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Full-Text Articles in Engineering

Evaluation Of Digital Twin Approaches For Thermal Modeling And Energy Optimization For Existing Buildings, Jason Bastie Muermann Sep 2023

Evaluation Of Digital Twin Approaches For Thermal Modeling And Energy Optimization For Existing Buildings, Jason Bastie Muermann

Theses and Dissertations

Residential, commercial, and industrial building sectors in the United States were responsible for 42% of the nation’s consumption of 100.2 quadrillion BTUs of energy in 2019 [1]. 80% of the nation’s energy is sourced from fossil fuels, including coal, natural gas, and petroleum. Fossil fuels are known contributors to carbon emissions and climate change, making energy reduction vital. Consequently, New Jersey Department of Military and Veterans Affairs (NJDMAVA) is tasked with evaluating energy consumption and efficiency in all New Jersey Army National Guard (NJARNG) facilities, as mandated by TAG Policy Letter 18-5, Executive Order 13990, and the Energy Independence and …


Heat Transfer To Rolling Or Sliding Drops On Inclined Heated Superhydrophobic Surfaces, Joseph Merkley Furner Jul 2023

Heat Transfer To Rolling Or Sliding Drops On Inclined Heated Superhydrophobic Surfaces, Joseph Merkley Furner

Theses and Dissertations

This thesis examines the time resolved heat transfer to drops rolling or sliding along inclined, subcritical heated non-wetting surfaces. Results were experimentally obtained using IR imaging for a smooth hydrophobic surface and post as well as rib structured superhydrophobic surfaces of varying solid fraction (f_s = 0.06 - 0.5). Tests were performed at varying inclination angle (α = 10, 15, 20, and 25°), drop volume (12, 20, 30, and 40 μL), and surface temperature (T_w = 50, 65, and 80 °C). Rib structured superhydrophobic surfaces were explored for drops moving parallel and perpendicular to the rib structures. The findings indicate …


Thermal Atomization Of Impinging Drops On Superheated Superhydrophobic Surfaces, Eric Lee May 2023

Thermal Atomization Of Impinging Drops On Superheated Superhydrophobic Surfaces, Eric Lee

Theses and Dissertations

Drop impact on a surface has an effect on nearly every industry and this impact may have adverse effects if not controlled. Superhydrophobic (SH) surfaces have been created with the extreme ability to repel water. These surfaces exist in nature but may also be fabricated using modern techniques. This thesis explores heat transfer from these SH surfaces to drops impacting them. This thesis is devoted to increasing the breadth of knowledge of thermal atomization during drop impingement on superheated SH surfaces. When a water drop impinges vertically on a horizontal superheated surface, intense atomization can occur. The atomization is caused …


The Deflection And Heat Transfer Analysis Of Injection Mold Cavity With Sla Cooling Channel Insert, Olumide Temidayo Aladesiun Dec 2022

The Deflection And Heat Transfer Analysis Of Injection Mold Cavity With Sla Cooling Channel Insert, Olumide Temidayo Aladesiun

Theses and Dissertations

Fast cooling in injection molding is the critical in the process economy. Among many different cooling channel designs available, conformal cooling offers the best and the most efficient cooling. However, limited awareness, accessibility, complexity, cost, knowledge, and experience limit the use of conformal cooling channels to be used into the mold in a molding process.

Typically, SLM(Selective Laser Melting) method is used to create cavity inserts with conformal cooling channels, however, due to the difficulties listed above, applications of conformal cooling channels are very limited. For an inexpensive alternative SLA (Stereolithography Apparatus) can print cavity inserts with conformal cooling channels. …


Flow And Thermal Transport In Additively Manufactured Metal Lattices Based On Novel Unit-Cell Topologies, Inderjot Kaur Aug 2022

Flow And Thermal Transport In Additively Manufactured Metal Lattices Based On Novel Unit-Cell Topologies, Inderjot Kaur

Theses and Dissertations

The emergence of metal Additive Manufacturing (AM) over the last two decades has opened venues to mitigate the challenges associated with stochastic open-cell metal foams manufactured through the traditional foaming process. Regular lattices with user-defined unit cell topologies have been reported to exhibit better mechanical properties in comparison to metal foams which extend their applicability to multifunctional heat exchangers subjected to both thermal and mechanical loads. The current study aims at investigating the thermal-hydraulic characteristics of promising novel unit cell topologies realizable through AM technologies. Experimental investigation was conducted on four different topologies, viz (a) Octet, (b) Face-diagonal (FD) cube, …


