heat diffusion equation
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Author(s):  
M. D. Asiddao ◽  
V. P. Bongolan

Abstract. Metro Manila, home to twelve-million residents scattered in densely populated cities, grows its population at a rate of 1.21% annually. Areas of the metro occupied by residents falling under the poverty line have only been increasing in density per year, and have been prone to fire incidents. One such area, Barangay Addition Hills in Mandaluyong City, has fallen victim to two disastrous fires four years apart: in 2016 and 2020. This study aims to accurately model a portion of Barangay Addition Hills when a fire starts in one of the most densely populated blocks while observing firefighters responding to the incident. The agent-based model adapts features from (Wilensky, 2006)’s Fire model and is virtually simulated with the help of two-dimensional satellite images of the area. The fire-spreading algorithm incorporates solving the heat diffusion equation to determine ignition time of combustible materials per unit area. Firefighters have been incorporated into the model with the help of the Bureau of Fire Protection (BFP)’s Operational Procedures Manual to determine their expected behavior when responding to a fire alarm. Simulations were run on a per-incident basis to determine the total affected area, estimated affected families, and time for the fire to be put under control under varying densities, traffic conditions, firefighter response times and manpower.


2021 ◽  
Vol 11 (04) ◽  
pp. 1-11
Author(s):  
Wanwan Li

In mechanical engineering educations, simulating fluid thermodynamics is rather helpful for students to understand the fluid’s natural behaviors. However, rendering both high-quality and realtime simulations for fluid dynamics are rather challenging tasks due to their intensive computations. So, in order to speed up the simulations, we have taken advantage of GPU acceleration techniques to simulate interactive fluid thermodynamics in real-time. In this paper, we present an elegant, basic, but practical OpenGL/SL framework for fluid simulation with a heat map rendering. By solving Navier-Stokes equations coupled with the heat diffusion equation, we validate our framework through some real-case studies of the smoke-like fluid rendering such as their interactions with moving obstacles and their heat diffusion effects. As shown in Fig. 1, a group of experimental results demonstrates that our GPU-accelerated solver of Navier-Stokes equations with heat transfer could give the observers impressive real-time and realistic rendering results.


2021 ◽  
Author(s):  
ANDO Shizutoshi

Edge preserving filters preserve the edges and its information while blurring an image. In other words they are used to smooth an image, while reducing the edge blurring effects across the edge like halos, phantom etc. They are nonlinear in nature. Exam?ples are bilateral filter, anisotropic diffusion filter, guided filter, trilateral filter etc. Hence these family of filters are very useful in reducing the noise in an image making it very demanding in computer vision and computational photography applications like de?noising, video abstraction, demosaicing, optical-flow estimation, stereo matching, tone mapping, style transfer, relighting etc. This paper provides a concrete introduction to edge preserving filters starting from the heat diffusion equation in olden to recent eras, an overview of its numerous applications, as well as mathematical analysis, various efficient and optimized ways of implementation and their interrelationships, keeping focus on preserving the boundaries, spikes and canyons in presence of noise. Furthermore it provides a realistic notion for efficient implementation with a research scope for hardware realization for further acceleration.


2021 ◽  
Vol 10 (9) ◽  
pp. 3141-3164
Author(s):  
Kwassi Anani

In this paper, we analysed the spherically symmetric heat diffusion equation, which governs the temperature distribution inside a heated but non-evaporating droplet. The spherical droplet, with an initial uniform temperature, is assumed at rest in an unsteady gas environment. The classical Fourier sine integral transform (FSIT) and the unilateral Laplace integral transform (LIT) are successively used to solve the resulting initial-boundary value problem, first reduced in a dimensionless form. An explicit solution in the Laplace domain is obtained for the temperature inside the droplet. Then, depending on the time-varying temperature of the gas environment at the immediate vicinity of the droplet, an exact series solution and an approximate analytical solution in short time limits are derived for the droplet internal temperature. In the case of steady gas environment at constant temperature, the standard series solution obtained in the literature for the symmetrical problem of heating or cooling of a solid spherical body, is recovered. The results may be useful for time step analysis in droplets and sprays vaporization models.


2021 ◽  
Vol 1999 (1) ◽  
pp. 012080
Author(s):  
Mohammed Rasheed ◽  
Ali Hassan Ali ◽  
Osama Alabdali ◽  
Suha Shihab ◽  
Ahmed Rashid ◽  
...  

