Thermodynamics is concerned with the amount of heat transfer as a system undergoes a process from one equilibrium state to another.

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1 ecture 1, 2, 3, 4, 5: Heat transfer: Introduction to Heat Transfer Heat transfer is that science which predicts the rate of energy transfer taking place between material bodies as a result of temperature difference between them. According to thermodynamics, this energy transfer is defined as heat. Heat: The form of energy that can be transferred from one system to another as a result of temperature difference. Thermodynamics is concerned with the amount of heat transfer as a system undergoes a process from one equilibrium state to another. The science of heat transfer not only explains how heat energy may be transferred but also predict the rate at which the exchange will take place under certain specified conditions. There is a difference between thermodynamics and heat transfer and it is the heat transfer rate which forms the basis for difference. Importance of Heat Transfer Study: (1) Energy Production and conversion (2) Refrigeration and air conditioning (3) Electric Machines (4) Civil Engineering (5) Manufacturing Process (6) Chemical and Petrochemical operation (7) Environmental Engineering (8) Earth Science Modes of Heat Transfer: (1) Conduction (2) Convection (3) Radiation Conduction: (Solid) Heat conduction is a mechanism of heat transfer from a region of high temperature to a region of low temperature within a medium or between different mediums in direct physical contact.

2 Convection: (iquid, Gas) It is the transfer of heat within a fluid by mixing or circulation of one portion of fluid with another Radiation: (Solid, iquid, Gas) Radiation is a process by which heat flows from a high temperature body to a body at lower temperature in the form of electromagnetic waves when the bodies are separated in space even when a vacuum exists between them. Mechanism of modes of heat transfer with example Heat transfer equipment such as heat exchangers, boilers, condensers, radiators, heaters, furnaces, refrigerators, and solar collectors are designed primarily on the basis of heat transfer analysis. The heat transfer problems encountered in practice can be considered in two groups: (1) rating and (2) sizing problems.

3 The rating problems deal with the determination of the heat transfer rate for an existing system at a specified temperature difference. The sizing problems deal with the determination of the size of a system in order to transfer heat at a specified rate for a specified temperature difference. An engineering device or process can be studied either experimentally (testing and taking measurements) or analytically (by analysis or calculations). The experimental approach has the advantage that we deal with the actual physical system, and the desired quantity is determined by measurement, within the limits of experimental error. However, this approach is expensive, time consuming, and often impractical. Conduction is the transfer of heat through solids or stationary fluids. Fourier s law of heat conduction Convection uses the movement of fluids to transfer heat. Newton s law of cooling Radiation require a medium for transferring heat; this mode uses the electromagnetic radiation emitted by an exchanging heat. Stefan Boltzmann law ecture 6, 7: Heat Transfer by Convection Convection: The heat exchange between a solid surface and a fluid in contact with it is known as convection Types of Convection (1) Free/Natural Convection (2) Force Convection

4 Free or Natural Convection: It may be caused by density difference produced by temperature gradient. Heat Exchange in such a situation is known as free or natural convection. e.x. Heat flow from a hot place to atmosphere Heating of room by a stove Force convection: It may be caused by some external agency such as a pump or blower or atmospheric winds. This type of heat transfer is known as forced convection e.x. Heat exchanger in condenser Air Conditioning equipment The rate of heat transfer by convection between a solid boundary and a fluid is given by Newton s law of cooing q = h AS (ts- t ) Boundary ayer: (1) Hydrodynamic boundary ayer (2) Thermal Boundary ayer Nusselt Number: Nu = h /k Nusselt number may be interpreted as the ratio of temperature gradient at the surface to an overall or reference temperature gradient. The Nusselt number is a convective measure of the convective heat transfer coefficient. ecture 8, 9: Determination of Nusselt number: (1) Dimensional analysis (2) Solution of boundary ayer equation (3) Analogy Between heat and momentum transfer Dimensional Analysis: It deals with the process whereby all the important variable involved in a physical phenomenon are systematically organized into dimensionless groups which are less numerous than the original variables.

