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Heat transfer

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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 …


Measurement Of Conduction, Radiation, And Convection Thermal Energy To Assess Baking Performance In Residential Ovens., Sean Simpson Aug 2023

Measurement Of Conduction, Radiation, And Convection Thermal Energy To Assess Baking Performance In Residential Ovens., Sean Simpson

Electronic Theses and Dissertations

Residential ovens are complicated thermal environments capable of delivering convection, conduction, and radiation heat transfer to food. The amount and mode of heat transfer can change based on the design of the oven cavity, cooling systems, and oven cycle algorithms. Studies have shown that the changes in one heat transfer mode can have an impact on the quality of baked goods. The many variables involved make designing residential ovens a time consuming and costly process. The goal of this study is to adapt thermal energy sensing technology to collect energy data from a residential oven and develop correlations to quality …


Thermal Boundary Condition Effects On Local Supercritical Co2 Heat Transfer Trends In Tubes, Nicholas C. Lopes Apr 2023

Thermal Boundary Condition Effects On Local Supercritical Co2 Heat Transfer Trends In Tubes, Nicholas C. Lopes

Doctoral Dissertations and Master's Theses

Supercritical carbon dioxide (sCO2) is a promising heat transfer fluid for the refrigeration and power generation industries due to its unique thermal properties and low environmental impact. To understand it as an alternative to traditional working fluids, the thermophysical and heat transfer phenomena of sCO2 are often studied using simplified geometries (tubes). Focus has been placed on investigating averaged heat transfer trends under an array of flow conditions with either a constant wall heat flux, constant wall temperature, or conjugate thermal boundary condition. Less emphasis has been placed on studying local sCO2 heat transfer developments. Tubular sCO2 numerical models that …


Thermal Analysis Based Design Of Hollow Shaft For Improved Cooling Of Induction Motors, Isabelle Dinh Jan 2023

Thermal Analysis Based Design Of Hollow Shaft For Improved Cooling Of Induction Motors, Isabelle Dinh

Electronic Theses and Dissertations

This thesis investigates methods of implanting a forced liquid convection heat recovery system within an induction motor’s shaft to cool the rotor.

The objective is to design a hollow shaft that can meet the target goals of keeping the components under an average temperature of 100℃ under different motor power conditions. Three hollow shaft design cases were studied at steady state conditions to evaluate their heat transfer performance and surface temperature to meet the goals of the study. This includes the design of a counterflow, counterflow with fins, and duct design.

It is found that third design is able to …


Measurement Of Low-Speed Impinging Jet Structure Using Temperature Sensitive Paint, Arthur Dean Woodworth Dec 2022

Measurement Of Low-Speed Impinging Jet Structure Using Temperature Sensitive Paint, Arthur Dean Woodworth

Masters Theses

Temperature sensitive paint (TSP) is used to analyze surface flow structures driven by a jet impinging on a heated steel sheet. Temperature and Nusselt number images are calculated from CCD images of the TSP surface. TSP calibration is discussed. Skin friction data is obtained from the temperature images.

Data is collected for metal and 3D-printed plastic nozzles of varying shape and size at one or two jet airspeeds depending on the nozzle. For the circular nozzles, data is collected for four Reynolds numbers at impinging angles of 90, 70, and 50 degrees. For the elliptical nozzles and the star-shaped nozzle, …


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. …


Biomass Characterization And Insulation Optimization Studies, Hussein Awad Kurdi Saad Nov 2022

Biomass Characterization And Insulation Optimization Studies, Hussein Awad Kurdi Saad

Doctoral Dissertations and Master's Theses

This study indicates how biomass materials can be effectively used as naturally sustainable alternatives to insulation materials. Barley grains and oak leaves, straw, and jute are collected, and crushed into powders/ chopped pieces. The physical characteristics are measured to characterize each powder. The biomass powder reinforced composites are manufactured in varying weight ratios. The density and thermal conductivity of composite materials are measured. The properties of composites compared to those of commercial insulation materials are found to be close to them. Furthermore, genetic algorithms (GA) can be used to achieve multi-objective optimization entailing maximizing insulation (minimizing heat transfer) and simultaneously …


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, …


Development And Applications Of A Sensor For Measurement Of Different Modes Of Heat Transfer On Foods In A Residential Oven., Kervins Petit-Bois Aug 2022

Development And Applications Of A Sensor For Measurement Of Different Modes Of Heat Transfer On Foods In A Residential Oven., Kervins Petit-Bois

