Heat Transfer PDF

Earlier energy was described as that property of the Universe which can cause change. Through the application of force, work is done. Every star radiates the energy it develops internally, and any associated planets at the appropriate distance can absorb and use this energy to evolve accordingly....

Earlier energy was described as that property of the Universe which can cause change. Through the application of force, work is done. Every star radiates the energy it develops internally, and any associated planets at the appropriate distance can absorb and use this energy to evolve accordingly. Heat is one form of energy, and in many cases the production of heat and its subsequent release can do useful work. The Conservation of Energy states that energy cannot be created or destroyed, only converted from one form to another. Energy concerning the application, loss or transfer of heat is termed thermal energy. According to the law of conservation of energy, thermal energy cannot be created or destroyed, but it is converted from, and to, other forms of energy. For example, thermal energy may be created from electrical, chemical, mechanical or nuclear energy. It can be converted to mechanical or kinetic energy. The heat in a thermal process can also add energy to chemical reactions. Although all substances can absorb and radiate heat energy, it is the gases that can most easily turn this into useful work. The work done by an expanding gas is one of the basic principles behind propulsion. HEAT TRANSFER Conduction Conduction requires physical contact between a body having a high level of heat energy and a body having a lower level of heat energy. When a cold object comes into contact with a hotter object, the action of the molecules in the hot material transfers some of their energy to the molecules in the colder material. Similarly, if one part of a body is heated then the energy will be transferred internally molecule to molecule as they become more agitated. Eventually the activity of the molecules in the two materials becomes equalised and thus the temperatures also equalise, before falling as heat is lost to the surroundings. Page 68 of 114 An example of heat transfer by conduction is the removal of heat from an engine cylinder by cooling fins. The combustion of gasoline in the cylinder releases heat which is conducted to the cylinder head and cooling fins. The heat is then conducted to the cooler air and carried away. Fig 3.1 CONVECTION Convection is the process by which heat is transferred by bulk movement of a fluid. As fluid is heated by a heat source, it becomes less dense and rises, being replaced by cooler fluid. Heating water in a kettle, heating air in a house and the circulation of atmospheric heat are examples of convection. The handle of the saucepan is made from a material that does not conduct heat very well. Therefore the handle will stay relatively cool while the metallic saucepan becomes hot. Convection currents Fig 3.2 RADIATION Page 69 of 114 Electromagnetic Radiation refers to the emission of energy from the surface of most objects, and is related to the acceleration of charged particles. EMR is energy propagation by periodic variation of the electric E, and magnetic field M, strengths caused by the acceleration of charged particles. There are charged particles within the molecules that make up a substance. The nature of the motion possessed by these particles is acceleration because they constantly change direction. Fig 3.3 These are not mechanical waves, but they display similar behaviour, and are able to travel through vacuum. The M and E waves are perpendicular to each other. At a certain frequency of this wave motion, approx 1013 Hz, the energy is propagated as heat. (Actually called Infra-Red as it is just lower than red light) Fig 3.4 All the energy we receive from the sun has been radiated to us across 93 million miles of vacuum. There is no need for intermediate matter to transfer radiant energy. Only a small part of the energy we receive from the sun is light. Much of the rest is radiant heat. Conduction and convection take place relatively slowly while radiation takes place at the speed of light. Page 70 of 114 Kinetic Theory of Matter It was discovered that the smallest particles of most substances, molecules, are constantly in random motion. (For elements, read atoms.) Heat is described as the kinetic energy associated with this motion The more heat energy there is in a material, the faster its molecules move, and changes will occur to the substance. Initially solids will expand as their