5 Application: (1) To check whether an equation of any physical phenomenon is dimensionally homogeneous or not. (2) To determine the dimension of a physical quantity (3) To Convert the units from one system to another (4) Use to plan experiments and to present the results meaningfully Raleigh s method: (1) Gather all the independent variable (2) Write the functional relationship (3) Express each of the quantities in some fundamental units (4) Utilize the principle of dimensional homogeneity to obtain a set of simultaneous equation involving exponent a, b, c (5) Solve the equation to get a, b, c (6) Substitute the values of exponent in the main equation and form the non dimensional parameter Buckingham s PI Theorem: If there are n variables in a dimensionally homogeneous equation and if these variables contain on primary dimensions then the variables can be grouped into (n-m) nondimensional parameters. Advantages and imitations of dimensional analysis: Advantages (1) It is a useful tool in the analysis and correlation of experimental data (2) The presentation of data in non-dimensional groups allows the application of empirical correlations to a wide range of physical condition. imitations: (1) Information from previous experiments is necessary (2) No information is given about the internal mechanism of the physical phenomenon. ecture 10, 11, 12: Significance of Dimensionless groups: (1) Reynolds Number (2) Grashof Number (3) Prandtl Number (4) Nusselt Number (5) Stanton Number

6 Free convection: Empirical Correlation for free convection: Bulk Temperature: it is then taken to be the arithmetic mean of the temperature at inlet and outlet from the heat exchanger tube. Mean Film Temperature: It is the arithmetic mean of the surface temperature of a solid and the undisturbed temperature of the fluid which flows past it. Correlations for Free Convection Horizontal Plates, Cylinders and wires (1) Plates : Heated surface up or cooled surface down aminar flow: 2*10 5 < Gr Pr< 2* 10 7 Nu = 0.54 (Gr Pr) 0.25 Turbulant flow: 2*10 7 < Gr Pr< 3* Nu = 0.14 (Gr Pr) 0.33 (2) Plates : Heated surface down or cooled surface up aminar flow: 3*10 5 < Gr Pr< 7* 10 8 Nu = 0.27 (Gr Pr) 0.25 Turbulant flow: 7*10 8 < Gr Pr< 11* Nu = (Gr Pr) 0.33 (3) ong Cylinder (/D > 60) aminar flow: 10 4 < Gr Pr< 10 9 Nu = 0.53 (Gr Pr) 0.25 Turbulant flow: 10 9 < Gr Pr< Nu = 0.13 (Gr Pr) 0.33 Vertical plates & arge cylinder (i) McAdams equation aminar flow: 10 4 < Gr Pr< 10 9 Nu = 0.59 (Gr Pr) 0.25 Turbulant flow: 10 9 < Gr Pr< 3* Nu = 0.13 (Gr Pr) 1/8

7 (ii) Eckert & Jackson Equation ecture 13, 14, 15: Force convection: Dimensional analysis applied to forced convection Correlations for forced convection in laminar flow and turbulent flow: The problem is that the equations to find Nu are very problem-specific. Generally, however, you can identify 2 distinguishing characteristics in your problem to find the exact equation you need: 1. Turbulent or aminar: For forced convection problems Re determines whether or not the flow is turbulent or laminar. For flow past flat plates, the transition region from laminar to turbulent is about 10 5 <Re<10 7. Go ahead and assume turbulence if Re is much higher than For convection problems with cylinders and spheres, (the length-scale) takes on slightly different meanings (and there isn t really an analog for the local dimensionless numbers). Nu is also called NuD in these situations sometimes. Also, with cylinders and spheres it may not be as cut and dry as saying laminar or turbulent. Certain equations have been developed to be accurate over a specific (and sometimes relatively small) range. For natural convection problems, the product Gr Pr is used to specify the flow regime. The laminar natural convection equations we re given hold from 10 4 <Gr Pr<10 9. The turbulent natural convection equations are valid from 10 9 <Gr Pr< High or ow Prandtl number: After examining whether we have a laminar or turbulent system, check the Prandtl number. There are typically different equations for different ranges of Prandtl numbers. Unless otherwise specified, a high Pr is one > 0.5 and a low Pr is < Flat Plate, Forced Convection aminar, ow Pr aminar, High Pr Turbulent, High Pr Nu = (1/ π ) Re Pr Nu = Re Pr Nu 0.8 = Re Pr Nu x = (2 / x π ) Re 0.5 Pr 0.5 Nu x = Re x 0.5 Pr Nu x = Re Flat Plate (Vertical), Natural Convection (also, can use Fig. 8.8 for 0.5<Pr<10) 10 4 <Gr Pr< <Gr Pr< <Pr<1000 works for most Pr but if 0.6<Pr<10 use but if 0.6<Pr<10 use 0.5 Nu Pr 2 / 5 7 / / 5 ( 2 / Nu = 0.246Gr Pr Pr ) = Gr + Pr ( ) x 0.8 Pr 1/ 3 1/ 3

