Heat Transfer

Heat transfer within the reactor

heat transfer in a fuel rod involves conduction across the fuel pellet, then conduction across the helium gap (refer to slide diagram). Because helium is subjected to the same heat throughout, no convection flow path is available. This is followed by conduction across the cladding and boundary layer of the core flow.

¡Nucleate boiling occurring at the surface of the fuel rod will?

increase convective heat transfer from the fuel rod to the coolant

Convection

involves the transfer of heat by a process of bulk motion and mixing of portions of a fluid. This involves the transfer of heat between a surface and a fluid takes place in both bulk fluid flow paths. One fluid convectively transfers heat to the tube wall, ¡The movement caused within a fluid by the tendency of hotter and therefore less dense material to rise, and colder, denser material to sink under the influence of gravity, which consequently results in transfer of heat.

Core thermal Power

is defined as the average power density of the core times the core volume. simply defined as the measure of heat input per unit time from the core to the reactor coolant system.

Condu-vec-tion

many of the heat transfer processes encountered in a PWR plant involve a combination of conduction and convection. Example ¡Heat transfer in a fuel rod involves conduction across the fuel pellet, then conduction across the helium gap. ¡Because helium is subjected to the same heat throughout, no convection flow path is available. This is followed by conduction across the cladding and boundary

Function of the main condenser in a power plant

normally maintained at a vacuum to increase cycle efficiency. is a specific example of a heat exchanger used in steam cycles. ¡The fluid flow in the tubes is single-phase flow, while the fluid flow in the shell is two-phase flow. It's a cross-flow heat exchanger

¡What type of boiling can be described as follows: Small bubbles of vapor are formed within the liquid at the heat transfer surface and then move away from the surface.

nucleate boiling

¡If the two fluids in a heat exchanger are travelling in the same direction, the exchanger is known as a _________ heat exchanger.

parallell flow

Counter Flow Heat Exchanger

the direction of flow of one working fluid is primarily opposite to the direction of flow of the other fluid. As fluids flow through a heat exchanger, the fluid temperatures change constantly. . If enough heat is transferred in this heat exchanger, the exiting temperature of the cold fluid (t2) may be higher than the exiting temperature of the hot fluid (T2). It can transfer a relatively large amount of heat energy for its size, compared with the parallel flow and cross flow types, because of the large deltaT present throughout the heat exchanger. For this reason, most shell and tube heat exchangers are This type of heat exchanger

nonregenerative heat exchanger

the hot fluid is cooled by a colder fluid, which is supplied by another system, where the heat is eventually transferred to a heat sink

Entropy

the quantitative measure of disorder in a system. a measure of the amount of energy which is unavailable to do work. is also a measure of the number of possible arrangements the atoms in a system can have. ¡So it is a property that will increase if heat is added

regenerative heat exchanger

the same fluid is used as the cooling fluid and the cooled fluid. exchanger reduces heat losses from the plant because it returns heat back to the purified water.

methods of determining core thermal power

¡CTP is normally calculated at regular intervals by a plant process computer. ¡ ¡However, if the computer is not available, the operator should be able to solve for CTP with comparable accuracy. ¡ ¡In some plants, nomograms and graphs are used to aid the operator in making these estimates. ¡ ¡CTP may also be determined from the nuclear instrumentation. The accuracy of this method depends upon the number, type, and location of neutron sensors. The primary advantage of this method is the short response time of the nuclear instrumentation.

Second law of thermodynamics

¡In any closed system, the entropy of the system will either remain constant or increase. In other words, each time a system goes through a thermodynamic process, the system can never completely return to precisely the same state it was in before.

Turbulent flow

¡In the immediate vicinity of the wall, heat can only flow by conduction, because the fluid particles are stationary relative to the boundary. We naturally expect a large temperature drop in this layer. As we move further from the wall, the movement of the fluid aids in the energy transport, and the temperature gradient will be less steep, eventually leveling out in the main stream.

Entropy Applied to the plant

¡No engine, actual or ideal, when operating in a cycle, can convert all heat supplied to it into work. ¡Energy (i.e. the capacity to perform work) is always degraded when heat flows from a high temperature to a low temperature A lot more work with high temperature liquid than lower temperature.

Percent reactor power

¡Nuclear instrumentation indicates percent reactor power. This is simply the percent of rated CTP that the reactor is operating at (actual core thermal power divided by rated core thermal power). %P_RX=(CTPActual)/(CTPRated )×100

Laminar Flow

¡The boundary layer is composed of three parts. The particles adjacent to the wall that are at zero velocity, the laminar sub-layer where flow is not stagnant yet remains laminar, and the buffer layer which is the region between the laminar sub-layer and the completely turbulent portion of flow. When the fluid velocity and the turbulence are small, the transport of energy across the fluid is not aided materially by mixing currents on a macroscopic scale. On the other hand, when the velocity is large, and the mixing between warmer and colder fluids contributes substantially to the energy transfer, the conduction becomes less important. Consequently, to transfer heat through a fluid at a given rate, a larger temperature gradient is required in a region of low velocity rather than in a region of high velocity.