Thermal Transport To Impinging Droplets On Superhydrophobic Surfaces, Jonathan C. Burnett Dec 2021

Thermal Transport To Impinging Droplets On Superhydrophobic Surfaces, Jonathan C. Burnett

Theses and Dissertations

An analytical model is developed to quantify the heat transfer to droplets impinging on heated superhydrophobic (SH) surfaces. Integral analysis is used to incorporate an apparent temperature jump at the superhydrophobic surface as a boundary condition. This Thesis considers the scenario of both isotropic and anisotropic slip, as would be realized on post-cavity style and rib-cavity style SH surfaces. This thermal model is combined with a hydrodynamic model which incorporates velocity slip at the surface. Use of the two models allows determination of the overall cooling effectiveness, a metric outlined in contemporary work. The effect of varying velocity slip and …


Optimizing Heat Pipes With Partially-Hybrid Mesh-Groove Wicking Structures And Its Capillary-Flowing Analysis By Simulation, Guanghan Huang Jul 2021

Optimizing Heat Pipes With Partially-Hybrid Mesh-Groove Wicking Structures And Its Capillary-Flowing Analysis By Simulation, Guanghan Huang

Theses and Dissertations

Heat pipes are known as efficient two-phase heat transfer devices and widely utilized in thermal management of power plants and electronics. The hybrid mesh-groove wick promises to attain a higher thermal performance of the heat pipe by balancing the permeability and capillarity. However, traditional fully hybrid mesh-groove wick presents considerable condensation thermal resistance due to the condensed quiescent working fluid and thick, saturated wick.

In this study, a novel partially hybrid mesh-groove wick has been proposed to enhance the evaporation of L-shaped copper-ethanol heat pipes. L-shaped heat pipe promotes high-efficient draining of condensed liquid by gravity, while traditional straight-shaped heat …


Steady-State And Transient Study Of Flow Boiling In Microchannels With Microgrooves/Micronozzles, Congcong Ren Oct 2020

Steady-State And Transient Study Of Flow Boiling In Microchannels With Microgrooves/Micronozzles, Congcong Ren

Theses and Dissertations

Microchannel flow boiling is one of the most desired cooling solutions for high power electronics. Owing to the high latent heat of vaporization, high heat fluxes can be achieved through phase-change heat transfer. However, the enhancements of (critical heat flux) CHF and heat transfer coefficient (HTC) are usually inhibited by the transitional flow patterns, which highly influence the liquid rewetting. In the past two decades, many techniques have been explored to enhance the liquid rewetting in microscale.

In this dissertation, four parallel micro-grooves fabricated on the bottom of five microchannels (W=200 μm, H=250 μm, L=10 mm) were designed to promote …


Jet Impingement Heat Transfer From Superheated, Superhydrophobic Surfaces, David Jacob Butterfield Jul 2020

Jet Impingement Heat Transfer From Superheated, Superhydrophobic Surfaces, David Jacob Butterfield

Theses and Dissertations

Liquid jet impingement is a technique ubiquitously used to rapidly remove large amounts of heat from a surface. Several different regions of heat transfer spanning from forced convection to nucleate, transition, and film boiling can occur very near to one other both temporally and spatially in quenching or high wall heat flux scenarios. Heat transfer involving jet impingement has previously shown dependency both on jet characteristics such as flow rate and temperature as well as surface material properties. Water droplets are known to bead up upon contact with superhydrophobic (SH) surfaces. This is due to reduced surface attraction caused by …


Modeling Nonlinear Heat Transfer For A Pin-On-Disc Sliding System, Brian A. Boardman Mar 2020

Modeling Nonlinear Heat Transfer For A Pin-On-Disc Sliding System, Brian A. Boardman

Theses and Dissertations

The objective of this research is to develop a numerical method to characterize heat transfer and wear rates for samples of Vascomax® 300, or Maraging 300, steel. A pin-on-disc experiment was conducted in which samples were exposed to a high-pressure, high-speed, sliding contact environment. This sliding contact generates frictional heating that influences the temperature distribution and wear characteristics of the test samples. A two-dimensional nonlinear heat transfer equation is discretized and solved via a second-order explicit finite difference scheme to predict the transient temperature distribution of the pin. This schematic is used to predict the removal of material from the …