8 Cylinder Oriented Normal to Flow Forced Convection (=length of cylinder) 1<Re<100, High Pr 100<Re<10 7, Re Pr>0.2 Horizontal Cylinder, Natural Convection (=πd/2) (also, can use Fig. 8.8 for 0.5<Pr<10) (Use Vertical Flat Plate Equations with =πd/2) for 10-5 <Gr Pr<10 12 ecture 16, 17: Hydrodynamic and thermal boundary layer over flat plate In physics and fluid mechanics, a boundary layer is the layer of fluid in the immediate vicinity of a bounding surface where the effects of viscosity are significant. Momentum equation for hydrodynamic boundary layer over flat plate 2 Vx Vx Vx Vx + Vy = ν x y 2 y Skin friction coefficient Cf is defined as the ratio of the shear stress at the plate to the dynamic head ocal skin friction coefficient c x = Re Average drag coefficient c f = Re Energy equation for thermal boundary layer over a flat plate Thickness of thermal boundary layer Case 1: Pr = 1 l x

9 y V γ x = β = δt V γx = 5 δ t /x = ρ/x Case 2: Pr<1 δ t /x >ρ/x Case 3: Pr>1 δ t /x < ρ/x ocal and average heat transfer coefficients in forced convection Staton number St 1 V h x = 0.332k Pr 3 ν x h = k Pr 1 3 Re Staton number Stx = Nux/RexPrx) StxPr 1/3 = (Cf)x/2 = jx Analogy between heat and momentum transfer- Reynolds Analogy: Reynolds established a relationship between friction force and heat transfer. This relation is called Reynold analogy. Statement of Reynolds analogy: Reynolds developed a relation between heat transfer and fluid friction applicable to fluids with Pr = 1. His analogy may be any of the following equations = Cf/2; Pr = 1 (q/a)/τ = -Cpdt/dvx; Pr = 1 ecture 18: Radiation:

10 All solid bodies as well as liquids and gases have a tenancy of radiating thermal energy in the form of electromagnetic waves and of absorbing similar energy emerging from the neighboring bodies. This type of heat transport is known as thermal radiation. For radiation no material medium is required. Nature of radiation: Two theories have been proposed to explain the phenomenon of radiation (1) Wave theory (2) Quantum theory The energy E = hγ Where h = Plank s constant γ = the frequency of the emitted quantum The higher the frequency, the larger the energy of quantum. Also the higher the temperature of emitter, the large the frequency of the quantum. Spectrum of electromagnetic radiation: Types of radiation Wavelength Y rays 10-4 to 1 X rays 0.1 to 600 Ultraviolet 200 to 5000 Visible 3500 to 8000 Infrared 8x10 3 to 5x10 6 Radio Waves 10 6 to 10 4 Adsorption, Transmission, reflection and emission of radiation: Absorption, Transmission, reflection and emission of radiation: The fraction of the incident radiation absorbed is called the absorptivity, α The fraction of the incident radiation reflected is called the reflectivity, ρ The fraction of radiation transmitted is called the transmissivity, τ Monochromatic absorptivity αλ = (Gα)λ/G λ α = = Gα/G = λg λd λ Monochromatic reflectivity ρλ ρ = λg λd λ Monochromatic transmissivity, τλ τ λg λd λ

