Heat Transfer, Conduction, Convection and Radiation

Click on the image to see an enhanced diagram.

HEAT TRANSFER

WHAT’S HEAT?

Heat is energy in transit from warmer to colder system.

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

There is a dilemma with the understanding of the previous paragraph. If heat is a form of energy associated to the particles’ rotational, translational and vibratory movements, what is the heat that moves through the empty space between the Sun and the Earth, where for the most part there are not molecules? Well, we should know that the heat could be transferred from any source by radiation. The thermal radiation is electromagnetic radiation that consists of quanta and waves, to be precise, photons and waves, like light’s propagation. Thus, the radiative heat transfer can take place through vacuum.

The energy always moves from a warm system to a colder system. The energy that 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 portion of a system at a higher temperature vibrate faster than the molecules of other regions of the same -or of another- system at lower temperature. The molecules with a higher movement collide with the molecules less energized 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 (a liquid or a gas). Convection is a movement of liquid or gaseous volumes. When a mass of a fluid warms because it is in contact with a hot surface, its molecules are expanded and scattered causing that the mass of that fluid becomes less dense. As the hotter volume of the fluid becomes less dense, it will be displaced vertically and/or horizontally, while the less hot but denser volumes of the fluid will sink (the less hot volume is displaced by the hotter volume of fluid). By this mechanism, the hotter volumes transfer heat towards the less hot volumes of that fluid (a liquid or a gas).

For example, when we heat water on a stove, the volume of water at the bottom of the pot will be warmed up by conduction from the metal of the pot and it will become less dense. Then, because it is less dense, it will shift upward to the surface of the volume of water and will displace to the upper -less hot and denser- mass of water.

Formula of Convection:

q = hA (Ts - T ∞)

Where h is the constant for the convective heat transfer coefficient, A is the area implied, and Ts - T ∞ is the difference between the final temperature and the initial temperature.

RADIATION: It is the transfer of heat by electromagnetic waves. It does not need a propagating medium. Radiated energy 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 T^4 is the the fourth power of the absolute temperature.

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 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 cannot maintain a generation of heat for longer periods than water because they have a thermal capacity lower than water. For equal volumes (1Kg of each medium), water absorbs more heat than air or soil, so water can absorb more heat, which will be converted into kinetic and potential energy, than the soil or the air can do. A body with a high energy density will last more for losing its inner energy 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 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 Infrared Radiation incoming from Sun 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 like Resonance Absorption.

We humans feel the heat radiated by the Sun and other systems with a higher temperature than our bodies because the last are formed by 55-75% of water. The Radiative Heat incising on our skin is absorbed for our bodies’ molecules of water by Resonance Absorption. At that moment, the Infrared Radiation directs a more intense internal vibration of the molecules of water in our bodies (our bodies get warmer). However, living beings in general possess systems that permit us to eliminate the excess of heat from our bodies to maintain a quasi-stable internal temperature (it is one of the many homeostatic processes of biosystems).

If Earth did not have water, nights would be extremely cold -even if its atmosphere had had "Greenhouse" Gases five times more concentrated than at present.

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 a lower density of the atmosphere, the concentration of CO2 in Mars 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 or oceans.

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 not true, because the real cause is the distance of Venus (nearly) and Mars (distant) from Sun, and that Mars and Venus do not have water as Earth has. If the “greenhouse” effect were the responsible, then Mars, a planet that has 95% of Carbon Dioxide, would not be an iced, but a tepid planet. Besides, Mars only receives 589.2 W/m+e2 of radiant energy from Sun, while Earth receives 1367.6 W/m+e2 of solar radiant energy (2.32 times higher than Mars). Mars’ core has a temperature of 1727 °C (Fei and Bertka, Science; 2005), while Earth has a core generator of heat at 7,200 °C, ¡A CORE TEMPERATURE FOUR TIMES HIGHER THAN MARS’ CORE TEMPERATURE!

Despite the low density of the Martian atmosphere, it has a concentration of Carbon of 0.95%, which is 29.5 times higher than in Earth’s atmosphere. If the global temperature were determined by Carbon Dioxide, Mars would be comfortably warm. Besides, NASA has reported a Climate Change on Mars -specifically, a Martian Global Warming because the "shrunk" of frozen deposits of carbon dioxide on Mars means that its atmosphere's temperature has risen 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.” (I have added the cursives). Scientists have also observed that Venus, Jupiter, Saturn and its satellite Titan are experiencing also Climate Changes, which indicates that the Climate Change and the Global Warming are phenomena taking place in the whole Solar System obeying to a cosmic origin, or... perhaps there are industrial activities on Mars and the other planets?