Thermal Conductivity

¡The higher the conductivity, the better heat transfer will result

Radiation(thermal radiation)

¡Transfer of heat by electromagnetic energy which arises due to the temperature of a body. ¡Electromagnetic energy excited by thermal agitation of molecules or atoms Does not need a medium such as air, metal, etc. to occur ¡ All bodies above absolute zero radiate some heat. Only dominant form of heat transfer in PWRs during accidental conditions.

Latent heat of vaporization

¡the amount of heat required to completely vaporize one pound mass of a saturated liquid Or enthalpy change of evaporation

Example of Convection heat transfer

. It involves the transfer of heat between a surface at temperature Ts and a fluid at temperature Tb, referred to as the bulk temperature of the fluid. The exact definition of the temperature of the bulk fluid (Tb) varies depending on the details of the situation. For flow adjacent to a hot or cold surface, Tb is the temperature far from the surface. For boiling or condensation, Tb is the saturation temperature.

Enthalpy

A thermodynamic quantity equivalent to the total heat content of a system. It is equal to the internal energy of the system plus the product of pressure and volume.

Conduction Heat Transfer

An INCREASE in the heat transfer through a material requires a GREATER temperature DROP across the material.

Fluid thermal conductivity

An increase in the thermal conductivity results in an increase of the heat transfer coefficient

What is the temperature profile for a parallel flow heat exchanger ?

Both temperatures start a certain distance in magnitude and approach each other through the heat exchanger

Nucleate Boiling

Bubbles break up the stagnant layer at the transfer surface Gives the layer at the surface a higher thermal conductivity Heat is carried away more rapidly Increased slope of the curve represents a greater heat transfer coefficient

3 different types of heat transfer

Conduction, Convection, Radiatoin

First law of thermodynamics

Energy cannot be created or destroyed ¡One form of energy (potential, kinetic, etc..) may be converted to another kind of energy but... ¡ ¡The sum of the energies entering a process must equal the sum of the energies leaving the process. ¡ ¡Here's another way of putting it- The change in a system's internal energy is equal to the difference between heat added to the system from its surroundings and work done by the system on its surroundings.

¡A measure of molecular disorder, a measure of the degradation of energy, and a measure of "unavailable energy" are all definitions of the __________ of a system.

Entropy

Saturation pressure/temperature relationship

Every temperature has a unique saturation pressure, and every pressure has a unique saturation temperature.

¡The sum of the energies entering a process must equal the sum of the energies leaving the process OR energy cannot be created or destroyed. These principles are known as the?

First Law of Thermodynamics

Factor Affecting Convection

Flow Rate -Higher or lower Flow Rate -Quantity Area -Surface Area that is able to transfer heat Heat transfer by convection is more difficult to analyze than heat transfer by conduction. This is because there is no single property of the heat transfer medium, such as the thermal conductivity, that can be defined to describe the mechanism. Heat transfer by convection varies from situation to situation, and it is frequently coupled with the mode of fluid flow. In practice, heat transfer by convection is treated empirically.

What are the four factors affecting heat transfer in a fluid?

Fluid viscosity, velocity, thermal conductivity and heat flux/nucleate boiling

Natural Convection

Heat input into the fluid causes density variations which induce motion and mixing within the fluid An example is the transfer of heat from a hot water radiator's surface to the surrounding air in a room

Latent Heat

Heat that causes a phase change with no change in temperature

Sensible Heat

Heat that causes an increase in temperature of the substance to which it is added

Heat flux/nucleate boiling

If the___________is sufficient to cause ________, the film thickness will effectively decrease (due to the turbulence cause by the bubbles) This will increase the heat transfer corfficient

What is the difference between a regenerative heat exchanger and non regenerative heat exchanger?

In a regenerative heat exchanger, the same fluid is used as the cooling fluid and the cooled fluid.

Convection Heat Transfer

It involves the transfer of heat between a surface at temperature Ts and a fluid at temperature Tb, referred to as the bulk temperature of the fluid. The exact definition of the temperature of the bulk fluid (Tb) varies depending on the details of the situation. For flow adjacent to a hot or cold surface, Tb is the temperature far from the surface. For boiling or condensation, Tb is the saturation temperature.

Forced Convection

Motion and mixing is caused by an outside force, such as pump or fan.

Describe the different flowpaths in heat exchangers commonly found in the plant.

Parallel, Counter Flow and Cross Flow

Factor that affect heat transfer rate

Q ̇=Uo AΔT Q= heat transfer rate (Btu/hr) Uo = overall heat transfer coefficient (Btu/hr ft2 °F) A = surface area for heat transfer (ft2) ΔT = difference between shell side average temperature and tube side average temperature (°F) The larger the temperature difference, surface area, or heat transfer coefficient, the more heat will be transferred.