11 A transparent body is one which transmits part of the radiation falling on its surface. Opaque body does not transmit any radiation at all. A body which neither reflects nor transmits any part of incident radiation but absorbs all of it is called a black body. White body is one which reflects all the incident radiation and does not absorb or transmit any part of it. If the absorptivity of a surface does not vary with temperature and wavelength of the incident radiation, it is termed gray body. If the absorptivity of a surface varies with the wavelength of radiation waves it is termed coloured body. ecture 19, 20 The energy emitted by a surface in all directions at a given wavelength is called the monochromatic emissive power of the surface Eλ. The monochromatic emissive power of a black body is denoted by (Eλ)b Wein purposed the formula for the monochromatic emissive power of black body (Eλ)b = ) Rayleigh Jeans for monochromatic emissive power (Eλ)b = 2πckT -4 Max plank equation 2 λ Eλ b = 2Πc h ch exp λkt ( ) 5 1 C= velocity of light, 2.998*10 10 cm/sec H = Plank s quantum constant, *10-34 joule-sec K = Boltzmann constant, *10-23 Joule-sec = wavelength, cm T = absolute temperature, K Plank s relation reduces to Wien s formula at small values of and to Rayleigh Jeans formula at large value of. Total emissive power E of a surface is defined as the total radiant energy emitted by the surface in all direction over the entire wavelength range per unit surface area per unit time.

12 Unit of E = cal/sec-cm 2 or J/m 2 Stefan Boltzmann law for total emissive power of black body Eb = σt 4 Σ Stefan Boltzmann constant = 56.7*10-9 W/m 2 K 4 Emissivity ϵ of a surface is defined as the ratio of the emissive power of the surface to the emissive power of the black body at the same temperature. The emissivity of substance may depend on T and wavelength Types of emissivity: (1) Monochromatic emissivity (2) Total emissivity (3) Normal total emissivity Monochromatic emissivity is the ratio of the monochromatic emissive power of a surface to the monochromatic emissive power of a black body at the same wavelength and T. Total emissivity is the ratio of the total emissive power of a surface to the total emissive power of a black body at the same temperature. Normal total emissivity is the ratio of the normal component of the total emissive power of a surface to the normal component of the total emissive power of a black body at the same temperature. Kirchhoff s law: Kirchoff s law states that at any temperature the ratio of the total emissive power E to the absorptivity α is a constant for all substances which are in thermal equilibrium with their environment. Kirchhof s law is also valid for monochromatic radiation. ecture 21, 22: Wein displacement law states that λmax T = constant Radiation shield: Radiation shields are used to reduce radiant heat transfer between two surfaces.

13 e.g. bulb of thermometer or a thermocouple junction Radiation transfer between surfaces, Radiation through semitransparent materials ecture 23, 24, 25: Heat Transfer with change of phase: The most important processes which are associated with change of phase Boiling Condensation Melting or Solidification Sublimation Nu and Pr are familiar for single phase convection, here some new dimensionless parameters are Jakob number Ja and Bond number Bo are used. Jakob number Ja = CpΔt/λ is the ratio of the maximum sensible energy absorbed to the latent heat. Bond number Bo = g(ρl - ρv) 2 / σ, is the ratio of the gravitational body force to the surface tension force Evaporation occurs at the liquid vapor interface when the vapor pressure is less than the saturation pressure of the liquid at a given temperature. Boiling occurs at the solid liquid interface when a liquid is brought into contact with a surface maintained at a temperature sufficiently above the saturation temperature of the liquid.

