Heat flux transmitted by radiation formula. This is heat flow. B6 Complex heat transfer and heat transfer

To express the overall effect of convection, we use Newton's law of cooling: = ℎ 6 3 - 47. Here, the rate of heat transfer is related to the total temperature difference between the wall and the liquid, and the surface area. Radiation Unlike the mechanisms of conduction and convection, when energy is transferred through a material medium, heat can also be transferred to areas where there is a perfect vacuum. In this case, the mechanism is electromagnetic radiation. Radiation can exhibit wavy or corpuscular properties.

Electromagnetic radiation propagating as a result of temperature difference; This is called thermal radiation. Thermodynamic considerations show that an ideal radiator or black body will radiate energy at a rate proportional to the fourth power of the absolute temperature of the body. Equation 5 is called the Stefan-Boltzmann law of thermal radiation, and they are applicable only to black bodies. Stable flat wall of conduction. Let's first consider a flat wall where a direct application of Fourier's law can be made.

Figure 3 shows a typical problem and its analog circuit. Rice. 3 One-dimensional heat flow through several cylindrical cuts and their electrical counterpart. Spherical systems can also be considered as one-dimensional when the temperature is only a function of the radius. critical isolation. Steam tube to illustrate the critical radius of the insulation. Let's say you have a steam pipe that you want to insulate to prevent energy loss and protect people from burns. If the steam is not superheated, some steam will condense in the pipe.

The surface temperature of the pipe-insulation is approximately equal to the saturation temperature of the steam, since the thermal resistance at the pipe wall tends to be small and disappears. Therefore, the temperature drop across the pipe wall will be very small. The following figure shows an electrical analog built for this simplified task. Inner and outer radii of insulation. To determine the critical radius of insulation, we will act as follows. Radial conduction of heat through a hollow sphere Figure 1 Conduction of heat through a hollow sphere Creating an energy balance in a differential volume element to determine the corresponding differential equation.

The above equation is a suitable differential equation for the temperature distribution in a hollow sphere. The two boundary conditions associated with this problem are as follows: since the thicker the insulator, the lower the heat transfer rate, since the wall area is constant, and when it is insulated, it increases thermal resistance without increasing convection resistance. But something different happens with cylinders and spheres when you isolate it. The process of exchanging energy in the form of heat between different bodies or between various parts the same body at different temperatures.

Heat transfer always occurs from more warm body to colder, as a result of the Second Law of Thermodynamics. Heat transfer occurs until the bodies and their surroundings reach thermal equilibrium. Heat is transferred by convection, radiation or conduction. Although these three processes may occur simultaneously, it may happen that one mechanism prevails over the other two.

Electromagnetic radiation is a combination of electric and magnetic fields, oscillating and perpendicular to each other, propagating through space, carrying energy from one place to another. Unlike conduction and convection, or other types of waves, such as sound, which require a material medium to propagate, electromagnetic radiation does not depend on matter to propagate; in fact, energy transfer by radiation is more efficient in a vacuum. However, the speed, intensity and direction of the energy flow is affected by the presence of matter.

Thus, these waves can pass through interplanetary and interstellar space and reach the Earth from. Volcanism, seismic activity, the phenomena of metamorphism and orogeny are some of the phenomena that are controlled by the transport and release of heat. In fact, the Earth's heat balance controls activity in the lithosphere, in the asthenosphere, and also in the interior of the planet.

The heat that reaches the Earth's surface has two sources: the interior of the planet and the sun. Some of this energy is returned to space. If it is assumed that the sun and the biosphere maintain the average temperature on the surface of the planet with small fluctuations, then the heat emanating from the inside of the planet determines the geological evolution of the planet, that is, it controls plate tectonics, magmatism, the generation of mountain ranges, the evolution of the inner part of the planet, including its magnetic field.

it physical property material and is a measure of a material's ability to "conduct" heat. If we consider the one-dimensional case, then the Fourier law is written. If the heat flux and temperature of the medium do not change with time, the process is considered to be stationary. If there is no heat in the volume of material, we will have. Where ρ is the density of the material. This expression allows you to calculate the temperature at points within the region, subject to the imposition of boundary conditions.

