Anand Dhanwani Heat Transfer Chapter 1: Overview of Heat Transfer 1.1 What is Heat Transfer? Thermal energy is related to the temperature of matter. For a given material and mass, the higher the temperature, the greater its thermal energy. Heat transfer is a study of the exchange of thermal energy through a body or between bodies which occurs when there is a temperature difference. When two bodies are at different temperatures, thermal energy transfers from the one with higher temperature to the one with lower temperature. Heat always transfers from hot to cold. Table 1 shows the common SI and English units and conversion factors used for heat and heat transfer rates. Heat is typically given the symbol Q, and is expressed in joules (J) in SI units. The rate of heat transfer is measured in watts (W), equal to joules per second, and is denoted by q. The heat flux, or the rate of heat transfer per unit area, is measured in watts per area (W/m2), and uses q" for the symbol. Table 1. Units and Conversion Factors for Heat Measurements SI Units English Units Thermal Energy (Q) 1 J 9.4787×10-4 Btu Heat Transfer Rate (q) 1 J/s or 1 W 5.4123 Btu/h Heat Flux (q") 1 W/m2 0.3171 Btu/h ft2 1.2 Three Modes of Heat Transfer There are three modes of heat transfer: conduction, convection, and radiation. Any energy exchange between bodies occurs through one of these modes or a combination of them. Conduction is the transfer of heat through solids or stationery fluids. Convection uses the movement of fluids to transfer heat. Radiation does not require a medium for transferring heat; this mode uses the electromagnetic radiation emitted by an object for exchanging heat. 1.5.1 Conduction Conduction is at transfer through solids or stationery fluids. When you touch a hot object, the heat you feel is transferred through your skin by conduction. Two mechanisms explain how heat is transferred by conduction: lattice vibration and particle collision. Conduction through solids occurs by a combination of the two mechanisms; heat is conducted through stationery fluids primarily by molecular collisions. In solids, atoms are bound to each other by a series of bonds, analogous to springs as shown in Figure 1.1. When there is a temperature difference in the solid, the hot side of the solid experiences more vigorous atomic movements. The vibrations are transmitted through the springs to the cooler side of the solid. Eventually, they reach an equilibrium, where all the atoms are vibrating with the same energy. Solids, especially metals, have free electrons, which are not bound to any particular atom and can freely move about the solid. The electrons in the hot side of the solid move faster than those on the cooler side. This scenario is shown in Figure 1.5. As the electrons undergo a series of collisions, the faster electrons give off some of their energy to the slower electrons. Eventually, through a series of random collisions, an equilibrium is reached, where the electrons are moving at the same average velocity. Conduction through electron collision is more effective than through lattice vibration; this is why metals generally are better heat conductors than ceramic materials, which do not have many free electrons. Anchor Institute for Chemical and Petrochemicals, DDU, Nadiad Page 1 Anand Dhanwani Heat Transfer Figure 1.1 Conduction by lattice vibration Figure 1.2 Conduction by particle collision In fluids, conduction occurs through collisions between freely moving molecules. The mechanism is identical to the electron collisions in metals. The effectiveness by which heat is transferred through a material is measured by the thermal conductivity, k. A good conductor, such as copper, has a high conductivity; a poor conductor, or an insulator, has a low conductivity. Conductivity is measured in watts per meter per Kelvin (W/mK). The rate of heat transfer by conduction is given by: (Eq. 1.1) where A is the cross-sectional area through which the heat is conducting, T is the temperature difference between the two surfaces separated by a distance Δx (see Figure 1.3). In heat transfer, a positive q means that heat is flowing into the body, and a negative q represents heat leaving the body. The negative Figure 1.3 Heating curve of water sign in Eqn. 1.1 ensures that this convention is obeyed. 1.5.2 Convection Convection uses the motion of fluids to transfer heat. In a typical convective heat transfer, a hot surface heats the surrounding fluid, which is then carried away by fluid movement such as wind. The warm fluid is replaced by cooler fluid, which can draw more heat away from the surface. Since the heated fluid is constantly replaced by cooler fluid, the rate of heat transfer is enhanced. Natural convection (or free convection) refers to a case where the fluid movement is created by the warm fluid itself. The density of fluid decrease as it is heated; thus, hot fluids are lighter than cool fluids. Warm fluid surrounding a hot object rises, and is replaced by cooler fluid. The result is a circulation of air above the warm surface, as shown in Figure 1.4. Figure 1.4 Natural convection Anchor Institute for Chemical and Petrochemical, DDU, Nadiad Page 2 Anand Dhanwani Heat Transfer Forced convection uses external means of producing fluid movement. Forced