14 Phenomena of Boiling: The boiling heat transfer process may occur in the following forms or different regimes of boiling are as follows: (A) According to applied forces: (I) Pool boiling (II) Forced Convection boiling (B) According to Temperature: (I) Sub cooled or local boiling (II) Saturated or boiling with net evaporation The first two forms of boiling depends upon the presence of bulk fluid motion while the last two forms depends on the bulk liquid temperature. Regimes of pool boiling: The phenomena of pool boiling is characterized by different regimes Nukiyama, in 1934 actually distinguished the existence of various regimes of boiling. Brew and Miller extended the theory further in Consider the case of pool boiling of water, over a heated flat plate or hot wire submerged in a pool or water, at tsat. After getting the data, the heat flux (q/a) is plotted against the excess temperature Δte = (tw tsat).

15 The boiling phenomena is divided in three types of boiling which takes place in six regimes as shown in the table Sr. No. Type of Boiling Regime Type of Regime No. 1 Interface Evaporation 1 Free convection boiling 2 Nucleate boiling 2 Bubbles form but condense as they rise. 3 3 Bubbles rise to interface causing rapid evaporation 4 Film Boiling 4 Partial nucleate boiling with unstable film 5 5 Stable film boiling 6 6 Radiation Predominant Regimes of Pool Boiling Critical heat flux point/ Burnout point/boiling crisis point eiden frost point: Point D on the boiling curve, where the heat flux becomes minimum due to the film resistance, is called eiden frost point. Here heat is a minimum qd = qmin and the surface is completely covered by a vapour blanket. Heat Transfer from the urface to the liquid occurs by conduction through the stable vapour film. Nucleate boiling The nucleate boiling is of maximum engineering importance. It involves two processes. (a) The nucleation or formation of bubbles (b) The subsequent growth and motion of these bubbles Factors affecting nucleate boiling: The nucleate boiling is affected by the following factors:

16 1. Material, Shape and condition of heating surface. 2. iquid properties 3. Pressure 4. Mechanical agitation (a) Nucleation - Three typical shapes of vapor bubbles may be observed as shown in the figure below (I) Unwetted Surface (II) Partially wetted surface (III) Totally wetted surface Bubble growth and collapse Bubble Growth and Motion: Phenomena of Condensation The condensation of vapor is the reverse phenomenon of the evaporation of liquid. Heat energy is released during the former while it is absorbed during the later process. When a saturated vapor is borough in contact with a surface at a lower temperature, heat is received by the surface from the vapor and condensation occurs. The heat exchange is equivalent to the latent heat. There are two distinct ways by which condensation may appear to be occurring: (a) Film wise condensation (b) Drop wise condensation ecture 26, 27: Evaporator: Introduction, Types of Evaporator Evaporation is the removal of solvent as vapor from a solution, slurry or suspension of solid in a liquid. The aim is to concentrate a non-volatile solute, such as organic compounds, inorganic salts, acids or bases from a solvent. Evaporation differs from the other mass transfer operations such as distillation and drying. In distillation, the components of a solution are separated depending upon their distribution between vapor and liquid phases based on the difference of relative volatility of the substances. Removal of moisture from a substance in presence of a hot gas stream to carry away the moisture leaving a solid residue as the product is generally called drying. Evaporation is normally stopped before the solute starts to precipitate in the operation of an evaporator. Classification of Evaporators: Accordingly, most evaporators are broadly classified as: (1) natural circulation, and (2) forced circulation. Evaporation can be divided into three categories on the basis of boiling phenomena.

