Basic Equations of Fluid Mechanics and Thermodynamics

Tóth, Anikó; Bobok, Elemer

doi:10.1016/b978-0-12-800277-3.00002-5

Cited by 5 publications

(5 citation statements)

References 2 publications

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“…"Hence, to maintain the constant amount of airflow along the area gradient, the wind velocity at the concentrator outlet had to increase. Therefore, the concentrator outlet velocity was greater than the inlet for all concentrators irrespective of the R r and the L r " [19].…”

Section: Discussionmentioning

confidence: 88%

“…"As the air flowed from the concentrator inlet along a decreasing cross-sectional area, the amount of the fluid passing through each point in time remained constant in accordance with the mass conservation principle" [19]. "Hence, to maintain the constant amount of airflow along the area gradient, the wind velocity at the concentrator outlet had to increase.…”

Section: Discussionmentioning

confidence: 97%

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Determination of Optimal Geometry for an Empty Concentrator Augmented Wind Turbine

Shonhiwa,

Makaka,

Mukumba

et al. 2023

PSIJ

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Aims: To determine the optimal concentrator geometrical parameters of an empty concentrator augmented wind turbine (CAWT), which are used to design and install CAWTs. Place and Duration of Study: Physics Department, University of Fort Hare, South Africa between March 2023, and October 2023. Methodology: The study used the concentrator length (L) to concentrator outlet diameter ratio (Lr) and the difference between inlet and outlet radii to concentrator outlet diameter ratio (Rr) to investigate the effect of concentrator geometry on wind velocity augmentation and air dynamics to determine the optimum concentrator geometrical parameters using computational fluid dynamics modelling. The modelled concentrators’ geometry was created in SolidWorks, prepared for meshing in SpaceClaim, meshed, and analysed in Fluent to solve the Reynolds-averaged Navier-Stokes equations, and validated by primary experimental results. To make the concentrators, six equally spaced Lr were used in the range 0.1 \(\le\) Lr \(\le\) 0.6 and thirteen equally spaced Rr in the range 0.025 \(\le\) Rr \(\le\) 0.325 . The concentrators’ performance was investigated in terms of velocity augmentation ratio (Vr) and concentrator efficiency (\(\eta\)c). Results: It was observed that the variation in Vr was influenced by the change in both Lr and Rr. The Vr and \(\eta\)c increased with an increase in Lr to a maximum at optimum Lr and decreased thereafter. The optimum Vr was obtained at Lr = 0.4 and Rr = 0.1 with a maximum velocity at the concentrator outlet. It was also shown that the energy losses due to friction negatively impact velocity augmentation more than energy losses due to a large concentrator tilt angle at high Lr . Conclusion: When constructing a CAWT, the turbine rotor should be placed at any distance between the concentrator outlet and 0.5L behind the concentrator, and the blade tips of the turbine in a CAWT system should be at least 10% smaller than the concentrator outlet radius, for the whole rotor to receive wind with augmented velocity.

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Section: Discussionmentioning

confidence: 88%

Section: Discussionmentioning

confidence: 97%

Determination of Optimal Geometry for an Empty Concentrator Augmented Wind Turbine

Shonhiwa,

Makaka,

Mukumba

et al. 2023

PSIJ

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“…Based on field observations, the geothermal area is located at a topographic height of 446 m above MSL and there are also sources of high temperature hot water (100°C -115°C) located in several places, the source is a surface manifestation of a geothermal system that has not yet been explored by researchers [2]. According to Toth and Bobok (2017), Geothermal Energy is heat energy that comes from the crust, mantle, and core of the earth with high temperatures, when the earth's components are in hotter conditions than conditions on the surface, heat energy will continue to move from hotter subsurface conditions to the surface through impermeable rock [3]. The existence of a geothermal energy system is usually characterized by surface manifestations.…”

Section: Introductionmentioning

confidence: 99%

Identification of Rock Characteristics Using the Microtremor Inversion Method at Air Putih Geothermal Field, Lebong Regency

