Fundamentals of heat transfer

Following over 170+ pages and additional appendixes are formed based on content of Course: Fundamentals of Heat Transfer. Mainly this summarizes relevant parts on Book of Fundamentals of Heat and Mass Transfer (Incropera), but also other references introducing the same concepts are included. Student’s point of view has been consideredwith following highlights: (1) Relevant topics are presented in a nutshell to provide fast digestion of principles of heat transfer. (2) Appendixes include terminology dictionary. (3) Totally 22 illustrating examples are connecting theory to practical applications and quantifying heat transfer to understandable forms as: temperatures, heat transfer rates, heat fluxes, resistances and etc. (4) Most important Learning outcomes are presented for each topic separately. The Book, Fundamentals of Heat and Mass Transfer (Incropera), is certainly recommended for those going beyond basic knowledge of heat transfer. Lecture Notes consists of four primary content-wise objectives: (1) Give understanding to physical mechanisms of heat transfer, (2)Present basic concepts and terminology relevant for conduction, convection and radiation (3) Introduce thermal performance analysis methods for steady state and transient conduction systems. (4) Provide fast-to-digest phenomenological understanding required for basic design of thermal models

Dynaamisen lämmönsiirtomallin kehittäminen

Dynaamisia simulointimalleja tarvitaan, jotta voidaan tarkastella järjestelmän käyttäytymistä ajan funktiona. Simulointimallilla voidaan simuloida järjestelmän lähtö erilaisilla herätteillä. Mallin avulla saadaan myös tarkempi käsitys järjestelmästä ja sen osa-alueista, koska simulointimallista voidaan tarkastella sellaisia asioita, jotka voivat olla oikeasta järjestelmästä vaikeasti mitattavia. Tässä työssä kehitetään LUT Energian hyötysuhdemittapaikan keskikokoista kalorimetriä approksimoiva dynaaminen lämmönsiirtomalli käyttäen Matlab® Simulink -ohjelmistoa. Kehitetyn lämmönsiirtomallin tarkkuutta arvioidaan todellisella järjestelmällä tehdyillä mittauksilla. Työssä käytetään karkeita approksimaatioita, jotka tulee korvata tarkemmilla matemaattisilla malleilla jatkokehitystä varten. Työssä kehitetty dynaaminen lämmönsiirtomalli approksimoi todellisen järjestelmän vastetta lämmitysvaiheessa keskimääräisenvirheen ±0,19 °C tarkkuudella.

Limestone Reactions in a Fluidized Bed Heat Exchanger of an Oxy-fuel Circulating Fluidized Bed Boiler

Oxy-fuel combustion in a circulating fluidized bed (CFB) boiler appears to be a promising option for capturing CO2 in power plants. Oxy-fuel combustion is based on burning of fuel in the mixture of oxygen and re-circulated flue gas instead of air. Limestone (CaCO3) is typically used for capturing of SO2 in CFB boilers where limestone calcines to calcium oxide (CaO). Because of high CO2 concentration in oxy-fuel combustion, calcination reaction may be hindered or carbonation, the reverse reaction of calcination, may occur. Carbonation of CaO particles can cause problems especially in the circulation loop of a CFB boiler where temperature level is lower than in the furnace. The aim of the thesis was to examine carbonation of CaO in a fluidized bed heat exchanger of a CFB boiler featuring oxy-fuel combustion. The calculations and analyzing were based on measurement data from an oxy-fuel pilot plant and on 0-dimensional (0D) gas balance of a fluidized bed heat exchanger. Additionally, the objective was to develop a 1-dimensional (1D) model of a fluidized bed heat exchanger by searching a suitable pre-exponential factor for a carbonation rate constant. On the basis of gas measurement data and the 0D gas balance, it was found that the amount of fluidization gas decreased as it flew through the fluidized bed heat exchanger. Most likely the reason for this was carbonation of CaO. It was discovered that temperature has a promoting effect on the reaction rate of carbonation. With the 1D model, a suitable pre-exponential factor for the equation of carbonation rate constant was found. However, during measurements there were several uncertainties, and in the calculations plenty of assumptions were made. Besides, the temperature level in the fluidized bed heat exchanger was relatively low during the measurements. Carbonation should be considered when fluidized bed heat exchangers and the capacity of related fans are designed for a CFB boiler with oxy-fuel combustion.