molecules take up more space with the movement. Railway tracks have expansion joints fitted to allow the track to move under hot sun. Expansion is calculated using the formula E = kL(T2 --T1) Fig 3.5 Where L is the original size, T2 -T1 is the temperature difference, and k is the Co- efficient of Linear Expansion for the material. Jeppesen Gen p. 2-18 Remember, if two dissimilar substances are joined and heated, they will expand at different rates and create stress in the structure. (Bi-metallic strip) The two metals in the bi-metallic strip expand different amounts with heating. Hence the strip bends with temperature changes. Fig 3.6 The bending operates the electrical contacts for thermostats, and keeps the clock wheel in balance for constant speed at differing temperatures. Change of State Eventually, as heat is added, the same molecules have become so far apart that the substance changes state to a liquid. Keep heating the material and it changes state again and becomes a gas. The molecules are so far apart now that they become independent of each other. Remember our goal is to understand the transfer of energy (as heat), to effect change by the application of force. It is fairly simple to see using incompressible substances such as solids, (hitting something with a hammer!), and liquids. (Hydraulic Systems) Page 71 of 114 For gasses, which are compressible, it is more complicated and we must investigate the behaviour of gasses as they absorb and release heat before we see how they help create propulsion. Firstly though, some terminology: UNITS OF HEAT Calorie (cal): one calorie is the quantity of heat required to raise the temperature of one gram of water by one degree Celsius. British thermal unit (Btu): one Btu is the quantity of heat required to raise the temperature of one pound of water by on degree Fahrenheit. Joule (J): the SI unit for all forms of energy. Energy provides the capacity for work to be done. Fig 3.7 One joule of energy can do one joule of work. The heat produced by burning one litre of gasoline is about 8 x 106 cal, 3 x 104 Btu, or 3 x 107 J (30 MJ). TEMPERATURE Temperature represents the degree of heat possessed by one mass over another. When heat flows from one body to another, the hotter is said to be at a higher temperature. However, a cup of water at 90°C contains less heat than a swimming pool at 20°C. For this reason we define two properties, one called the Specific Heat of a substance, and the other, the Heat Capacity. (Jeppesen General p. 2-30) Specific Heat and Heat Capacity The specific heat of a substance is the number of calories required to raise the temperature of 1 gram of the substance by 1°C. or, the number of Btu's required to raise the temperature of 1 pound of the substance by 1°F. Water is used as the benchmark as it takes 1 calorie to raise 1 gram of water by 1°C. Other substances, notably metals, take very much less energy to raise their temperature. The high specific heat of water is why ocean temperature does not vary as much as land temperature. This allows the oceans and large lakes of the earth to act as heat sinks or temperature stabilisers. The heat capacity C of a substance is the amount of heat required to change its temperature by one degree, and has units of energy per degree. Page 72 of 114 Temperature Scales Temperature represents the average kinetic energy of molecules and is measured in degrees (°). There are four main temperature scales: degrees Celsius (°C), degrees Fahrenheit (°F), degrees Rankine (°R) and Kelvin (K). With the Kelvin scale, the unit 'degrees' and its symbol(°) is not used. It is said that water boils at 373 K. Thermometers are used to measure temperature and they are constructed using the fact that changes of state occur at a constant temperature. The heat added during change of state is not used to expand the substance so mercury in a thin glass tube will expand and contract between the temperature of melting ice and boiling water This provides fixed marks to relate other temperatures to. Fig 3.8 Calling the melting point of pure ice 0° , and the boiling point of pure water 100° gives us the Centigrade or Celsius scale divided into 100 increments. The Kelvin scale also has 100 increments between the freezing and boiling point of water, but zero on the Kelvin scale represents the minimum temperature at which molecular activity ceases, (absolute zero). This point is equivalent to -- 273°C. To convert temperatures between Kelvin and Celsius scales is relatively easy: K = °C + 273 °C = K - 273 The Fahrenheit scale has 180 increments between the freezing point and