Electronic Theses and Dissertations

Thermal characterization of an oven is an important part of designing an oven. Understanding how changes in cooking algorithm, oven construction, and oven materials affect cooking performance is critical in ensuring that an oven is properly designed. Often temperature data is used to characterize oven behavior, but this neglects the mode of heat transfer used to achieve these temperatures. Several studies have compared the different modes of heat transfer and cooking performance and have shown that cooking performance in radiation dominated modes are different than in convection dominated modes. The goal of this study is to develop a heat flux …


Mmteg Heatsink Design, Peyton Nienaber, Kadin Feldis, Alec Savoye, Jack Waeschle Jun 2022

Mmteg Heatsink Design, Peyton Nienaber, Kadin Feldis, Alec Savoye, Jack Waeschle

Mechanical Engineering

In this document, Cal Poly Senior Design Team F16 presents a summary of its work developing a suitable heatsink for Gas Technology Institute’s Methane Mitigation Thermoelectric Generator. After several months of iterating between experimental testing and simulated heat transfer, a suitable prototype was selected for use in further refining simulation parameters. This was called the structural prototype and it allowed Team F16 to confirm several remaining unknowns relating to component thermal conductivity. All documentation of this process can be found in Preliminary, Critical, and Interim Design Review documents (PDR, CDR, IDR), included in this report. Having a realistic model …


Thermal Management Using Liquid-Vapor Phase Change In Nanochannels, Sajag Poudel May 2022

Thermal Management Using Liquid-Vapor Phase Change In Nanochannels, Sajag Poudel

Dissertations - ALL

Superior wettability of porous medium marks their potential to be used in the field of thermal management employing phase-change heat transfer. Comprehending the phenomena of wicking and liquid-vapor phase-change in micro/nano structured surfaces are key aspects towards advancing heat transfer solutions. In this work, fundamental understanding of droplet wicking, thin-film evaporation, and their subsequent application of heat-flux removal for cooling technology is first reported. The latter part of the dissertation is related to the disjoining pressure driven flow of nanoscale liquid film and liquid-vapor phase change in nano confinement. First, experimental and numerical investigation of droplet wicking in ∼728 nm …


Thermodynamic Analysis Of A Novel Cycle For Nuclear Smr And Heat Transfer Performance Validation Of The Related Supercritical Working Fluids, Benjamin M. Pepper May 2022

Thermodynamic Analysis Of A Novel Cycle For Nuclear Smr And Heat Transfer Performance Validation Of The Related Supercritical Working Fluids, Benjamin M. Pepper

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Currently, all operating nuclear power facilities in the U.S. follow the same general design and process: light-water reactors boil water into steam using bundles of nuclear fuel rods as a heat source, pumping that steam through a turbine which powers a generator to produce clean year-round electricity. Water is an effective coolant, but other facilities around the world have demonstrated the ability to use non-water-based coolants in nuclear reactor designs, which consequently have their own trade-offs. Some positive consequences of using different reactor designs include enhanced safety, better economics, and cheaper clean consumer energy. The work described in this paper …


Cooling Systems Analysis For Plastic Mold Injection Tools, Veronica Flores Quijada Apr 2022

Cooling Systems Analysis For Plastic Mold Injection Tools, Veronica Flores Quijada

Electronic Thesis and Dissertation Repository

The Plastic Injection Mold (PIM) industry has been searching for new technologies that improve the manufacturing of parts by reducing the production time and cost as well as increasing the quality of the product. The cooling systems in the PIM are designed initially to be straight-drilled into the mold, but this manufacturing process has traditionally not been very effective, since for molded parts with complex geometries, the cooling channels are not able to reach certain areas. This limitation has led the industry to develop conformal cooling channels that use the additive manufacturing technology, which allows the cooling channels to conform …


Computational Sodium Heat Pipe Simulation In Three Dimensions For Transient Nuclear Reactor Analysis With Variable Surface Heat Flux, Valerie Jean Lawdensky Dec 2021

Computational Sodium Heat Pipe Simulation In Three Dimensions For Transient Nuclear Reactor Analysis With Variable Surface Heat Flux, Valerie Jean Lawdensky

