SKPN 3133 Transport Processes (Nuclear Heat Transport) Heat Transfer Mohsin Mohd Sies Nuclear Engineering, Universiti Teknologi Malaysia Outline Introduction to Heat Transfer Heat Transfer and Fluid Flow (Nonmetallic coolants) Convective Heat Transfer Boiling Heat Transfer Boiling Regimes Boiling Crisis Two Phase Flow

Thermal Design of Reactor 2 Cooling of Reactors The most suitable coolant depends on the reactor type Fast reactors cannot use coolants that are good moderators (containing hydrogen, carbon light/heavy water, organic fluids) CANDU reactors (natural uranium) cannot use light water (high neutron absorption cross section) Compromise between conflicting

requirements Coolant selection Economic Low initial cost Availability (He, heavy water, liquid metals are less available than light water and other gases) Low pumping losses (highest for gases) High heat transfer coefficient Coolant selection Physical Low melting points (so it stays fluidized during shutdown)

Low vapor pressures (high boiling point to avoid high pressurization) Compatibility with fuel, cladding, heat exchangers, pumps, structural materials (to avoid expensive materials like titanium & molybdenum) Good thermal stability (organic liquids decompose at high temperatures) Coolant selection Neutronics Low neutron absorption cross section Moderating power to suit reactor type Low induced radioactivity Good radiation stability (organic liquids suffer

from nuclear radiation damage) INTRODUCTION TO HEAT TRANSFER 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. Heat Transfer deals with the determination of the rates of such energy transfers as well as variation of temperature. The transfer of energy as heat is always from the highertemperature medium to the lower-temperature one. Heat transfer stops when the two mediums reach the same temperature. Heat can be transferred in three different modes:

conduction, convection, radiation All modes of heat transfer require the existence of a temperature difference. 7 What is Heat Transfer? Energy in transit due to temperature difference. Thermodynamics tells us: How much heat is transferred (Q) How much work is done (W) Final state of the system Heat transfer tells us: How (with what modes) Q is transferred At what rate Q is transferred

Temperature distribution inside the body Heat transfer complementary Thermodynamics 8 9 APPLICATIONS OF HEAT TRANSFER Energy production and conversion

- steam power plant, solar energy conversion etc. Refrigeration and air-conditioning Domestic applications - ovens, stoves, toaster Cooling of electronic equipment Manufacturing / materials processing - welding,casting, soldering, laser machining Automobiles / aircraft design Nature (weather, climate etc) Application Areas of Heat Transfer 1111

Historical Background Kinetic theory: Treats molecules as tiny balls that are in motion and thus possess kinetic energy. Heat: The energy associated with the random motion of atoms and molecules. Caloric theory: Heat is a fluidlike substance called the caloric that is a massless, colorless, odorless, and tasteless substance that can be poured from one body into another It was only in the middle of the

nineteenth century that we had a true physical understanding of the nature of heat. Careful experiments of the Englishman James P. Joule published in 1843 convinced the skeptics that heat was not a substance after all, and thus put the caloric theory to rest. 12 13 ENGINEERING HEAT TRANSFER 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. 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, timeconsuming, and often impractical.

The analytical approach (including the numerical approach) has the advantage that it is fast and inexpensive, but the results obtained are subject to the accuracy of the assumptions, approximations, and idealizations made in the analysis. 14 APPLICATIONS OF HEAT TRANSFER a) Applications of conduction Uses of good conductors of heat: 1. Cooking utensils e.g. saucepans, frying pans boilers, base of electric irons. 15

USES OF GOOD CONDUCTORS OF HEAT 16 USES OF GOOD CONDUCTORS OF HEAT 2. Mercury is used in thermometers as it is a good conductor. 17 USES OF GOOD CONDUCTORS OF

HEAT 3. A metal door knob feels cold to touch as the heat is conducted away from the hand. 18 USES OF BAD CONDUCTORS OF HEAT 1. Materials such as cork, fibreglass and styrofoam are bad conductor of heat. - This is due to a lot of air trapped in them. - Air is a good insulator of heat.