17 i) Pool boiling: In this phenomena bulk or pool of liquid boils. Examples are kettle boiling, natural circulation boiling units, thermo siphon reboilers in distillation. ii) Convection heating and boiling: Example is forced circulation-boiling units. iii) Film evaporation: In film evaporation, a thin liquid film is maintained on the heating surface. Evaporators can be classified as: Short-Tube Vertical Falling Film Evaporators Agitated Thin Film Evaporators Evaporator Basket-type Vertical Rising or Climbing Film Casketed Plate Evaporator Evaporators Evaporators ong-tube Vertical Forced Circulation Evaporators Evaporators There is wide variation in characteristics of liquor to be concentrated that requires judgment and experience in designing and operating evaporators. Some of the properties of evaporating liquids that influence the process of evaporation are: (1) Concentration (2) Foaming (3) Scale (4) Temperature sensitivity (5) Materials of construction The simplest method of evaporation is to feed the solution to the evaporator which is provided with sufficient heat transfer area. The vapour generated is condensed using a 'surface condenser' or a 'direct contact condenser'. The concentrated product is drawn from the bottom. This is called a single-effect evaporator. Although simple in operation, a single-effect evaporator does not utilize steam efficiently. Some amount of heat loss from the evaporator to the ambient always occurs. Now let us consider an arrangement in which two evaporators are put in series such that the vapour generated in one is fed to the steam chest of the second for heating. Partly concentrated solution flows from the first to the second where it attains the desired final concentration. The vapour generated in the second evaporator is sent to a condenser. The arrangement is called the double-effect evaporator. One important point is to be noted in this connection. The vapour leaving evaporator-1 is at the boiling temperature of the liquid leaving the first effect. In order that transfer of heat occurs from the condensing vapour (from evaporator-1) to the boiling liquid in evaporator-2 (i.e. the second effect), the liquid in evaporator-2 must boil at a temperature considerably less than the condensation temperature of the vapour in order to ensure reasonable driving force for the transfer of heat. A method of achieving this is to maintain a suitable lower pressure in the second effect (evaporator-2) so that the liquid boils in it at a lower temperature. If the first evaporator operates at atmospheric pressure, the second one must do so under vacuum.

18 ecture 28: Methods of feeding of evaporator Evaporators are classified by the number of effects. In case of a single-effect evaporator, the vapor from the boiling liquor is condensed and the concentrated product is withdrawn from the bottom of the evaporator. Although the operation is simple, the device does not use steam efficiently. Typically 1.1 to 1.3 kg of steam is required to evaporate 1 kg of water. The steam consumption per unit mass of water evaporated can be increased by putting more than one evaporator in series such that the vapor from one evaporator is used in the second evaporator for heating. The vapor from the second evaporator is condensed and the arrangement is called doubleeffect evaporators. The heat from the vapor generated in the first evaporator is used in the second evaporator. Evaporation of water is nearly doubled in double effect evaporation system compared to single effect per unit mass of steam used. Additional effects can be added in series in the same way to get a triple-effect evaporator, quadruple-effect evaporator and so on. There are several configurations based on feeding arrangement. Multiple Effect Evaporators: A multiple-effect evaporator has been shown in Fig., and its operating principles have been briefly described. The type of the multiple-effect evaporator shown in Fig. is called the backward feed because the steam and the liquor flow in opposite directions. There are other types of feeding arrangements too. Evaporators up to fifteen effects are known to be in use. Multiple-effect evaporators allow high steam economy. Multiple effect evaporators are classified as: i) Forward feed arrangement. ii) Backward feed arrangement. iii) Parallel feed arrangement. iv) Mixed feed arrangement. Comparison between the Forward and Backward Feed Modes Advantages and limitations of different modes of feed supply to multiple-effect Evaporators Criteria for Selection of Evaporator: The selection of evaporator is done on the basis of: 1. Factor related to process 2. Factor related to mechanical design

19 ecture 29, 30: Performance of evaporator (Capacity and Economy), Thermal and Process Design consideration Performance of tubular evaporators: The performance of a steam heated tubular evaporator is evaluated in terms of (i) capacity and (ii) economy Capacity: Capacity of an evaporator is defined as the number of kilogram of water vaporized or evaporated per hour. Evaporator economy: Economy of an evaporator is defined as the number of kilogram of water evaporated per kilogram of steam fed to the evaporator. It is also called as steam economy. In single-effect evaporator the amount of water evaporated per kg of steam fed is always less than one and hence economy is less than one. The fact that the latent heat of evaporation of water decreases as the pressure increases tends to make the ratio of water vapour produced per kg of steam condensed less than unity, Increase in economy of an evaporator is achieved by reusing the vapour produced. The methods of increasing the economy are: (1) use of multiple effect evaporation system (2) vapour recompression, Boiling point elevation Material and enthalpy balances for single-effect evaporator Overall material balance

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