Syah,

Al-Ansory,

Hardiansa

et al. 2024

J. Technomaterial Phys.

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Research has been carried out to identify rock characteristics based on Vs values using the microtremor method in the Air Putih geothermal field, Lebong Regency, which aims to determine the geothermal prospect area on rock characteristics using Vs values based on the microtremor method. The data obtained in this study were 20 measurement points obtained from data analysis by obtaining the H/V curve through Geopsy software and HVSR inversion to obtain the Vs value of the inverse. The results of this calculation indicate that at a depth of 0-4 meters the homogeneous Vs value 200 m/s, at a depth of 4 meters the Vs value 200-440 m/s, at a depth of 20 meters the value of Vs 440 -880 m/s and a depth of 20 meters homogeneous Vs value of 880 m/s and for the distribution of Vp values, at a depth of 0-5 meters the Vp values vary between 2000-2900 m/s, at depths of 6-20 meters in general the value of the Vp wave velocity is the same in the range of 3100-3800 m/s and at depth 21-100 meters the Vp value ranges from 3900-5100 m/s. This shows that the greater the depth, the denser the rock.

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“…For assuming, knowing the solution at the time and all directions can be used as a PDE and describes a system to analytical and/or numerically estimate the solution after a very small change in time and all directions [21]. The law for energy conservation in solids and fluids can be described as a PDE for expressing the changes in temperature (T) in the space, therefore in this case, the temperature (T) is called the dependent variable [22]. It is can be selected a position in space and time for getting a unique value for the temperature by solving the PDEs, therefore-called the temperature depends on x, y, z, and t. However, a value of the temperature taken from the solution by PDEs, but does not automatically give us the position in time and space.…”

Section: Introductionmentioning

confidence: 99%

PDE-Based Mathematical Models to Diagnose the Temperature Changes Phenomena on the Single Rectangular Plate-Fin

Goeritno¹,

Prayudyanto²,

Eosina³

et al. 2023

MMEP

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The ideas of the studies in this article are back-grounded by the work diligently and carefully to relate the influence of two independent variables, e.g., distance and time on one dependent variable, i.e., temperature changes which are solved by a partial differential equation. In this article, we explain the particular features of a naturally physical system that it seeks to understand. The diagnosis of the temperature changes in a metal rod to consider a conduction phenomenon can be covered by all-natural physical phenomena through conduction. By making the mathematical equations based on partial differential equations (PDEs), it is shown that the temperature change is influenced by distance and time. The objectives of this study are (i) to make a prototype of the problem based on the one-dimensional heat conduction equation, (ii) to process the solution of the mathematical equation based on the parabolic partial differential equation (PDE) using the separation of variables, and (iii) to display the phenomena of the temperature changes as a function of the length in the copper bar and the time. Achieving the research objectives takes several stages in the research methods which include (a) making the prototype of the problem, (b) processing the solution of a mathematical equation, and (c) displaying the temperature changes phenomenon in the form of a curve. The results are (i) a mass balance is developed for a finite segment ∆𝑧 along the tank's longitudinal axis in order to derive a differential equation, (ii) the final complete solution in the form of a Fourier sine series, and (iii) a three-dimensional curve as an indication of the existence of the phenomenon of temperature changes. In general, it can be concluded that the making of a mathematical model based on partial differential equations with the method of separating variables as an analytical solution can be used to diagnose the phenomenon of temperature changes as a function of distance and time.

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Basic Equations of Fluid Mechanics and Thermodynamics

Cited by 5 publications

References 2 publications

Determination of Optimal Geometry for an Empty Concentrator Augmented Wind Turbine

Determination of Optimal Geometry for an Empty Concentrator Augmented Wind Turbine

Identification of Rock Characteristics Using the Microtremor Inversion Method at Air Putih Geothermal Field, Lebong Regency

PDE-Based Mathematical Models to Diagnose the Temperature Changes Phenomena on the Single Rectangular Plate-Fin

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