19 USES OF BAD CONDUCTORS OF HEAT 2. Woolen clothes are used to keep people warm in winter. Animals have thick fur/feathers to reduce heat loss of heat to the cold surrounding. 20 USES OF BAD CONDUCTORS OF HEAT 3. Handles of cooking utensils are made of

wood or plastic. 21 b) Applications of convection 1. The heating coil of an electric kettle is placed at the bottom so that convection current can occur. 22 APPLICATIONS OF CONVECTION 2. Ventilation in homes which is used to keep rooms cool.

Windows, doors or other vents can be opened or closed as needed to reduce the temperature and improve the quality of the air you're breathing 23 . APPLICATIONS OF CONVECTION 3. Convection currents in a fridge. 24 APPLICATIONS OF CONVECTION 4. Domestic hot water supply.

25 APPLICATIONS OF CONVECTION 5. Cloud formation as warm moist air rises before condensing. 26 APPLICATIONS OF CONVECTION 6. i) Natural convection currents in sea breeze 27

APPLICATIONS OF CONVECTION Convection inside the earth 28 APPLICATIONS OF CONVECTION Convection inside the earth 29 C) APPLICATIONS OF RADIATION 1. Why are houses painted white in hot countries? - White reflects heat radiation and so keeps the house cooler.

30 APPLICATIONS OF RADIATION 2. White clothing/light coloured clothes reduces absorption of heat in hot climates help students stay cool in summer keep students warm in winter 31

APPLICATIONS OF RADIATION Radiators in cars are painted black. It loses energy easily! 32 APPLICATIONS OF RADIATION Fuel storage tanks are painted silvery

- reflect away energy from the Sun will not overheat 33 APPLICATIONS OF RADIATION Warmed air & floor emit infra-red radiation But this infra-red radiation can't escape easily through the glass.

infra-red radiation is trapped inside the greehouse keeps greenhouse warm plants can grow even in cold weather 34 Examples of heat transfer by radiation The thermos or vacuum flask It keeps food hot or cold by heat exchange between

food & environment through conduction, convection & radiation. 35 The thermos or vacuum flask cap plastic / cork stopper heat loss by conduction & convection

insulated support heat loss by conduction 36 The thermos or vacuum flask Silvery glass wall heat loss by radiation vacuum flask

vacuum between the double glass walls heat loss by conduction & convection outer case 37 Surface Energy Balance A surface contains no volume or mass, and thus no energy. Thereore, a surface can be viewed as a fictitious system whose energy content remains constant during a process.

This relation is valid for both steady and transient conditions, and the surface energy balance does not involve heat generation since a surface does not have a volume. 38 16-2 CONDUCTION Conduction: The transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles.

In gases and liquids, conduction is due to the collisions and diffusion of the molecules during their random motion. In solids, it is due to the combination of vibrations of the molecules in a lattice and the energy transport by free electrons. The rate of heat conduction through a plane layer is proportional to the temperature difference across the layer and the heat transfer area, but is inversely proportional to the thickness of the layer. Heat conduction through a large plane wall of thickness x

and area A. 39 When x 0 Fouriers law of heat conduction Thermal conductivity, k: A measure of the ability of a material to conduct heat. Temperature gradient dT/dx: The slope of the temperature curve on a T-x diagram. Heat is conducted in the direction of decreasing temperature, and the temperature gradient becomes

negative when temperature decreases with increasing x. The negative sign in the equation ensures that heat transfer in the positive x direction is a positive quantity. In heat conduction analysis, A represents the area normal to the direction of heat transfer. The rate of heat conduction through a solid is directly proportional to its thermal

conductivity. 40 41 Thermal Conductivity Thermal conductivity: The rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference. The thermal conductivity

of a material is a measure of the ability of the material to conduct heat. A high value for thermal conductivity indicates A simple experimental setup that the material is a to determine the thermal good heat conductor, conductivity of a material. and a low value indicates that the material is a poor heat conductor or