Calculate the rate of heat addition for a heat exchanger operating with these conditions: Coolant temperature in = 535F Coolant temperature out = 551F Coolant flow rate = 7 x10^7 lbm/hr Coolant specific heat = 1.3 Btu/lbm F

Q ̇=m ̇cp ΔT Q ̇=(7×10^7 (lb_m)/hr)(1.3 Btu/(lb_m°F))(551°-535°F) Q ̇=1.456×10^9 Btu/hr

Heat transfer Equation

Q=mcpΔT ¡Q = heat addition or removal rate (Btu/hr) ¡m = mass flow rate (lbm/hr) ¡cp = specific heat (Btu/lbm °F) ¡∆T = change in temperature (°F)

Overall Heat Transfer

Qo = UoAo(ΔTo) ¡Q=overall heat transfer rate across all slabs (Btu/hr) ¡Uo=overall heat transfer coefficient (Btu/hr ft2 °F) ¡Ao=overall cross-sectional area for heat transfer (ft2) ¡ΔTo=overall temperature difference (°F)= ΔT1 + ΔT2 + ΔT3

Temperature profile

Represent the fluid temperature transition from surface temperature to fluid bulk temperature.

Factors That affect Conduction

Resistance to Heat Transfer by the specific material -Thickness, metallurgical properties Driving Force - Temperature Difference Area - Surface area that is able to transfer heat

¡If a liquid is saturated and pressure remains constant, the addition of heat will?

Result in vaporization of the liquid

¡Concerning heat transfer in the main condenser, if an extraordinary amount of ___________ is removed by the circulating water, then ______________ will occur.

Sensible heat, more condensate depression

Film Boiling

Stable film of steam will form radiation is the predominant form of heat transfer structural failure of the heat transfer surface material is likely

Transition Boiling

Steam blanketing reduces the heat transfer rate convection is reduced primary heat transfer through the voids is conduction and radiation

Condensate Depression

Steam to liquid and the loss of energy in that changing of state. is the amount of subcooling below saturation temperature for a fluid. will occur when additional heat is removed from the steam, necessary to condense it to water

Use of saturation curves in the plant

T< Tsat identifying region of subcooled liquid in relation to the saturation curve. pressure margins/Temperature Margines/point of operation

Fluid velocity

The greater the velocity of the fluid stream, the thinner the fluid film with be which causes the heat transfer coefficient to increase

Saturation Pressure

The pressure at which a liquid will boil at a given temperature if heat is added to the liquid.

Conduction

The process by which heat is directly transmitted through a substance when there is a difference of temperature between adjoining regions, without movement of the material. takes place across the heat exchanger tubes and the stagnant boundary layers ¡Heat Exchangers ¡Boilers ¡Condensers

Heat Capacity(Cp)

The relationship between the heat added (Q) and the change in temperature (ΔT)

Fluid viscosity

The smaller the _______, the thinner the film, and the larger the heat transfer coefficient

Saturation Temperature

The temperature at which a liquid will boil at a given pressure if heat is added to the liquid.

subcooled water

Water that exists at a temperature below saturation temperature for the pressure of the water.

¡The temperature of a subcooled liquid is a) above, b) below, or c) at, the saturation temperature for a given pressure.

below

Parallel flow heat exchanger

both fluids in the heat exchanger flow in the same direction. When the cold fluid enters the heat exchanger, the heat transfer rate is large because the temperature difference (deltaT) is large. As heat is transferred from the hot fluid to the cold fluid, their temperatures become closer together, and the deltaT becomes smaller. Therefore, the heat transfer rate decreases, as the fluids travel through the heat exchanger.

Single Phase

both the cooling (heating) fluid and the cooled (heated) fluid remain in their initial gaseous or liquid phase (i.e., no phase change occurs). Examples are liquid cooled oil cooler or an aircooled automobile radiator.

Explain the overall heat transfer coefficient (Uo).

combines the heat transfer coefficient and the cross-sectional area for each process to properly describe the overall process. The total Heat transfer rate (Qo), the overall cross-sectional area for heat transfer(Ao), and the overall temperature difference ΔTo are commonly related using this term.

The basic mode of heat transfer that involves the transfer of heat by interaction between adjacent molecules of a solid is called _________ heat transfer.

conduction

¡A plant is operating at 60% power. Which one of the following is the primary heat transfer mechanism responsible for the transfer of heat from the surface of the steam generator tubes to the feedwater?

convection

Operational concerns of Condensate Depression

decreases the operating efficiency of the plant since the subcooled condensate must be reheated, thus requiring more heat from the reactor core. Also allows for an increased absorption of air by the condensate that causes accelerated oxygen corrosion of plant materials. (A higher dissolved gas concentration can reduce heat transfer and raise the likelihood of corrosion to the condensate system components.)

Film thickness and fluid thermal confuctivity

determines the heat transfer coefficient To rapidly transfer large quantities of heat, one attempts to reduce the boundary layer thickness as much as possible. This can be accomplished by increasing the velocity and/or the turbulence of the fluid.

Two Phase

heat exchangers, either the cooling (heating) fluid or the cooled (heated) fluid changes phase. The gland exhaust condenser, the air ejector condenser, and the feedwater heaters are this type of heat exchanger