Thermal Atomization Due To Boiling During Droplet Impingement On Superhydrophobic Surfaces, Preston Todd Emerson Jan 2020

Thermal Atomization Due To Boiling During Droplet Impingement On Superhydrophobic Surfaces, Preston Todd Emerson

Theses and Dissertations

Superhydrophobic (SH) surfaces are characterized by their extraordinary water repellent qualities. When water comes in contact with these surfaces, it beads up and rolls around. This phenomenon is due partially to surface chemistry which promotes weak adhesive forces between liquid and solid. However, micro- and nanoscale surface roughness also plays a crucial role by trapping air beneath the liquid, reducing liquid-solid contact. Many advantages of these surfaces have been identified, including drag reduction and self-cleaning properties, and the body of research regarding them has grown rapidly over the past few decades.This thesis is concerned with water droplets impinging superheated, superhydrophobic …


Enhanced Heat Transfer In Spray Cooling Through Surface Modifications: An Experimental And Computational Study, Azzam Saadi Salman Oct 2019

Enhanced Heat Transfer In Spray Cooling Through Surface Modifications: An Experimental And Computational Study, Azzam Saadi Salman

Theses and Dissertations

Today, dissipating high heat flux safely is one of the greatest challenges for thermal engineers in thermal management systems, and it becomes a critical barrier to technological developments for many engineering applications. Due to technological advances and aggressive micro-miniaturization of electronic components, the surface area of most devices has shrunk while the computational power increased exponentially. Therefore, the amount of heat dissipated from surfaces has increased significantly. Numerous cooling techniques have been introduced to replace the traditional air cooling systems and to maintain the efficiency and reliability of electronic components. Microelectronics work efficiently and safely at surface temperatures of < 100 ℃ and 125 ℃ for general and defense applications, respectively. One of the proposed alternative schemes is spray cooling, which is considered one of the most advanced cooling methods. It is used for high and ultra-high heat flux dissipation, as it can dissipate 150-200 W/cm2 while maintaining the surface temperature within this range. Also, spray cooling removes a large amount of energy at a lower liquid flow rate compared to other cooling techniques, such as jet impingement and microchannel heat sink. The thermal performance of spray cooling systems can be enhanced either actively or passively. Active enhancement is a very efficient technique; however, it adds more pumping power. The present work focuses on three main objectives: evaluating and analyzing spray cooling performance, developing a three-dimensional numerical multi-phase model for heat transfer process in spray cooling and enhancing the thermal performance of spray cooling passively.

First, …


A Model For Condensation Heat Transfer In Hydrophobic-­Hydrophilic Surfaces, Abdulwahab E. Alhashem Jul 2019

A Model For Condensation Heat Transfer In Hydrophobic-­Hydrophilic Surfaces, Abdulwahab E. Alhashem

Theses and Dissertations

The primary focus of this research is to provide a validated model for a comprehensive understanding of hydrophobic-­‐hydrophilic condensation on patterned-­‐ hybrid surface. Establishing the model requires the modeling of fully dropwise condensation (DWC) before applying modifications to evaluate heat transfer performance of patterned-­‐hybrid condensation surface.

The model for fully DWC consists of defining expressions for heat transfer through a single drop, maximum radius of the drop and drop-­‐size distribution which all are primarily based on the work in the literature. In this work the author utilized a proposed modified version of the simulation for drop-­‐size distribution for fully DWC, …


Numerical Analysis On Convective Cooling Augmented By Evaporative Heat And Mass Transfer For Thermal Power Plant Application, Sudipta Saha Apr 2019

Numerical Analysis On Convective Cooling Augmented By Evaporative Heat And Mass Transfer For Thermal Power Plant Application, Sudipta Saha

Theses and Dissertations

This thesis work describes a numerical study on the effect of evaporative cooling on the augmentation of forced convective cooling. In recent years, on-demand phase change boosted cooling has drawn major interest where convective heat transfer is augmented/aided by evaporative heat and mass transport processes. This dual mode (convection and evaporation) cooling method is envisioned to drastically enhance the heat transfer coefficient where conventional convective cooling has already reached its maximum value and furthermore dry cooling is still a desired objective. A multi- dimensional mathematical model has been developed to conduct simulations over a range of operating parameters to obtain …