boiling point of water. The freezing point is at 32°F and the boiling point is 212°F. The Rankine scale has the same number of increments but, like the Kelvin scale, uses absolute zero as the zero point for the scale. This point corresponds to -460°F. Therefore, to convert between these two scales, the following formulas are used: °R = °F + 460 Page 73 of 114 °F = °R -- 460 To convert between Kelvin/Celsius to Rankine/Fahrenheit takes a little more calculation. Because there are 5 Kelvin units for every 9 Rankine degrees and both scales start at absolute zero, the formulae for converting them are: K = 5/9 °R ° R = 9/5 K There are 5 Celsius degrees to every 9 Fahrenheit degrees. To convert between these scales, the same fractional factors apply, but because 0°C = 32°F, the formulas are: ° F = 9/5 °C + 32 ° C = 5/9 (°F -- 32) (Jeppesen General p 2-21) LATENT and SENSIBLE HEAT A thermometer is constructed using the change of state of water. It was noted that the mercury does not expand or contract during the change of state. This is because the heat added once the change has begun, is used to overcome the bonding forces rather than change the temperature of the water. Once the water starts to boil, the heat that enters the water is used to convert the liquid into a gas and the temperature of the water remains constant until all the liquid has evaporated. No temperature change occurs during the change of state, even though heat is added. This heat that causes a substance to change its state with no change in temperature is known as 'latent heat'. The amount of heat required to boil, or vaporise, the liquid is called the latent heat of vaporisation (or evaporation). The amount of heat required to melt a solid is called the latent heat of fusion. Sensible heat is heat, when applied, causes a temperature change that can be detected. Latent heat is used to break down intermolecular bonds, and sensible heat is stored in intermolecular forces, increasing kinetic energy of the molecules. If heat is extracted from a substance then the changes of state will eventually occur the other way. The amount of heat extracted to condense a vapour is still called the latent heat of vaporisation (or evaporation). and, Page 74 of 114 The amount of heat extracted to solidify a liquid is still called the latent heat of fusion. Example Fig 3.9 540 calories of latent heat will cause one gram of water at 100°C to change to steam at 100°C. One gram of steam at 100°C condenses to liquid water at 100°C if it loses 540 calories of heat. 100 calories of heat changes one gram of water at 0°C to one gram of water at 100°C. (Sensible heat) Latent Heat and the Refrigeration Cycle. The compressed gas heats up as it is pressurized Fig 3.10 The coils on the back of the refrigerator let the hot ammonia gas dissipate its heat. The ammonia gas condenses into ammonia liquid (dark blue) at high pressure The high-pressure ammonia liquid flows through the expansion valve. The liquid ammonia immediately boils and vaporizes using its own latent heat (light blue), its temperature dropping to -27 F. This makes the inside of the refrigerator cold. The cold ammonia gas is sucked up by the compressor, and the cycle repeats AIR CONDITIONING (Cold Cycle) Page 75 of 114 Fig 3.11 AIR CONDITIONING (Reverse Cycle) HEAT PUMP INSIDE 25°C OUTSIDE 5°C Condenses to a liquid giving up heat to the room -10°C 5°C 40°C 25°C Hot gas Evaporates to cold gas using its own Latent Heat Extracts heat from the air A is the EVAPORATOR B is the COMPRESSOR or HEAT PUMP Fig 3.12 INSIDE 20°C OUTSIDE 35°C -20°C 10°C 60°C 40°C Hot gas Condenses to a liquid giving up heat to the air Evaporates to cold gas using its own Latent Heat Extracts heat from the room A is the EVAPORATOR B is the COMPRESSOR or HEAT PUMP Page 76 of 114 GAS LAWS It has been stated that gasses differ from solids and liquids by being compressible. This affects how they transmit forces that can use the thermal energy to effect change by doing useful work. The work done by an expanding gas in an engine is a prime example. Before looking at actual power plants, we must investigate the general behavior of a confined quantity of gas subjected to changes of pressure and temperature. Boyles Law A gas can be easily compressed. As it is compressed, its pressure increases and its volume decreases, assuming temperature remains constant. This is because the same number of molecules are bombarding a smaller area, as the volume of the container decreases. In reality, the compression raises the temperature, but if the container is cooled, then the ratio holds. If the