convection is what makes a windy, winter day feel much colder than a calm day with same temperature. The heat loss from your body is increased due to the constant replenishment of cold air by the wind. Natural wind and fans are the two most common sources of forced convection. Convection coefficient, h, is the measure of how effectively a fluid transfers heat by convection. It is measured in W/m2K, and is determined by factors such as the fluid density, viscosity, and velocity. Wind blowing at 5 mph has a lower h than wind at the same temperature blowing at 30 mph. The rate of heat transfer from a surface by convection is given by: (Eq. 1.2) where A is the surface area of the object, T is the surface temperature, and T is the ambient temperature. surface ∞ 1.5.3 Radiation Radiative heat transfer does not require a medium to pass through; thus, it is the only form of heat transfer present in vacuum. It uses electromagnetic radiation (photons), which travels at the speed of light and is emitted by any matter with temperature above 0 degrees Kelvin (-273 °C). Radiative heat transfer occurs when the emitted radiation strikes another body and is absorbed. We all experience radiative heat transfer everyday; solar radiation, absorbed by our skin, is why we feel warmer in the sun than in the shade. The electromagnetic spectrum classifies radiation according to wavelengths of the radiation. Main types of radiation are (from short to long wavelengths): gamma rays, x-rays, ultraviolet (UV), visible light, infrared (IR), microwaves, and radio waves. Radiation with shorter wavelengths are more energetic and contains more heat. X-rays, having wavelengths ~10-9 m, are very energetic and can be harmful to humans, while visible light with wavelengths ~10-7 m contain less energy and therefore have little effect on life. A second characteristic which will become important later is that radiation with longer wavelengths generally can penetrate through thicker solids. Visible light, as we all know, is blocked by a wall. However, radio waves, having wavelengths on the order of meters, can readily pass through concrete walls. Any body with temperature above 0 Kelvin emits radiation. The type of radiation emitted is determined largely by the temperature of the body. Most "hot" objects, from a cooking standpoint, emit infrared radiation. Hotter objects, such as the sun at ~5800 K, emits more energetic radiation including visible and UV. The visible portion is evident from the bright glare of the sun; the UV radiation causes tans and burns. The amount of radiation emitted by an object is given by: (Eq. 1.3) where A is the surface area, T is the temperature of the body, σ is a constant called Stefan-Boltzmann constant, equal to 3.67×10-8 W/m2K4, and ε is a material property called emissivity. The emissivity has a value between zero and 1, and is a measure of how efficiently a surface emits radiation. It is the ratio of the radiation emitted by a surface to the radiation emitted by a perfect emitter at the same temperature. The emitted radiation strikes a second surface, where it is reflected, absorbed, or transmitted (Figure 1.5). The portion that contributes to the heating of the surface is the absorbed radiation. The percentage of the incident radiation that is absorbed is called the absorptivity, α. The amount of heat absorbed by the surface is given by: (Eq. 1.4) where I is the incident radiation. The incident radiation is determined by the Figure 1.5 Interaction between a amount of radiation emitted by the object and how much of the emitted surface and incident radiation radiation actually strikes the surface. The latter is given by the shape factor, Anchor Institute for Chemical and Petrochemical, DDU, Nadiad Page 3 Anand Dhanwani Heat Transfer F, which is the percentage of the emitted radiation reaching the surface. The net amount of radiation absorbed by the surface is: (Eq. 1.5) For an object in an enclosure, the radiative exchange between the object and the wall is greatly simplified: (Eq. 1.6) This simplification can be made because all of the radiation emitted by the object strikes the wall (F ) object→wall Anchor Institute for Chemical and Petrochemical, DDU, Nadiad Page 4 Anand Dhanwani Heat Transfer Chapter 2: Steady-State Conduction 2.1 Steady State and Transient State If you heat a pan on a stove, it takes a while for the pan to heat up to cooking temperature, after which the temperature of the pan remains relatively constant. The latter state is called the steady state, where there is no temporal change in temperatures. When the system is still changing with time, it is in transient state. The rate of conduction through an object at steady-state is given by: (Eq. 5.1) where k is the conductivity of the material, A is the cross-sectional area through which the heat is conducting, and ΔT is the temperature difference between two surfaces separated by a distance Δx. 2.2 One-Dimensional Conduction One-dimensional heat transfer refers to special cases where there is only one spatial variable – the temperature varies in one direction only. A model used often to calculate the heat transfer through a 1-D system is called the thermal circuit model. This model simplifies the analysis of heat conduction through composite materials. In