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 5110
Author(s):  
Yangyu Guo ◽  
Masahiro Nomura ◽  
Sebastian Volz ◽  
Jose Ordonez-Miranda

Heat transport guided by the combined dynamics of surface phonon-polaritons (SPhPs) and phonons propagating in a polar nanowire is theoretically modeled and analyzed. This is achieved by solving numerically and analytically the Boltzmann transport equation for SPhPs and the Fourier’s heat diffusion equation for phonons. An explicit expression for the SPhP thermal conductance is derived and its predictions are found to be in excellent agreement with its numerical counterparts obtained for a SiN nanowire at different lengths and temperatures. It is shown that the SPhP heat transport is characterized by two fingerprints: (i) The characteristic quantum of SPhP thermal conductance independent of the material properties. This quantization appears in SiN nanowires shorter than 1 μm supporting the ballistic propagation of SPhPs. (ii) The deviation of the temperature profile from its typical linear behavior predicted by the Fourier’s law in absence of heat sources. For a 150 μm-long SiN nanowire maintaining a quasi-ballistic SPhP propagation, this deviation can be as large as 1 K, which is measurable by the current state-of-the-art infrared thermometers.


2021 ◽  
Vol 26 (3) ◽  
pp. 52
Author(s):  
Anthony S. Walker ◽  
Kyle E. Niemeyer

The partial differential equations describing compressible fluid flows can be notoriously difficult to resolve on a pragmatic scale and often require the use of high-performance computing systems and/or accelerators. However, these systems face scaling issues such as latency, the fixed cost of communicating information between devices in the system. The swept rule is a technique designed to minimize these costs by obtaining a solution to unsteady equations at as many possible spatial locations and times prior to communicating. In this study, we implemented and tested the swept rule for solving two-dimensional problems on heterogeneous computing systems across two distinct systems and three key parameters: problem size, GPU block size, and work distribution. Our solver showed a speedup range of 0.22–2.69 for the heat diffusion equation and 0.52–1.46 for the compressible Euler equations. We can conclude from this study that the swept rule offers both potential for speedups and slowdowns and that care should be taken when designing such a solver to maximize benefits. These results can help make decisions to maximize these benefits and inform designs.


2021 ◽  
Vol 23 (06) ◽  
pp. 1244-1251
Author(s):  
K. Sivakumar ◽  
◽  
Sakthiraam. B ◽  
Santosh Snehal. V ◽  
Yogashivasankarri. S ◽  
...  

Preserving the edges and information is one of the main purposes of edge-preserving filters. That is, they’re employed to smooth a picture, and minimize halos, phantoms, and edge blur over the edge. They have a nonlinear relationship between one thing and another. Bilateral filters, anisotropic diffusion filters, directed filters, and trilateral filters are all types of example filters. The filter family may be used in a wide range of image processing tasks, such as denoising, video abstraction, demosaicing, optical flow estimation, stereo matching, tone mapping, style transfer, relighting, and others. The paper gives a clear description of edge-preserving filters, from the heat diffusion equation in ancient times to the present, explaining their numerous applications and detailing their numerous uses. Additionally, mathematical analysis is included, as well as efficient and optimized implementations. The focus is on preserving the boundaries, spikes, and canyons, and the information is given clearly and in detail. Finally, it offers a realistic representation of efficient implementation, as well as a comprehensive research scope for future hardware implementation.


2021 ◽  
Author(s):  
Carlos Adriano Ribeiro ◽  
João Roberto Ferreira ◽  
Sandro Metrevelle Marcondes Lima e Silva

Abstract In machining processes, cutting tools reach temperatures higher than 900ºC, thus deteriorating their mechanical properties. To reduce this problem, cutting tools are coated with materials possessing thermal insulation characteristics. Such coatings benefit machining, providing faster cutting speeds and tools life. However, the heating of the tools is still present. Therefore, this work simulates the transient heating phenomenon of a tool and its tool holder, considering the presence of the coating. The effects of convection, radiation, and contact resistance between the tool and the tool holder are also considered. The thermophysical properties of the tool elements depend on temperature. Experimental measurements of parameters related to contact resistance were carried out to make the thermal model closer to real situations. The COMSOL program was used to solve the heat diffusion equation using the Finite Element Method. Comparisons of calculated temperatures are presented for the uncoated (substrate only) and coated inserts with aluminum oxide (Al2O3) and titanium nitride (TiN), respectively. Finally, the results and the consequences of the assembly parameters in the fields of temperature and contact resistance are discussed.


2021 ◽  
Vol 20 (1) ◽  
pp. 52
Author(s):  
C. B. P. Sa ◽  
M. F. Curi

Thermal insulation is present in several engineering areas, such as in civilconstruction, in industrial ovens, in satellites and launch vehicles and even indomestic applications, such as refrigerators. This work aims to presentmultilayer insulation for civil construction, thus reducing electrical energyexpenditure on air conditioning the environment and increasing thermalcomfort. To determine the heat flow through the wall, it was necessary tosolve the heat diffusion equation in rectangular Cartesian coordinates for eachinsulation layer, and the boundary conditions of each differential equationdepend on the neighboring layers, thus forming a system of equations. TheWolfram Mathematica computational software was used to solve themathematical equations. The heat flow was determined for the four seasonsof the year throughout the day for different configurations of thermalinsulation, varying the insulating material and its thickness. After analyzingthe results, it was possible to observe the great efficiency of the models withthermal insulation compared to traditional walls, making the internal wall'stemperature profile more constant throughout the day.


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