volume is halved, the pressure doubles. This relationship acts in accordance with Boyle's Law which states that the volume of a confined body of gas varies inversely as pressure varies, assuming temperature remains constant. Fig 3.13 This can be expressed by the formula: V1 = P2 V2 P1 (temperature constant) This is called an Isothermal process. That is, a process taking place at constant temperature. CHARLES' LAW Just as changes in gas volume are related to pressure changes, they are also related to temperature changes. Page 77 of 114 This characteristic is explained by Charles' Law which states that the volume of a gas varies in direct proportion to its temperature, assuming pressure remains constant. V1 = T1 (pressure constant) V2 T2 In other words, heating a quantity of gas in a very flexible container will cause the container to increase in size. Doubling the temperature will approximately double the volume and vice versa. Fig 3.14 If a gas is confined in a solid container, so that the volume remains constant, Charles' Law becomes: P1 = T1 (volume constant) P2 T2 Welding gas bottles left out in the sun could over pressurise, hence the need for relief valves. BBQ gas suddenly released to a lower pressure feels very cold on your fingers. The temperature change could occur without the addition of external heat, or removal of heat by external means. A temperature change like this is called an adiabatic process. Another example is the increase in cylinder temperature when the fill rate is too high. Fig 3.15 GENERAL GAS LAW Page 78 of 114 In reality, if the container is at all flexible, then P, T, and V will change simultaneously. The general gas law is derived by combining Boyle's and Charles' laws. It is expressed by the equation: P1V1 = P2V2 Temps and Pressures must be absolute values to avoid T1 T2 negative values Jeppesen General p. 2-24 In a snow making machine, high pressure air expands at A, with pressure and volume reducing. This makes temperature drop below zero. When mixed with water B, the correct consistency of snow is created by the time it reaches F. Fig 3.16 Page 79 of 114 THERMAL ENERGY and LAWS OF THERMODYNAMICS The first law of thermodynamics is similar to the law of conservation of energy: Heat energy cannot be destroyed, it can only be changed from one form of energy to another. For example, the heat energy of combustion in an engine is transformed into mechanical energy, but there are losses or inefficiencies as some of the energy is transformed to sound energy. The second law of thermodynamics states that heat cannot flow from a body of a given temperature to a body of a higher temperature. That is, heat will only flow from a warmer body to a cooler body. This is a logical process and the theory behind it is used in car radiators, heat exchangers, oil coolers etc. We can now look at how we make heat work for us HEAT OF COMBUSTION Any time fuel is burnt (combustion), heat is produced. Sometimes the heat is useful and sometimes the heat is unwanted. We say that heat is a by-product of the combustion process. Combustion can range from lighting a match through to the furnace of a coal-fired power station. Combustion can use liquid, solid or gaseous fuel. The domestic fireplace is desirable combustion! When fuel is burnt in a combustion engine to produce power, the presence of heat is inevitable. Often heat is wasted and needs to be dissipated for the engine to work optimally. For example, most car engines have water circulating around the engine. The water is cooled by a radiator, allowing the engine temperature to remain within a specified range. If too much heat is allowed to build up, the engine can be damaged. In a gas turbine (jet) engine, the heat of combustion is necessary to expand gases and do work while flowing through the engine. It is the higher volume of gas which drives a turbine, making the engine self- sustaining and it is the gas which contributes to the reactive force of thrust. Nevertheless, it is also important for gas turbine engines for maximum operating temperatures to be observed. Materials used for construction of engine components cannot withstand temperatures above a certain range WORK DONE BY EXPANDING GASES Page 80 of 114 Sometimes heat is not an unwanted by-product of combustion. Sometimes the expansion of gas created by the heat is the prime purpose for the combustion. For example, when a gun fires a bullet, the heat produced by the ignition of a small pyrotechnic charge increases the volume of gas available to push the bullet out of the barrel. Heat is necessary for the process to occur. Likewise, a