Characterisation of Laser Beam and Paper Material Interaction

It is known already from 1970´s that laser beam is suitable for processing paper materials. In this thesis, term paper materials mean all wood-fibre based materials, like dried pulp, copy paper, newspaper, cardboard, corrugated board, tissue paper etc. Accordingly, laser processing in this thesis means all laser treatments resulting material removal, like cutting, partial cutting, marking, creasing, perforation etc. that can be used to process paper materials. Laser technology provides many advantages for processing of paper materials: non-contact method, freedom of processing geometry, reliable technology for non-stop production etc. Especially packaging industry is very promising area for laser processing applications. However, there are only few industrial laser processing applications worldwide even in beginning of 2010´s. One reason for small-scale use of lasers in paper material manufacturing is that there is a shortage of published research and scientific articles. Another problem, restraining the use of laser for processing of paper materials, is colouration of paper material i.e. the yellowish and/or greyish colour of cut edge appearing during cutting or after cutting. These are the main reasons for selecting the topic of this thesis to concern characterization of interaction of laser beam and paper materials. This study was carried out in Laboratory of Laser Processing at Lappeenranta University of Technology (Finland). Laser equipment used in this study was TRUMPF TLF 2700 carbon dioxide laser that produces a beam with wavelength of 10.6 μm with power range of 190-2500 W (laser power on work piece). Study of laser beam and paper material interaction was carried out by treating dried kraft pulp (grammage of 67 g m-2) with different laser power levels, focal plane postion settings and interaction times. Interaction between laser beam and dried kraft pulp was detected with different monitoring devices, i.e. spectrometer, pyrometer and active illumination imaging system. This way it was possible to create an input and output parameter diagram and to study the effects of input and output parameters in this thesis. When interaction phenomena are understood also process development can be carried out and even new innovations developed. Fulfilling the lack of information on interaction phenomena can assist in the way of lasers for wider use of technology in paper making and converting industry. It was concluded in this thesis that interaction of laser beam and paper material has two mechanisms that are dependent on focal plane position range. Assumed interaction mechanism B appears in range of average focal plane position of 3.4 mm and 2.4 mm and assumed interaction mechanism A in range of average focal plane position of 0.4 mm and -0.6 mm both in used experimental set up. Focal plane position 1.4 mm represents midzone of these two mechanisms. Holes during laser beam and paper material interaction are formed gradually: first small hole is formed to interaction area in the centre of laser beam cross-section and after that, as function of interaction time, hole expands, until interaction between laser beam and dried kraft pulp is ended. By the image analysis it can be seen that in beginning of laser beam and dried kraft pulp material interaction small holes off very good quality are formed. It is obvious that black colour and heat affected zone appear as function of interaction time. This reveals that there still are different interaction phases within interaction mechanisms A and B. These interaction phases appear as function of time and also as function of peak intensity of laser beam. Limit peak intensity is the value that divides interaction mechanism A and B from one-phase interaction into dual-phase interaction. So all peak intensity values under limit peak intensity belong to MAOM (interaction mechanism A one-phase mode) or to MBOM (interaction mechanism B onephase mode) and values over that belong to MADM (interaction mechanism A dual-phase mode) or to MBDM (interaction mechanism B dual-phase mode). Decomposition process of cellulose is evolution of hydrocarbons when temperature is between 380- 500°C. This means that long cellulose molecule is split into smaller volatile hydrocarbons in this temperature range. As temperature increases, decomposition process of cellulose molecule changes. In range of 700-900°C, cellulose molecule is mainly decomposed into H2 gas; this is why this range is called evolution of hydrogen. Interaction in this range starts (as in range of MAOM and MBOM), when a small good quality hole is formed. This is due to “direct evaporation” of pulp via decomposition process of evolution of hydrogen. And this can be seen can be seen in spectrometer as high intensity peak of yellow light (in range of 588-589 nm) which refers to temperature of ~1750ºC. Pyrometer does not detect this high intensity peak since it is not able to detect physical phase change from solid kraft pulp to gaseous compounds. As interaction time between laser beam and dried kraft pulp continues, hypothesis is that three auto ignition processes occurs. Auto ignition of substance is the lowest temperature in which it will spontaneously ignite in a normal atmosphere without an external source of ignition, such as a flame or spark. Three auto ignition processes appears in range of MADM and MBDM, namely: 1. temperature of auto ignition of hydrogen atom (H2) is 500ºC, 2. temperature of auto ignition of carbon monoxide molecule (CO) is 609ºC and 3. temperature of auto ignition of carbon atom (C) is 700ºC. These three auto ignition processes leads to formation of plasma plume which has strong emission of radiation in range of visible light. Formation of this plasma plume can be seen as increase of intensity in wavelength range of ~475-652 nm. Pyrometer shows maximum temperature just after this ignition. This plasma plume is assumed to scatter laser beam so that it interacts with larger area of dried kraft pulp than what is actual area of beam cross-section. This assumed scattering reduces also peak intensity. So result shows that assumably scattered light with low peak intensity is interacting with large area of hole edges and due to low peak intensity this interaction happens in low temperature. So interaction between laser beam and dried kraft pulp turns from evolution of hydrogen to evolution of hydrocarbons. This leads to black colour of hole edges.