Many authors on climate say that “Greenhouse” gases act as a “blanket” that 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 many authors that stated thermal events as did it the writers that I 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 numerous pseudo-environmentalists and politicians that enforce the erroneous and unreasonable concept of "Greenhouse Gases", “Anthropogenic Global Warming” and “Manmade Climate Change”, closing their eyes before the Laws of Thermodynamics, the Heat Transfer, the Thermal Expansion, the Physical Laws, etc.

The atmosphere is not a “glass”, nor acts like a glass. It is neither a blanket that “reradiates” the heat, or that obstructs the convection. Absolutely not! Far from impede the heat transfer through convection, the gases allow convection.

As all substances, Carbon Dioxide has a capacity to absorb heat from ground and oceans and transform it into kinetic and inner potential energy. Through this transformation from one form of energy into another, the Carbon Dioxide generates heat that is transferred slowly by convection to the upper atmospheric layers. After transferred, the heat is released from the highest atmospheric layers to the outer space (Heat Sink). However, we have understood that the current concentration of Carbon Dioxide is not the source of “Global Warming”. We would need about 1200 ppmv to rise the Earth’s surface temperature up to 0.5 °C.

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

The atmosphere stratifies by means 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 the altitude increases. At the sea level and at 288.2 K (15.2 °C or 59.36 °F), the density of air in the troposphere is 1.225 Kg/m+e3 and its thermal conductivity is 0.02596 W/m/degree Kelvin.

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 the firewood stove and stood myself to wait awhile. I do not know how long it delayed, but the flask was cracked and, after some minutes, it exploded (yes, yes... I know what I have to say... 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, the heat leaded this incident.

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 horizontal heat transfer by the horizontal displacement of 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 m and the water's density is 1.00 Kg/cubic m, 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 Kg/cubic m X 10+e3..." 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%).

ALGORITHM AND EXAMPLE FROM REAL LIFE

Earth receives 697.04 W/m2 of energy from a total of 1367 W/m2 of energy incoming from the Sun. 14% of the heat incoming to Earth is absorbed by air.

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 Δ T by 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 (Ts – T ∞) 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:

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 (Ts – T ∞) = 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 Δ T 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 because:

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.

Considering the whole mixture of air the Δq by Solar Irradiance absorbed-emitted by the mixed air would be only of 0.734 W/m^2*K (0.175 th-cal). From this quantity, the CO2 can store 0.012 W/m^2*K (0.003 th-cal) by radiation for the period of only one second, which is equivalent to 0.01 °C. However, the averaged change observed in the tropospheric temperature since 1997 has been of 0.52 °C; then, the discrepancy is - 0.5 °C. The mathematical expression for the experimental data is as follows:

Known Data:

Mass = 0.000614 kg

Cp = 871 J/kg*K = 208.17 cal-th

Δ T = 0.62 K

Δ t = 60 s

Indicated Formula:

q Stored = m (Cp) (Δ T) / Δ t

Replacing with magnitudes:

q Stored = 0.000614 Kg (871 J/kg*K) (0.62 K) / 60 s

q Stored = 0.534794 J/K (0.0103 K/s) = 0.00551 J/s = 0.00551 W

0.00551 W = 0.00132 cal-th/s

Equivalence in Δ T = q / m (Cp) = 0.001317 (cal-th/s) / 0.000614 kg (208.17 cal-th/Kg*°C) = 0.01 °C/s

If the Sun were not brighter, the Earth would not be warming up. Favorably, our Sun now is shining more than 400 years ago, and we do not have to fear a natural cycle that has occurred through the whole existence of our Solar System.

The discrepancy between the observed Δ T and the derived Δ T through the last 400 years is -0.54 °C. Thus, CO2 cannot be responsible of the observed change in the tropospheric temperature experienced through the last 150 years. The reason is that CO2 is not so good in absorbing-emitting heat.

If we multiply the factor of 0.185 °C per each 3.27 W/m^2.K of increase in Solar Irradiance through the last 400 years, we will obtain a variability of the tropospheric temperature of 0.61 °C. The discrepancy between this result and the observed variability of the tropospheric temperature is only 0.09°C, which is an accepted gradient attributable to mitigating factors in the atmosphere.

The density of the CO2 and its Cp is inversely proportional to altitude and it has been obtained by experimentation, so we cannot multiply nor add linearly the increase of the temperature with altitude. If you want to know the change of temperature by CO2 at different altitudes you have to refer to the tables on thermal properties of gases obtained experimentally.

The Δ ∂ CO2 increases its internal temperature by 0.029 C by the increase in the density of heat incoming from the Sun, but it holds only 0.001 C that ends in molecular movement of CO2 and it is transferred by convection to other colder volumes of air.

Water and steam are really efficient in absorbing, convecting and emitting heat because the Cp and the emissivity (E) of water and steam are four times higher than those of CO2.