UNLV Theses, Dissertations, Professional Papers, and Capstones

Heat pipes are used to transfer heat through phase change in a liquid/vapor contained in a metal tube. They are passive devices that require no pumps to circulate the fluid and can transfer heat far more efficiently than a solid copper rod of the same diameter. They are commonly used in laptop computers where copper heat pipes filled with water take heat away from the CPU and transfer the heat to air through a heat exchanger. Heat pipes were also used in the Kilopower nuclear reactor where higher temperatures required sodium as the working fluid with stainless steel tubes. Computer …


Investigation Of Microdroplet Generation, Morphological Evolution, And Applications Under Quasi-Steady And Dynamic States, Li Shan Aug 2021

Investigation Of Microdroplet Generation, Morphological Evolution, And Applications Under Quasi-Steady And Dynamic States, Li Shan

McKelvey School of Engineering Theses & Dissertations

Microscale droplets are commonly encountered in the fields of materials processing, thermal fluids, and biology. While these droplets are naturally occurring, recent advances in microfabrication have enabled researchers to harness their enhanced transport characteristics for numerous laboratory and industrial applications from controlled chemical synthesis to inkjet printing and thermal management. Smaller droplets have larger specific surface area and a greater perimeter-to-area ratio when resting on a surface (i.e., sessile), which accelerates processes occurring at droplet surfaces like evaporation, chemical reaction, or combustion. The demand for microdroplets with smaller and more uniform sizes has motivated investigation of how such droplets can …


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 …


Binary Particle Mixtures As A Heat Transfer Media In Shell-And-Plate Moving Packed Bed Heat Exchangers, Chase Ellsworth Christen May 2021

Binary Particle Mixtures As A Heat Transfer Media In Shell-And-Plate Moving Packed Bed Heat Exchangers, Chase Ellsworth Christen

Boise State University Theses and Dissertations

Solid particles are being considered in several high temperature thermal energy storage systems and as heat transfer media in concentrated solar power (CSP) plants. The downside of such an approach is the low overall heat transfer coefficients in shell-and-plate moving packed bed heat exchangers caused by the inherently low packed bed thermal conductivity values of the low-cost solid media. Choosing the right particle size distribution of currently available solid media can make a substantial difference in packed bed thermal conductivity, and thus, a substantial difference in the overall heat transfer coefficient of shell-and-plate moving packed bed heat exchangers. Current research …


Relationship Between Thermal Conductivity And Free Electrons In Metal, Yansong Liu Apr 2021

Relationship Between Thermal Conductivity And Free Electrons In Metal, Yansong Liu

Senior Theses

An experiment was designed and conducted to explore the relationship between thermal conductivity with free electrons in metal. In the experiment, copper, iron, aluminum, and titanium rods with close diameters were used to carry out the experiment. Each rod was heated up by a heat unit at one end while cooled on the other end with a heat sink to maintain a steady state. DC current was applied to rods in the direction along, as well as against, the heat flow. Thermal conductivities were measured in these two situations for each rod. Results showed electrons do dominate thermal flow inside …


Heat Transfer Modeling And Optimization Of A Carbonized Microvascular Solar Receiver, Taylor Brown Dec 2020

Heat Transfer Modeling And Optimization Of A Carbonized Microvascular Solar Receiver, Taylor Brown

Boise State University Theses and Dissertations

Concentrating solar power is an emerging renewable energy source. The technology can collect and store thermal energy from the sun over long durations, generating electricity as needed at a later time. Current CSP systems are limited to a maximum operational temperature due to constraints of the working fluid, which limits the maximum possible efficiency of the system. One proposed pathway forward is to utilize a gas phase for the working fluid in the system such as supercritical carbon dioxide.

A composite gas phase modular receiver is being developed by researchers at Boise State University and the University of Tulsa. The …


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 …


Transient Thermal Modeling Of Bioprocessing Equipment, Cody M. Cummings Aug 2020

Transient Thermal Modeling Of Bioprocessing Equipment, Cody M. Cummings

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Bioprocessing is leveraging cells to produce high value, lifesaving products. Precise environmental control is needed to maintain integrity of the bioprocessing production process. Temperature control requires both appropriate equipment choice and correct control parameter selection. To aid in the equipment selection process, enable better understanding of equipment capacity, and enable optimization of control parameters, a transient thermal model of both heat transfer characteristics and control systems was created in silico.