Design of an amplifier and an instrumentation setup for a harsh environment heat flux measurement application – case axial flux electric machine

Measurement is a tool for researching. Therefore, it is important that the measuring process is carried out correctly, without distorting the signal or the measured event. Researches of thermoelectric phenomena have been focused more on transverse thermoelectric phenomena during recent decades. Transverse Seebeck effect enables to produce thinner and faster heat flux sensor than before. Studies about transverse Seebeck effect have so far focused on materials, so in this Master’s Thesis instrumentation of transverse Seebeck effect based heat flux sensor is studied, This Master’s Thesis examines an equivalent circuit of transverse Seebeck effect heat flux sensors, their connectivity to electronics and choosing and design a right type amplifier. The research is carried out with a case study which is Gradient Heat Flux Sensors and an electrical motor. In this work, a general equivalent circuit was presented for the transverse Seebeck effect-based heat flux sensor. An amplifier was designed for the sensor of the case study, and the solution was produced for the measurement of the local heat flux of the electric motor to improve the electromagnetic compatibility.

The effects of welding heat input on the usability of high strength steels in welded structures

High strength steel (HSS) has been in use in workshops since the 1980s. At that time, the significance of the term HSS differed from the modern conception as the maximum yield strength of HSSs has increased nearly every year. There are three different ways to make HSS. The first and oldest method is QT (quenched and tempered) followed by the TMCP (thermomechanical controlled process) and DQ (direct quenching) methods. This thesis consists of two parts, the first of which part introduces the research topic and discusses welded HSS structures by characterizing the most important variables. In the second part of the thesis, the usability of welded HSS structures is examined through a set of laboratory tests. The results of this study explain the differences in the usability of the welded HSSs made by the three different methods. The results additionally indicate that usage of different HSSs in the welded structures presumes that manufacturers know what kind of HSS they are welding. As manufacturers use greater strength HSSs in welded structures, the demands for welding rise as well. Therefore, during the manufacturing process, factors such as heat input, cooling time, weld quality, and more must be under careful observation.

Pressure drop coefficients for elliptic and circular sections in one, two and three-row arrangements of plate fin and tube heat exchangers

The objective of the present work is the experimental determination of pressure drop coefficients (loss coefficients) for elliptic and circular sections in one, two and three-row arrangements of plate fin and tube heat exchangers. The experiments permitted to correlate the dimensionless loss coefficient with the flow Reynolds number in the rectangular channel formed by the plate fins. The experimental technique consisted of the measurement of the longitudinal pressure distribution along the flow channel, for several values of air mass flow rate. The total number of data runs, each one characterized by the flow Reynolds number, was 216. The present geometry is used in compact heat exchangers for air conditioning systems, heaters, radiators, and others. Also, it is verified the influence of the utilization of elliptic tubes, instead of circular ones, in the pressure drop. The measurements were performed for Reynolds numbers ranging from 200 to 1900.