Characterization Of Pyrolysis Products From Fast Pyrolysis Of Live And Dead Vegetation, Mohammad Saeed Safdari Dec 2018

Characterization Of Pyrolysis Products From Fast Pyrolysis Of Live And Dead Vegetation, Mohammad Saeed Safdari

Theses and Dissertations

Wildland fire, which includes both planned (prescribed fire) and unplanned (wildfire) fires, is an important component of many ecosystems. Prescribed burning (controlled burning) is used as an effective tool in managing a variety of ecosystems in the United States to reduce accumulation of hazardous fuels, manage wildlife habitats, mimic natural fire occurrence, manage traditional native foods, and provide other ecological and societal benefits. During wildland fires, both live and dead (biomass) plants undergo a two-step thermal degradation process (pyrolysis and combustion) when exposed to high temperatures. Pyrolysis is the thermal decomposition of organic material, which does not require the presence …


Material Thermal Property Estimation Of Fibrous Insulation: Heat Transfer Modeling And The Continuous Genetic Algorithm, Elora Frye Jan 2018

Material Thermal Property Estimation Of Fibrous Insulation: Heat Transfer Modeling And The Continuous Genetic Algorithm, Elora Frye

Theses and Dissertations

Material thermal properties are highly sought after to better understand the performance of a material under particular conditions. As new materials are created, their physical properties will determine their performance for various applications. These properties have been estimated using many techniques including experimental testing, numerical modeling, and a combination of both. Existing methods can be time consuming, thus, a time-efficient and precise method to estimate these thermal properties was desired. A one-dimensional finite difference numerical model was developed to replicate the heat transfer through an experimental apparatus. A combination of this numerical model and the Continuous Genetic Algorithm optimization technique …


Design And Analysis Of Compressed Air Power Harvesting Systems, Zachary James Sadler Dec 2017

Design And Analysis Of Compressed Air Power Harvesting Systems, Zachary James Sadler

Theses and Dissertations

Procedure for site discovery, system design, and optimization of power harvesting systems is developed with an emphasis on application to air compressors. Limitations for the usage of infrared pyrometers is evaluated. A system of governing equations for thermoelectric generators is developed. A solution method for solving the system of equations is created in order to predict power output from the device. Payback analysis is proposed for determining economic viability. A genetic algorithm is used to optimize the power harvesting system payback with changing quantities and varieties of thermoelectric generators, as well as the back work put into cooling the thermoelectric …


Design And Analysis Of Compressed Air Power Harvesting Systems, Zachary James Sadler Dec 2017

Design And Analysis Of Compressed Air Power Harvesting Systems, Zachary James Sadler

Theses and Dissertations

Procedure for site discovery, system design, and optimization of power harvesting systems is developed with an emphasis on application to air compressors. Limitations for the usage of infrared pyrometers is evaluated. A system of governing equations for thermoelectric generators is developed. A solution method for solving the system of equations is created in order to predict power output from the device. Payback analysis is proposed for determining economic viability. A genetic algorithm is used to optimize the power harvesting system payback with changing quantities and varieties of thermoelectric generators, as well as the back work put into cooling the thermoelectric …


Hydrodynamic And Thermal Effects Of Sub-Critical Heating On Superhydrophobic Surfaces And Microchannels, Adam M. Cowley Nov 2017

Hydrodynamic And Thermal Effects Of Sub-Critical Heating On Superhydrophobic Surfaces And Microchannels, Adam M. Cowley

Theses and Dissertations

This dissertation focuses on the effects of heating on superhydrophobic (SHPo) surfaces. The work is divided into two main categories: heat transfer without mass transfer and heat transfer in conjunction with mass transfer. Numerical methods are used to explore the prior while experimental methods are utilized for the latter. The numerical work explores convective heat transfer in SHPo parallel plate microchannels and is separated into two stand-alone chapters that have been published archivally. The first considers surfaces with a rib/cavity structure and the second considers surfaces patterned with a square lattice of square posts. Laminar, fully developed, steady flow with …


Modeling Atypical Building Use With Commercially Available Building Simulation Software, Sarah E. Schanck Jul 2016

Modeling Atypical Building Use With Commercially Available Building Simulation Software, Sarah E. Schanck