Experimental Evaluation Of Heat Leak And Convective Heat Transfer In A Household Freezer., Catherine E. Berghuis May 2020

Experimental Evaluation Of Heat Leak And Convective Heat Transfer In A Household Freezer., Catherine E. Berghuis

Electronic Theses and Dissertations

Heat leak into household refrigerated cabinets is a key driver affecting energy consumption and efficiency of the cooling system. Additionally, knowledge of heat transfer coefficients of internal surfaces is valuable in the development of cabinet and system level performance simulations. Several studies have examined heat leak of refrigeration units using heat flux sensors (HFS); however, no such studies have used heat flux measurements to derive convective heat transfer coefficients of the refrigerated unit walls. The goal of this study is to evaluate the use of HFS to quantify heat leak into a 490-liter freezer and determine the wall convective heat …


Thermal Contact Resistance Measurement And Related Uncertainties, Amanda Elizabeth Stark Apr 2020

Thermal Contact Resistance Measurement And Related Uncertainties, Amanda Elizabeth Stark

Mechanical & Aerospace Engineering Theses & Dissertations

Thermal contact resistance is an important parameter in detailed thermal analysis and design of aerospace systems. The ability to determine thermal contact resistance reliably can have a significant impact on the fidelity of thermal models—particularly for space applications. The 2004 NASA Langley Research Center thermal contact resistance test apparatus has been employed to evaluate two methods for inferring estimated interface surface temperatures so that thermal contact resistance can be calculated more accurately. The traditional method of extrapolation is a steady-state approach, while the new method utilizes inverse heat transfer techniques to account for inherent unsteadiness in these quasi-steady-state measurements. The …


Assessment And Improvement Of Computational Fluid Dynamics Methods For Separated Turbulent Flows At Low Reynolds Numbers, Tom Mancuso Jan 2020

Assessment And Improvement Of Computational Fluid Dynamics Methods For Separated Turbulent Flows At Low Reynolds Numbers, Tom Mancuso

Dissertations, Master's Theses and Master's Reports

This study investigates the accuracy of Computational Fluid Dynamics (CFD) models to predict heat transfer in turbulent separated flows at low Reynolds numbers. A novel improvement of a Scale Adaptive technique is also presented. A spectrum of turbulence models is used to simulate flow and heat transfer of two geometries; fully developed flow through a staggered tube bank and a square prism in cross flow. Experimental data for both local heat transfer and velocity data are available in the literature for these cases and have been used extensively evaluate various CFD methods. Six unsteady models were used and the results …


Heat Exchanger, Chance Linarez Jan 2020

Heat Exchanger, Chance Linarez

All Undergraduate Projects

A water jet cutting machine can cause excess heat and humidity within a closed building, while also making it more difficult for the user to pick material off the cutting table. Water temperatures can reach as high as 150 degrees Fahrenheit in the tank. A system that would reduce the temperature of the water in a water jet tank would be beneficial for the occupants in the room in providing a better more comfortable work environment. Data was collected while the machine was in use. The data includes; temperature of water leaving the nozzle, the rate of change of tank …


Critical Radius Of Insulation, Maria N. Ambrose, Samuel J. Sayre, Travis W. Martin, Matt T. Sterling Dec 2019

Critical Radius Of Insulation, Maria N. Ambrose, Samuel J. Sayre, Travis W. Martin, Matt T. Sterling

Mechanical Engineering

The critical radius of insulation is a counterintuitive concept within the study of heat transfer. The theory states that adding insulation to a cylindrical or spherical object will increase the rate of heat loss rather than decrease it, if the radius (thickness) of the insulation is at its “critical” value. The Critical Radius of Insulation Senior Project is designed to demonstrate this phenomenon to Heat Transfer students via a portable apparatus. The concept will be demonstrated with a cylindrical object which is heated by way of a separate voltage source. Thermocouples will display the temperature of the cylinder while insulation …


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, …


Development Of Heat Transfer Correlations For Low-Reynolds Numbers, Flows In Horizontal Circular Pipes, Latif Eyada Ibraheem Jun 2019

Development Of Heat Transfer Correlations For Low-Reynolds Numbers, Flows In Horizontal Circular Pipes, Latif Eyada Ibraheem

Dissertations

Turbulent flows are intrinsic to most fluid-based engineering systems, including internal combustion engines. In these devices, mixing, scalar transport and heat transfer are both critical for proper operation and challenging to model. In previous work, Kreun et al. [1] modeled a pre-heated intake manifold of a Diesel engine for cold-start simulations. Accurately predicting the heat transfer at the intake port proved to be a challenging task. Existing heat transfer correlations yielded predictions which were (at best) within 20% of the measured values. The discrepancy was attributed to a mismatch between the range of applicability of existing heat transfer models and …


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 …