Turbulent heat transfer and pressure drop in pinned annular regions

Experiments were performed to determine average heat transfer coefficients and friction factors for turbulent flow through annular ducts with pin fins. The measurements were carried out by means of a double-pipe heat exchanger. The total number of pins attached to the inner wall of the annular region was 560. The working fluids were air, flowing in the annular channel, and water through the inner circular tube. The average heat transfer coefficients of the pinned air-side were obtained from the experimental determination of the overall heat transfer coefficients of the heat exchanger and from the knowledge of the average heat transfer coefficients of the circular pipe (water-side), which could be found in the pertinent literature. To attain fully developed conditions, the heat exchanger was built with additional lengths before and after the test section. The inner circular duct of the heat exchanger and the pin fins were made of brass. Due to the high thermal conductivity of the brass, the small tube thickness and water temperature variation, the surface of the internal tube was practically isothermal. The external tube was made of an industrial plastic which was insulated from the environment by means of a glass wool batt. In this manner, the outer surface of the annular channel can be considered adiabatic. The results are presented in dimensionless forms, in terms of average Nusselt numbers and friction factors as functions of the flow Reynolds number, ranging from 13,000 to 80,000. The pin fin efficiency, which depends on the heat transfer coefficient, is also determined as a function of dimensionless parameters. A comparison of the present results with those for smooth sections (without pins) is also presented. The purpose of such a comparison is to study the influence of the presence of the pins on the pressure drop and heat transfer rate.

Comparison between one-dimensional uncoupled and convection-conduction conjugated approaches in finned surface heat transfer

This work studies the forced convection problem in internal flow between concentric annular ducts, with radial fins at the internal tube surface. The finned surface heat transfer is analyzed by two different approaches. In the first one, it is assumed one-dimensional heat conduction along the internal tube wall and fins, with the convection heat transfer coefficient being a known parameter, determined by an uncoupled solution. In the other way, named conjugated approach, the mathematical model (continuity, momentum, energy and K-epsilon equations) applied to tube annuli problem was numerically solved using finite element technique in a coupled formulation. At first time, a comparison was made between results obtained for the conjugated problem and experimental data, showing good agreement. Then, the temperature profiles under these two approaches were compared to each other to analyze the validity of the one-dimensional classical formulation that has been utilized in the heat exchanger design.

Thermalhydraulic behavior of electrically heated rod during a critical heat flux transient

In nuclear reactors, the occurrence of critical heat flux leads to fuel rod overheating with clad fusion and radioactive products leakage. To predict the effects of such phenomenon, experiments are performed using electrically heated rods to simulate operational and accidental conditions of nuclear fuel rods. In the present work, it is performed a theoretical analysis of the drying and rewetting front propagation during a critical heat flux experiment, starting with the application of an electrical power step from steady state condition. After the occurrence of critical heat flux, the drying front propagation is predicted. After a few seconds, a power cut is considered and the rewetting front behavior is analytically observed. Studies performed with various values of coolant mass flow rate show that this variable has more influence on the drying front velocity than on the rewetting one.

Inverse convection problem of simultaneous estimation of two boundary heat fluxes in parallel plate channels

This paper deals with the use of the conjugate gradient method of function estimation for the simultaneous identification of two unknown boundary heat fluxes in parallel plate channels. The fluid flow is assumed to be laminar and hydrodynamically developed. Temperature measurements taken inside the channel are used in the inverse analysis. The accuracy of the present solution approach is examined by using simulated measurements containing random errors, for strict cases involving functional forms with discontinuities and sharp-corners for the unknown functions. Three different types of inverse problems are addressed in the paper, involving the estimation of: (i) Spatially dependent heat fluxes; (ii) Time-dependent heat fluxes; and (iii) Time and spatially dependent heat fluxes.