Theses and Dissertations

National Guard armories are audited to provide recommendations for future energy reduction measures. The annual energy consumption of a New Jersey National Guard Armories cannot be modeled directly with commercially available building simulation software, due to discrepancies between the modeling capabilities of the software and the reality of the armory. A building simulation software, eQUEST, was chosen for use in this project. Discrepancies between eQUEST inputs and reality were identified and correction factors developed to minimize the effect of each discrepancy on predicted energy consumption, with the end goal of accuracy between predicted and actual energy consumption. In addition, an …


Measurement And Modeling Of Fire Behavior In Leaves And Sparse Shrubs, Dallan R. Prince Jul 2014

Measurement And Modeling Of Fire Behavior In Leaves And Sparse Shrubs, Dallan R. Prince

Theses and Dissertations

Wildland fuels and fire behavior have been the focus of numerous studies and models which provide operational support to firefighters. However, fuel and fire complexity in live shrubs has resulted in unexpected and sometimes aggressive fire behavior. The combustion of live fuels was studied and modeled, and the results were assimilated into a shrub-scale fire behavior model which assumes fire spread by flame-fuel overlap. Fire spread models have usually assumed that radiation heat transfer is responsible for driving fire spread, but that assumption is a topic of continuing debate, and appears to contradict some experimental observations. A convection-based shrub-scale fire …


Characterization And Optimization Of Thermal Protective Fabrics Designed To Protect Against Splash Hazards, Jeremy Osguthorpe Jun 2014

Characterization And Optimization Of Thermal Protective Fabrics Designed To Protect Against Splash Hazards, Jeremy Osguthorpe

Theses and Dissertations

Thermal textiles used in Personal Protective Equipment (PPE) are used to protect individuals from the hazards of thermal energy. An analytical model of the diffusion of thermal energy within the fabric was developed to simulate the transfer of thermal energy due to a hot liquid splash. Based on the model results, it was determined that that the use of an orthotropic material in which the thermal conductivities in the radial and axial directions are different can be used to decrease the amount of heat transferred through the fabric and thereby increase amount of protection in PPE. An orthotropic material particularly …


Heat Transfer Enhancement By Three-Dimensional Surface Roughness Technique In Nuclear Fuel Rod Bundles, Kang Liu Jan 2014

Heat Transfer Enhancement By Three-Dimensional Surface Roughness Technique In Nuclear Fuel Rod Bundles, Kang Liu

Theses and Dissertations

DISS_abstract> This thesis investigate thermal characteristic of a single-phase nano-fluid in a single heater element loop tester and provides a comparison between heat transfer enhancement results achieved using water as a coolant and using nano-fluids with different volume percentage. The experimental investigation is performed on two simulated nuclear fuel rods with two different types of modified outer surfaces roughness. The fuel rod surfaces modified are termed as two-dimensional surface roughness (square transverse ribbed surface) and three-dimensional surface roughness (Diamond shaped blocks). The nano-fluid used are 0.5% and 2% ZnO-Deionized water based nano-fluid. The maximum heat transfer co-efficient enhancement achieved compared …


Thermal Transport To Sessile Water Droplets On Heated Superhydrophobic Surfaces Of Varying Cavity Fraction, Robb C. Hays Aug 2013

Thermal Transport To Sessile Water Droplets On Heated Superhydrophobic Surfaces Of Varying Cavity Fraction, Robb C. Hays

Theses and Dissertations

The hydrophobicity of a surface is defined as the degree to which it repels water molecules, and the internal contact angle that the droplet makes with the surface is a measure of the hydrophobicity. Contact angles less than 90° occur on hydrophilic surfaces, while contact angles greater than 90° occur on hydrophobic surfaces. If a surface's contact angle is greater than 120° the surface is commonly defined as superhydrophobic (SH). Superhydrophobicity is accomplished through a combination of microscale surface roughness and water repellant surface chemistry. The roughness creates cavities, or pockets, of vapor underneath the droplet which act to increase …