insulator. 42 The range of thermal conductivity of various materials at room temperature. 43 The thermal conductivities of gases such

as air vary by a factor of 104 from those of pure metals such as copper. Pure crystals and metals have the highest thermal conductivities, and gases and insulating materials the lowest. The mechanisms of heat conduction in different phases of a substance. 44 The variation of the thermal conductivity of

various solids, liquids, and gases with temperature. 45 Thermal Diffusivity cp Specific heat, J/kg C: Heat capacity per unit mass cp Heat capacity, J/m3C: Heat capacity per unit volume Thermal diffusivity, m2/s: Represents how fast heat diffuses through a material A material that has a high thermal

conductivity or a low heat capacity will obviously have a large thermal diffusivity. The larger the thermal diffusivity, the faster the propagation of heat into the medium. A small value of thermal diffusivity means that heat is mostly absorbed by the material and a small amount of heat is conducted further. 46 Example: The wall of an industrial furnace is constructed from 0.2 m thick fireclay brick having a thermal conductivity of 2.0 W/mK. Measurements made

during steady state operation reveal temperatures of 1500 and 1250 K at the inner and outer surfaces, respectively. What is the rate of heat loss through a wall which is 0.5 m by 4 m on a side ? 47 16-3 CONVECTION Convection: The mode of energy transfer between a solid surface and the adjacent liquid or gas that is in motion, and it involves the combined effects of

conduction and fluid motion. The faster the fluid motion, the greater the convection heat transfer. In the absence of any bulk fluid motion, heat transfer between a solid surface and the adjacent fluid is by pure conduction. Heat transfer from a hot surface to air by convection. 48

Forced convection: If the fluid is forced to flow over the surface by external means such as a fan, pump, or the wind. Natural (or free) convection: If the fluid motion is caused by buoyancy forces that are induced by density differences due to the variation of temperature in the fluid.

The cooling of a boiled egg by forced and natural convection. Heat transfer processes that involve change of phase of a fluid are also considered to be convection because of the fluid motion induced during the process, such as the rise of the vapor bubbles during boiling or the fall of the liquid droplets during condensation. 49 50 Newtons law of cooling h

As Ts T convection heat transfer coefficient, W/m2 C the surface area through which convection heat transfer takes place the surface temperature the temperature of the fluid sufficiently far from the surface. The convection heat transfer coefficient h is not a property of the fluid. It is an experimentally determined parameter

whose value depends on all the variables influencing convection such as - the surface geometry - the nature of fluid motion - the properties of the fluid - the bulk fluid velocity 51 52 16-4 RADIATION Radiation: The energy emitted by matter in the form of electromagnetic waves (or photons) as a result of the changes in the electronic

configurations of the atoms or molecules. Unlike conduction and convection, the transfer of heat by radiation does not require the presence of an intervening medium. In fact, heat transfer by radiation is fastest (at the speed of light) and it suffers no attenuation in a vacuum. This is how the energy of the sun reaches the earth. In heat transfer studies we are interested in thermal radiation, which is the form of radiation emitted by bodies because of their temperature. All bodies at a temperature above absolute zero emit thermal radiation. Radiation is a volumetric phenomenon, and all solids, liquids, and gases emit, absorb, or transmit radiation to varying degrees. However, radiation is usually considered to be a surface phenomenon for solids. 53

StefanBoltzmann law = 5.670 108 W/m2 K4 StefanBoltzmann constant Blackbody: The idealized surface that emits radiation at the maximum rate. Radiation emitted by real surfaces Emissivity : A measure of how closely a surface approximates a blackbody for which = 1 of the surface. 0 1. Blackbody radiation represents the maximum amount of radiation that can be emitted from a surface at a specified temperature.