this model, each layer is replaced by an equivalent resistor called the thermal resistance. An analysis much like a circuit analysis follows. For conduction, the thermal resistance is expressed as: (Eq. 5.2) where L is the thickness of the layer, k is the thermal conductivity of the layer, and A is the cross-sectional area. When there is more than one layer in the composite, the total resistance of the circuit must be calculated. The total resistance for layers in series is simply the sum of the resistances: (Eq. 5.3) For resistors in parallel, the total resistance is given by: (Eq. 5.4) The convection at the surface must also be expressed as a resistor: (Eq. 5.5) Once the total resistance of a structure is found, the heat flow th rough the layers can be found by: (Eq. 5.6) where T and T refers to the temperatures at the two ends of the thermal circuit (analogous to voltage initial final difference in an electrical circuit) and q is the heat flow through the circuit (current). Example Problem Consider a composite structure shown on below. Conductivities of the layer are: k = k = 10 W/mK, k = 16 1 3 2 W/mK, and k = 46 W/mK. The convection coefficient on the right side of the composite is 30 W/m2K. 4 Calculate the total resistance and the heat flow through the composite. Anchor Institute for Chemical and Petrochemical, DDU, Nadiad Page 5 Anand Dhanwani Heat Transfer First, draw the thermal circuit for the composite. The circuit must span between the two known temperatures; that is, T and T . 1 ∞ Next, the thermal resistances corresponding to each layer are calculated: Similarly, R = 0.09, R = 0.15, and R = 0.36 2 3 4 To find the total resistance, an equivalent resistance for layers 1, 2, and 3 is found first. These three layers are combined in series: The equivalent resistor R is in parallel with R : 1,2,3 4 Anchor Institute for Chemical and Petrochemical, DDU, Nadiad Page 6 Anand Dhanwani Heat Transfer Finally, R is in series with R The total resistance of the circuit is: 1,2,3,4 3. ← total R = R + R = 0.46 thermal total 1,2,3,4 5 resistance The heat transfer through the composite is: ← heat flow through the = 175.9 W. composite Anchor Institute for Chemical and Petrochemical, DDU, Nadiad Page 7 Anand Dhanwani Heat Transfer Chapter 3: Convection 3.1 Overview of Convection Heat transfer using movement of fluids is called convection. In natural convection, the flow is induced by the differences between fluid densities which result due to temperature changes. Forced convection uses externally induced flow, such as wind. The heat transfer rate for convection is given by the following equation: (Eq. 3.1) where h is the convection coefficient, A is the surface area, and T and T are the surface and ambient surface ∞ temperatures, respectively. The convection coefficient is a measure of how effective a fluid is at carrying heat to and away from the surface. It is dependent on factors such as the fluid density, velocity, and viscosity. Generally, fluids with higher velocity and/or higher density have greater h. 3.2 Natural Convection Density of fluid changes with temperature. In general, fluids expand as the temperature rises, and thus the density decreases (density is the mass per unit volume). Warm fluids therefore are more buoyant than cooler fluids. A hot object will heat the surrounding fluid, which rises due to the buoyancy force. The warm fluid is then replaced by cool (unheated) fluids. Similarly, cool objects will draw heat away from the surrounding fluid, which then fall due to the increased density. The cool fluid is then replaced by the warm fluid, initiating convective currents. For a hot horizontal plate surrounded by air, convection currents form when the air above the plate start to rise, as shown in Figure 3.1. The air below the plate, however, cannot rise because the plate is blocking the flow. The heated fluid under Figure 3.1 Natural convection the plate will eventually escape through the sides of the plate; however, the around a horizontal hot plate convective flow below the plate is very small compared to the flow on top. In general, natural convection is more pronounced (has a higher h) on the topside of a hot plate or the bottom side of a cold plate. The convection coefficient for natural convection in gas is generally between 1 W/m2K and 20 W/m2K; typical values for liquids fall between 100 W/m2K and 1000 W/m2K. 3.3 Forced Convection Fluid flow caused by a fan or any other external forces create forced convection. Forced convection is generally more efficient than natural convection due to the faster velocity of the currents. In forced convection, buoyancy has little effect on the direction of flow. The relation between flow velocity, direction, and temperature is illustrated in Figure 3.2 for a hot, horizontal surface under forced convection. Since the buoyancy does not affect the flow, the bottom side of the plate will have the same patterns. Close to the surface, the flow velocity is inevitably slowed down due to friction. Right at the surface, the velocity is actually zero. This region of retarded flow is called the boundary layer. The region of warm airflow is generally well within the velocity boundary layer, and is called the thermal boundary layer. Figure 3.2 Forced convection currents The