Boiling And Evaporation On Micro/Nanoengineered Surfaces, Xianming Dai Jan 2013

Boiling And Evaporation On Micro/Nanoengineered Surfaces, Xianming Dai

Theses and Dissertations

Two-phase transport is widely used in energy conversion and storage, energy efficiency and thermal management. Surface roughness and interfacial wettability are two major impact factors for two-phase transport. Micro/nanostructures play important roles in varying the surface roughness and improving interfacial wettability. In this doctoral study, five types of micro/nanoengineered surfaces were developed to systematically study the impacts of interfacial wettability and flow structures on nucleate boiling and capillary evaporation. These surfaces include: 1) superhydrophilic atomic layer deposition (ALD) coatings; 2) partially hydrophobic and partially hydrophilic composite interfaces; 3) micromembrane-enhanced hybrid wicks; 4) superhydrophilic micromembrane-enhnaced hybrid wicks, and 5) functionalized carbon …


Measurement Of Thermal Diffusivities Using The Distributed Source, Finite Absorption Model, James B. Hall Nov 2012

Measurement Of Thermal Diffusivities Using The Distributed Source, Finite Absorption Model, James B. Hall

Theses and Dissertations

Thermal diffusivity in an important thermophysical property that quantifies the ratio of the rate at which heat is conducted through a material to the amount of energy stored in a material. The pulsed laser diffusion (PLD) method is a widely used technique for measuring thermal diffusivities of materials. This technique is based on the fact that the diffusivity of a sample may be inferred from measurement of the time-dependent temperature profile at a point on the surface of a sample that has been exposed to a pulse of radiant energy from a laser or flash lamp. An accepted standard approach …


Radiation And Convection Heat Transfer In Wildland Fire Environments, David J. Frankman Jul 2009

Radiation And Convection Heat Transfer In Wildland Fire Environments, David J. Frankman

Theses and Dissertations

Wildland fire research has been extensive and on going since before 1950. The motivation behind this research is to prevent loss of property and lives. In spite of this research, the heat transfer of fuel ignition and flame spread is not well understood. This dissertation seeks to fill gaps in this understanding through modeling and also by experimentation. The effect of water vapor on the transmission of thermal radiation from the flame to the fuel was investigated. The Spectral Line Weighted-sum-of-gray-gases approach was adopted for treating the spectral nature of the radiation. The study reveals that water vapor has only …


The Impact Of Heat Release In Turbine Film Cooling, Dave S. Evans Jun 2008

The Impact Of Heat Release In Turbine Film Cooling, Dave S. Evans

Theses and Dissertations

The Ultra Compact Combustor is a design that integrates a turbine vane into the combustor flow path. Because of the high fuel-to-air ratio and short combustor flow path, a significant potential exists for unburned fuel to enter the turbine. Using contemporary turbine cooling vane designs, the injection of oxygen-rich turbine cooling air into a combustor flow containing unburned fuel could result in heat release in the turbine and a large decrease in cooling effectiveness. The current study explores the interaction of cooling flow from typical cooling holes with the exhaust of a fuel-rich well-stirred-reactor operating at high temperatures over a …


Evolution Of Turbine Blade Deposits In An Accelerated Deposition Facility: Roughness And Thermal Analysis, James Edward Wammack Nov 2005

Evolution Of Turbine Blade Deposits In An Accelerated Deposition Facility: Roughness And Thermal Analysis, James Edward Wammack

Theses and Dissertations

During the operation of a gas turbine, ingested contaminants present in the air form deposits on the surfaces of the turbine blades. These deposits grow over time, resulting in an increasingly rough surface. This gradual increase in roughness results in several negative consequences, among which is an increase in the rate of heat transfer to the blade which shortens blade life. This thesis presents research in which deposits were evolved on three different turbine blade coupons and their evolution was studied. A trend in roughness change over time was discovered. Also, an attempt was made to find the effect of …


Approximate Thermal Modeling Of Radiofrequency Cardiac Ablation, Aaron Joseph Walter Aug 2005

Approximate Thermal Modeling Of Radiofrequency Cardiac Ablation, Aaron Joseph Walter

Theses and Dissertations

The ultimate objective of the research which led to this thesis is to increase the efficacy and safety of radiofrequency catheter ablation (RFCA) of cardiac tissue. The purpose of RFCA is to carefully heat selected locations in the heart. The resulting thermal injury creates lesions which prevent the generation or propagation of arrhythmias. The ability to predict the appropriate amount of energy required at any ablation site is essential to increasing the efficacy and safety of RFCA. The research documented in this thesis focuses on the development of an approximate thermal model of the time-dependent temperature profile within the myocardium …