54 Absorptivity : The fraction of the radiation energy incident on a surface that is absorbed by the surface. 0 1 A blackbody absorbs the entire radiation incident on it ( = 1). Kirchhoffs law: The emissivity and the absorptivity of a surface at a given temperature and wavelength are equal. The absorption of radiation incident on an opaque surface of absorptivity . 55 Net radiation heat transfer: The difference between the rates of

radiation emitted by the surface and the radiation absorbed. The determination of the net rate of heat transfer by radiation between two surfaces is a complicated matter since it depends on the properties of the surfaces their orientation relative to each other the interaction of the medium between the surfaces with radiation Radiation is usually

significant relative to conduction or natural convection, but negligible relative to forced convection. When a surface is completely enclosed by a much larger (or black) surface at temperature Tsurr separated by a gas (such as air) that does not intervene with radiation, the net rate of radiation heat transfer between these two surfaces is given by Radiation heat transfer between a surface

56 and the surfaces surrounding it. When radiation and convection occur simultaneously between a surface and a gas: Combined heat transfer coefficient hcombined Includes the effects of both convection and radiation 57 16-5 SIMULTANEOUS HEAT TRANSFER MECHANISMS Heat transfer is only by conduction in opaque solids,

but by conduction and radiation in semitransparent solids. A solid may involve conduction and radiation but not convection. A solid may involve convection and/or radiation on its surfaces exposed to a fluid or other surfaces. Heat transfer is by conduction and possibly by radiation in a still fluid (no bulk fluid motion) and by convection and radiation in a flowing fluid. In the absence of radiation, heat transfer through a fluid is either by conduction or convection, depending on the presence of any bulk fluid motion. Convection = Conduction + Fluid motion Heat transfer through a vacuum is by radiation.

Most gases between two solid surfaces do not interfere with radiation. Although there are three mechanisms of Liquids are usually strong absorbers of heat transfer, a medium may involve 58 radiation. only two of them simultaneously. 59 Example: An uninsulated steam pipe passes through a room in which the air and walls are at 25C.

The outside diameter of pipe is 80 mm, and its surface temperature and emissivity are 180C and 0.85, respectively. If the free convection coefficient from the surface to the air is 6 W/ m2K, what is the rate of heat loss from the surface per unit length of pipe ? 60 C1: Introduction Problem 1.63: A rectangular forced air heating duct is suspended from the ceiling of a basement whose air and walls are at a temperature of T = Tsur = 5C. The

duct is 15m long and its cross section is 350 mm x 200 mm. i) For an uninsulated duct whose average surface temperature is 50C, estimate the rate of heat loss from the duct. The surface emissivity and convection coefficient are approximately 0.5 and 4 W/m 2K, respectively. ii) If heated air enters the duct at 58C and a velocity of 4 m/s and the heat loss corresponds to the result part (i), what is the outlet temperature ? Density and specific heat of the air may be assumed to be 1.10 kg/m3 and 1008 J/kgK, respectively. 61 C1: Introduction Problem 1.65:

During its manufacture, plate glass at 600C is cooled by passing air over its surface such that the convection heat transfer coefficient is 5 W/m2K. To prevent cracking, it is known that the temperature gradient must not exceed 15C/mm at any point in the glass during the cooling process. If the thermal conductivity of the glass is 1.4 W/mK and its surface emissivity is 0.8, what is the lowest temperature of the air that can initially be used for the cooling ? Assume that the temperature of the air equals that of the surroundings. 62

Thermal Resistance The conduction heat transfer rate can be calculated: . Ts ,1 Ts , 2 dT kA Q x kA Ts ,1 Ts , 2 dx L L / kA

(3.2a) Similarly for heat convection, Newtons law of cooling applies: . (TS T ) Q x hA(TS T ) 1 / hA (3.2b) And for radiation heat transfer:

.Q rad (Ts Tsur ) hr A(Ts Tsur ) 1 / hr A (3.2c) Recall electric circuit theory - Ohms law for electrical resistance: Electric current

Potential Differenc e Resistance Thermal Resistance We can use this electrical analogy to represent heat transfer problems using the concept of a thermal circuit (equivalent to an electrical circuit). . Overall Driving Force Toverall Q Resistance