gas turbine engine relies on heat to expand gas. The expanded volume of gas drives the engine turbines and contributes to the reactive force of thrust. In this sense, expanding gases do work similar to other mechanical processes Remember, work is calculated by multiplying the force applied by distance: W = Fs. The greater the force applied to an object or the greater the distance an object moves, the more work has been done. If expanding gases in a rifle create a force of 10,000 newtons and move a bullet 0.5 metres along the barrel of the rifle: W = Fs = 10,000 x 0.5 = 5,000 joules of work has been expended. Fig 3.17 Remember, also, that power is the time rate of doing work. A man may expend 5,000 joules pushing a wheelbarrow for 1 hour. The rifle has expended the 5,000 joules in a split second. It has generated a great deal more power than the wheelbarrow man. IDEAL HEAT ENGINE GAS CYCLES During compression of a gas, the molecules of the gas are squeezed so that the empty space between them is reduced. The total molecular content may not change, but the space available for their motion is reduced. Therefore, the collisions between the molecules themselves and between molecules and the walls of the container are greatly increased. It is this increased kinetic activity which causes a temperature rise in a compressed gas. Fig 3.18 In both piston engines and gas turbine engines, the compression of air is necessary before fuel is introduced and ignited. Page 81 of 114 In both these types of engines there is a significant increase in temperature of the air medium due to this compression process. Piston Engine. (Otto Cycle) A typical piston engine turns reciprocating motion into rotary motion to drive a propeller in a four cycle operation as shown below. Fig 3.19 Crankshaft Intake Air and fuel are sucked into the cylinder through the intake valve. Compression This mixture (15:1) is adiabatically compressed into a smaller volume. (Charles Law) Power The compressed mixture is ignited with a spark plug and the piston is forced down by the sudden expansion of hot gas, which cools adiabatically. Exhaust. The exhaust gases are forced out of the exhaust valve by the ascending piston which then descends in the next intake stroke. I It is standard practice to have multiple cylinders connected to the same crankshaft to increase the number of power strokes per revolution. Page 82 of 114 Plotting how pressure varies with volume shows how the cycle develops its power. Fig 3.20 The work done by the engine is equal to the enclosed area of the graph, Power is work/time so more rpm = more power. Note that the combustion process occurs at approximately constant volume, (3 - 4 on the graph), so the Piston engine is called a Constant Volume engine. Page 83 of 114 Gas Turbine Engine (Brayton Cycle) A gas turbine is similar to a piston in that it compresses a mixture of air and fuel which is burnt to release its energy. However, the cycle differs from there. Fig 3.21 Intake Air only is drawn in directly, at the front. Compression This air is gradually squeezed into a smaller volume through a series of compressing fans. Power Fuel is added into a combustion chamber where, once ignited during the start procedure, it is continuously burnt with the compressed air. The expanding hot gas proceeds through another series of fans, (turbines) forcing them to rotate. The power part of the cycle. The turbines are connected back to the compressor causing it to keep rotating and continually supply air for combustion. This uses about 50% of the power generated leaving plenty to provide thrust. Exhaust The hot gasses leave the engine through a suitably shaped duct providing thrust because of the acceleration given to the mass of air originally taken in. Page 84 of 114 Once again, plot P against V: This time the combustion takes place at approximately constant pressure, (B -- C) Hence the name Constant Pressure cycle Fig 3.22 The gas turbine cycle can deliver its power in more than one way. Turbojet All thrust is delivered via the exhaust, as above picture. Turboprop Extra turbines transfer the power to a propeller. Fig 3.23 Page 85 of 114 Turbofan The extra turbines transfer the power to a multi-bladed and shrouded fan which accelerates the air mass similarly to a propeller. About 70% of the thrust is from the fan FAN SHROUD Fig 3.24 Turboshaft These are similar to turboprops and fan engine in that they utilizes extra turbines to deliver the power to a variety of applications, such as electrical generators, ship's propellers, and helicopter rotors. SHAFT Fig 3.25 Page 86 of 114