Heat Source Estimation with the Conjugate Gradient Method in Inverse Linear Diffusive Problems

In this work, we present the solution of a class of linear inverse heat conduction problems for the estimation of unknown heat source terms, with no prior information of the functional forms of timewise and spatial dependence of the source strength, using the conjugate gradient method with an adjoint problem. After describing the mathematical formulation of a general direct problem and the procedure for the solution of the inverse problem, we show applications to three transient heat transfer problems: a one-dimensional cylindrical problem; a two-dimensional cylindrical problem; and a one-dimensional problem with two plates.

Simulation of Steady-State Nonlinear Heat Transfer Problems Through the Minimization of Quadratic Functionals

In this work it is presented a systematic procedure for constructing the solution of a large class of nonlinear conduction heat transfer problems through the minimization of quadratic functionals like the ones usually employed for linear descriptions. The proposed procedure gives rise to an efficient and easy way for carrying out numerical simulations of nonlinear heat transfer problems by means of finite elements. To illustrate the procedure a particular problem is simulated by means of a finite element approximation.

Effects of condensation in microchannels with a porous boundary: analytical investigation on heat transfer and meniscus shape

In two-phase miniature and microchannel flows, the meniscus shape must be considered due to effects that are affected by condensation and/or evaporation and coupled with the transport phenomena in the thin film on the microchannel wall, when capillary forces drive the working fluid. This investigation presents an analytical model for microchannel condensers with a porous boundary, where capillary forces pump the fluid. Methanol was selected as the working fluid. Very low liquid Reynolds numbers were obtained (Re~6), but very high Nusselt numbers (Nu~150) could be found due to the channel size (1.5 mm) and the presence of the porous boundary. The meniscus calculation provided consistent results for the vapor interface temperature and pressure, as well as the meniscus curvature. The obtained results show that microchannel condensers with a porous boundary can be used for heat dissipation with reduced heat transfer area and very high heat dissipation capabilities.

Työkoneiden dieselmoottoreiden hyötysuhteen parantaminen lämmöntalteenoton avulla

Tämä diplomityö on osa Lappeenrannan teknillisessä yliopistossa tehtävää tutkimusta polttomoottoreiden energiatehokkuuden parantamisessa. Työn tavoitteena on saada tutkimustietoa polttomoottoreiden hukkalämpövirtojen hyödyntämisestä sähköntuotannossa. Tavoitteena on muodostaa näkemys Mikro-ORC energiamuuntimen mahdollisuuksista ja reunaehdoista osana työkoneluokan (150 kW… 400 kW) dieselmoottorikokonaisuutta, erityisesti maataloussektorilla. Työssä tarkasteltaviksi moottoreiksi valittiin kaksi eri AGCO Sisu Powerin dieselmoottoria. Laskennat suoritettiin moottorin valmistajan antamien hukkalämpövirtojen arvojen perusteella. Laskennan perusperiaatteena oli tutkia ORC-prosessin tuottamaa lisäsähkötehoa hyödyntämällä pakokaasujen lämpöenergiaa korkea-, keski- ja matalalämpötiloissa. Työssä vertailtiin kahden eri kiertoaineen prosessihyötysuhdetta, saatava sähkötehoa sekä prosessin sisäisiä parametreja. Lisäksi työssä tutkittiin ORC-prosessin laskentaa suunnittelupisteessä (design) ja suunnittelupisteen ulkopuolella (off-design), prosessisuureiden optimointia ja lämmönsiirtimien mitoitusta. Diplomityössä tarkasteltiin moottorin energiataseen mukaisten arvojen lisäksi moottorin parametrien muuttamisen vaikutusta hukkalämpövirroista saatavan tehoon. Työssä saatiin arvokasta tietoa polttomoottoreiden hukkalämpövirtojen muuntamisesta sähköksi ORC:lla sekä moottorin energiatehokkuuden parantamisesta.