R Compare with equations 3.2a-3.2c The temperature difference is the potential or driving force for the heat flow and the combinations of thermal conductivity, convection coefficient, thickness and area of material act as a resistance to this flow: Rt ,cond L 1 1

, Rt ,conv , Rt ,rad kA hA hr A Chapter 3 : One-dimensional, Steady state conduction (without thermal generation) 3.2.1 Thermal resistances & Thermal circuits - Interestingly, there exists an analogy between the diffusion of heat and electrical charge. For example if an electrical resistance is associated with the conduction of electricity, a thermal resistance may be associated with the conduction of heat. - Defining thermal resistance for conduction in a plane wall: - For convection :

- For previous simplest case, thermal circuit for plane wall with adjoining fluids: 65 Chapter 3 : One-dimensional, Steady state conduction (without thermal generation) 3.2.1 Thermal resistances & Thermal circuits - In case of radiation : (3.13) where,

(1.9) Surface temperature Surrounding temperature 66 Chapter 3 : One-dimensional, Steady state conduction (without thermal generation) Example: (Problem 3.2a) The rear window of an automobile is defogged by passing warm air over its inner surface. If the warm air is at T,ii = 40C and the corresponding convection coefficient is hi = 30 W/m2K, what are the inner and outer surface temperatures of 4-mm thick

window glass, if the outside ambient air temperature is T,io = -10C and the associated convection coefficient is ho = 65 W/m2K. 67 Chapter 3 : One-dimensional, Steady state conduction (without thermal generation) Example (problem 3.5): The walls of a refrigerator are typically constructed by sandwiching a layer of insulation between sheet metal panels. Consider a wall made from fibreglass insulation of thermal conductivity, ki = 0.046 W/mK and thickness Li = 50 mm and steel panels, each of thermal conductivity kp = 60 W/mK and thickness Lp = 3 mm. If the wall separates refrigerated air at T,o = 25C, what is the heat gain per unit surface area ? Coefficients associated with natural convection at the inner and outer surfaces can be

approximated as hi = ho = 5 W/m2K 68 Chapter 3 : One-dimensional, Steady state conduction (without thermal generation) 3.2.2 The composite wall (with negligible contact resistance) 69 Chapter 3 : One-dimensional, Steady state conduction (without thermal generation) The composite wall (series type)

Composite wall with negligible contact resistance: where, Overall heat transfer coefficient: * A modified form of Newtons Law of cooling to encompass multiple resistances to heat transfer 70 Composite Walls What is the heat transfer rate for this system?

.Q Alternatively x UA T Rtot T 1 Rt

q UA where U is the overall heat transfer coefficient and T the overall temperature difference. U 1 Rtot A

1 [(1 / h1 ) ( LA / k A ) ( LB / k B ) ( LC / kC ) (1 / h4 )] 72 PROBLEM-SOLVING TECHNIQUE

Step 1: Problem Statement Step 2: Schematic Step 3: Assumptions and Approximations Step 4: Physical Laws Step 5: Properties Step 6: Calculations Step 7: Reasoning, Verification, and Discussion 73 Review Describe the three kinds of heat transfer. a. Conduction transfer of heat energy from one particle to another by direct contact.

(Primarily in solids) b. Convection transfer of heat energy in fluidsgases and liquids) through the bulk movement of matter from one place to another. (Produces currents) c. Radiation transfer of energy through electromagnetic waves. (Matter is not required!) (Radiant & infrared radiation from the sun) 74 Conduction Radiation

Direct contact of particles Solids/ liquids/ gases The handle of a cooking utensil Transfer of energy by waves Only radiant energy that

is absorbed becomes thermal energy Lightbulb Fireplace Convection Transfer of energy by bulk movement of matter (fluids)

Currents (wind,water) Hot air balloon 75 Summary Conduction Fouriers law of heat conduction Thermal Conductivity Thermal Diffusivity Convection Newtons law of cooling

Radiation StefanBoltzmann law Simultaneous Heat Transfer Mechanisms 76