convection coefficient for forced convection in gasses generally range between 50 W/m2K and 250 W/m2K. For liquids, values start around 100 W/m2K, and can be as high as 10,000 W/m2K. Anchor Institute for Chemical and Petrochemical, DDU, Nadiad Page 8 Anand Dhanwani Heat Transfer Chapter 4:Evaporation Evaporation is a special case of heat transfer to a boiling liquid. This particular heat transfer application is so common and important that it is treated as a separate unit operation. The intent is to concentrate a non-volatile solute from a solvent, usually water. This is done by boiling off the solvent. Concentration by evaporation is normally stopped before the solute begins to precipitate; if not, the operation is better considered as crystallization. Evaporation is usually treated as the separation of a liquid mixture into a liquid product (concentrate or thick liquor) and a vapor byproduct, although in special cases such as water treating and desalination, the vapor is the product instead of the thick liquor. In this course, we will limit evaporation to systems with non-volatile solutes. Evaporation is similar to drying in that both drive off volatiles, but is different in that the product is a liquid. Evaporation differs from distillation because both components in a distillation system are volatile. Evaporation normally produces a single vapor fraction, distillation several. An evaporator consists of a heat exchanger for boiling the solution and a means to separate the vapor from the boiling liquid. Different types are categorized by the length and alignment (horizontal or vertical) of the evaporator tubes. The evaporation tubes may be located inside or outside of the main vessel where the vapor is driven off. Because many materials cannot tolerate high temperatures, evaporators often operate at reduced pressure so that the boiling point will also be reduced. In many (most?) cases, evaporators operate under a vacuum. This means that a vacuum pump or jet ejector vacuum system is required on the last effect. Evaporators are commonly used in the inorganic and organic chemical, pulp and paper, and food industries (especially sugar). Examples are the concentration of fruit juices and of NaOH. Performance Measures: There are three main measures of evaporator performance: 1. Capacity (kg vaporized / time) 2. Economy (kg vaporized / kg steam input) 3. Steam Consumption (kg / hr) Note that the measures are related, since Consumption = Capacity/Economy. Economy calculations are determined using enthalpy balances. The key factor in determining the economy of an evaporator is the number of effects. The economy of a single effect evaporator is always less than 1.0. Multiple effect evaporators have higher economy but lower capacity than single effect. Anchor Institute for Chemical and Petrochemical, DDU, Nadiad Page 9 Anand Dhanwani Heat Transfer The thermal condition of the evaporator feed has an important impact on economy and performance. If the feed is not already at its boiling point, heat effects must be considered. If the feed is cold (below boiling) some of the heat going into the evaporator must be used to raise the feed to boiling before evaporation can begin; this reduces the capacity. If the feed is above the boiling point, some flash evaporation occurs on entry. Multiple Effect Evaporators Evaporators are classified by the number of effects. In a single-effect evaporator, steam provides energy for vaporization and the vapor product is condensed and removed from the system. In a double-effect evaporator, the vapor product off the first effect is used to provide energy for a second vaporization unit. Triple- effect evaporator problems are familiar to generations of engineering students. This cascading of effects can continue for many stages. Multiple-effect evaporators can remove much larger amounts of solvent than is possible in a single effect. In a multiple effect arrangement, the latent heat of the vapor product off of an effect is used to heat the following effect. Effects are thus numbered beginning with the one heated by steam. It will have the highest pressure. Vapor from Effect I will be used to heat Effect II, which consequently will operate at lower pressure. This continues through the train: pressure drops through the sequence so that the hot vapor will travel from one effect to the next. Normally, all effects in an evaporator will be physically the same in terms of size, construction, and heat transfer area. Unless thermal losses are significant, they will all have the same capacity as well. Evaporator trains may receive their feed in several different ways. The feed order is NOT related to the numbering of effects. Effects are always numbered according to decreasing pressure (steam flow). Forward Feed arrangements follow the pattern I, II, III. These require a single feed pump (reduced fixed costs). They typically have reduced economy (higher operating costs) since the cold feed must be raised to the highest operating temperature. These also tend to have the most concentrated liquour, which tends to be the most viscous, in the lowest temperature effects, so their may be difficulties getting a good overall heat transfer coefficient. Anchor Institute for Chemical and Petrochemical, DDU, Nadiad Page 10