioxide:

ΔT = 0.4 J / 0.00067 Kg (871 J/Kg °C) = 0.7 °C

Applying the algorithm to know the load of heat absorbed by CO2:

q Stored = m (Cp) (ΔT) / Δt

Known Data:

Mass of atmospheric CO2 = 0.00067 kg
Cp CO2 = 871 J/kg K
ΔT = 48 K (348.15 K - 300.15 K)
Δt = 60 s

Introducing magnitudes:

q Stored = 0.00067 Kg (871 J/kg K) (48 K / 60 s) = 0.47 J/s

Δ T = q / m (Cp) = (0.47 J/s)/ |0.00067 kg (871 J/Kg*°C)| = 0.8 °C

Therefore, water vapor is the main driver of the warming effect of the atmosphere. On this case, water vapor absorbed the infrared radiation, emitted by the surface, 14 times more efficiently than CO2. (Martin Chaplin. 2009)

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The following diagrams illustrate the mechanisms of heat transfer between the surface and the atmosphere in Earth, as well as how clouds and rain and hail are produced, and the effect of induced emission upon spontaneous emission.

Any questions on this topic must be addressed to biophysics@biocab.org
HEAT TRANSFER
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Copyright© April, 2006 by Biology Cabinet Organization
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I have included the formulas to calculate the heat stored through the three means of heat transfer. In addition, I have added algorithms to calculate the variation of the tropospheric temperature by increasing the density of atmospheric CO2 as well as examples from nature applied to water vapor and carbon dioxide. The heat transfer in clouds and air is shown in schematically. References are here.

Updated on April 25, 2009
Left click on the schemes for enhanced images.

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8. FURTHER READING

Bakken, G. S., Gates, D. M., Strunk, Thomas H. and Kleiber, Max. Linearized Heat Transfer Relations in Biology. Science. Vol. 183; pp. 976-978. 8 March 1974.

Boyer, Rodney F. Conceptos de Bioquímica. 2000. International Thompson Editores, S. A. de C. V. México, D. F.

Guth, Alan H. The Inflationary Universe: The Quest for a New Theory of Cosmic Origins. Perseus Books Group, 1999, New York, New York. Pp. 29-31.

Manrique, José Ángel V. Transferencia de Calor. 2002. Oxford University Press. England.

Maoz, Dan. Astrophysics. 2007. Princeton University Press. Princeton, New Jersey.

McGrew, Jay L., Bamford, Frank L and Thomas R. Rehm. Marangoni Flow: An Additional Mechanism in Boiling Heat Transfer. Science. Vol. 153. No. 3740; pp. 1106 - 1107. 2 September 1966.

Petit, J.R., J. Jouzel, D. Raynaud, N.I. Barkov, J.-M. Barnola, I. Basile, M. Benders, J. Chappellaz, M. Davis, G. Delayque, M. Delmotte, V.M. Kotlyakov, M. Legrand, V.Y. Lipenkov, C. Lorius, L. Pépin, C. Ritz, E. Saltzman, and M. Stievenard. Climate and Atmospheric History of the Past 420,000 Years from the Vostok Ice Core, Antarctica. Nature, Vol. 399, June 3, 1999 pp.429-43.

Pitts, Donald and Sissom, Leighton. Heat Transfer. 1998. McGraw-Hill.

Potter, Merle C. and Somerton, Craig W. Thermodynamics for Engineers. Mc Graw-Hill. 1993.

Schwartz, Stephen E. 2007. Heat Capacity, Time Constant, and Sensitivity of Earth's Climate System. Journal of Geophysical Research. [Revised 2007-07-16]

Van Ness, H. C. Understanding Thermodynamics. 1969. McGraw-Hill, New York.

Wagner, Friederike, Bohncke, Sjoerd J. P., Dilcher, David L., Kürschner, Wolfram M., Geel, Bas van, Visscher, Henk. Century-Scale Shifts in Early Holocene Atmospheric CO2 Concentration. Science; 18 June 1999: Vol. 284. No. 5422, pp. 1971 - 1973

Wilson, Jerry D. College Physics-2nd Edition; Prentice Hall Inc. 1994.

http://www.uah.edu/News/newsread.php?newsID=210 (Last reading on 25 August 2007)

http://www.atmos.uah.edu/data/msu/t2lt/tltglhmam_5.2 (Last reading on 25 August 2007)

http://www.cgd.ucar.edu/cas/papers/bams99/ (Last reading on 25 August 2007)

http://scienceandpublicpolicy.org/monckton_papers/greenhouse_warming_what_greenhouse_warming_.html
(Last reading on 25 August 2007)

http://www.ipcc.ch/SPM2feb07.pdf (Last reading on 25 August 2007)

http://www.gsfc.nasa.gov/topstory/20011212methane.html (Last reading on 25 August 2007)

Chaplin, Marin. Water Absorption Spectrum. http://www.lsbu.ac.uk/water/vibrat.html (Last reading on 25 April 2009)

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Heat Transfer from Surface to Clouds
Heat Transfer During Daytime
Heat Transfer During Nighttime