We can apply this equation to try to learn something about the temperature distribution inside the planet, using the flow and temperature known surfaces as boundary conditions. Integrating this equation again gives. This last expression can be used to determine the change in temperature with depth. Consider, therefore, the case of the Earth, assuming that heat is transported mainly by conduction. The temperature-depth curve is called "geothermal". An analysis of the figure shows that at depths greater than 100 km, the mantle must have significant melting, while for depths greater than 150 km, the entire mantle must melt.

These "predictions" do not agree with the information obtained from the study of seismic wave propagation, so we must conclude that the thermal conductivity model does not correctly predict the temperature profile in the mantle. Even though the driving model is not in predicting the temperature in the upper mantle, it represents significant success when applied to the outer part of the planet, i.e. the earth's crust, where the internal heat is mainly from radioactive decay and transported to the surface, by driving.

We will return to this problem when studying the heat flow on the continents. Consider a layer of liquid heated at the bottom and cooled at the top. When a liquid is heated, its density decreases due to expansion. In the case under consideration, the upper part of the liquid layer will be colder and, therefore, denser than the lower one. This situation is gravitationally unstable, preventing the liquid liquid from cooling, and the more it heats up, the faster convection currents arise. The movement of a fluid is driven by driving forces.

Consider, therefore, a rectangular fluid element, as shown in the figure. The forces acting on a fluid element are: the forces due to the pressure gradient, the force of gravity, and the force of thrust. For the latter, the density of the liquid must be taken into account. The vertical component of the resulting force will be then.

Although radioactive isotopes exist in small amounts in the earth's crust and are also less common in the mantle, its natural decay produces a significant amount of heat, as can be seen from the table on the left. The most important elements of this process are uranium, thorium and potassium; it can be seen that the contribution of uranium and thorium is higher than that of potassium.

The following table presents the concentration of radioactive elements and the thermal generation of some rocks. Granite is the stone that releases more heat due to the decay of radioactive materials as it has the highest concentration of these elements. The measurement of heat generated by the earth's crust at the present time can be used to calculate the heat generated in the past. On the other hand, the concentration of radioactive elements can be used in rock dating.

The decay rate of a radioactive isotope is given by the formula. Although the rate of heat generation in the Earth's crust is about two orders of magnitude higher than that of the mantle, the rate of mantle production must be taken into account, since the volume of the mantle is much larger than the volume of the crust. This reaction was carried out in the laboratory at temperatures and pressures on the order of those at the core-mantle boundary.

The figure shows the distribution of heat flow along the Earth. The heat lost through the planet's surface is evenly distributed. The following table shows the main contributions: 73% of heat is lost through the oceans, which make up 60% of the Earth's surface. Most of the heat is lost during the creation and cooling of the oceanic lithosphere, when new material departs from the middle ridges. Plate tectonics is fundamentally related to the cooling of the Earth. On the other hand, it appears that average speed the creation of the ocean floor is determined by the balance between the rate of heat generation and the overall rate of loss of the same high temperature over the entire surface of the planet.

In plate tectonics models, the ascent of mantle materials occurs at ocean ridges. These materials, when cooled, lead to the formation of new oceanic crust. When moving away from the ascending zone, the new crust cools down to great depths, forming a thicker and thicker rigid plate.

The following figure shows the observed values ​​of the heat flux as a function of the age of the oceanic lithosphere, as well as the values ​​calculated from the theoretical model. Considering what was said in the previous paragraph, this plot can be interpreted as representing flux values ​​as a function of distance to the ridge. As can be seen, the heat flux near oceanic ridges has high values, decreasing with distance from the ascending zone of mantle materials. By comparing the observed values ​​with the calculated values, it is verified that the fluxes derived from the models are higher than those observed near the ridge.