Search results for: Thermal Williams-Comstock equation

Authors: Sarun Phibanchon

Abstract:

The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.

Keywords: soliton, iterative method, spectral method, plasma

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Authors: T. Sikram, M. Ichinose, R. Sasaki

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In the tropics, indoor thermal environment is usually provided by a cooling mode to maintain comfort all year. Indoor thermal environment performance is sometimes different from the standard or from the first design process because of operation, maintenance, and utilization. The field study of thermal environment in the green building is still limited in this region, while the green building continues to increase. This study aims to clarify thermal performance and subjective perception in the green building by testing the temperature set-points. A Thai green office was investigated twice in October 2018 and in May 2019. Indoor environment variables (temperature, relative humidity, and wind velocity) were collected continuously. The temperature set-point was normally set as 23 °C, and it was changed into 24 °C and 25 °C. The study found that this gap of temperature set-point produced average room temperature from 22.7 to 24.6 °C and average relative humidity from 55% to 62%. Thermal environments slight shifted out of the ASHRAE comfort zone when the set-point was increased. Based on the thermal sensation vote, the feeling-colder vote decreased by 30% and 18% when changing +1 °C and +2 °C, respectively. Predicted mean vote (PMV) shows that most of the calculated median values were negative. The values went close to the optimal neutral value (0) when the set-point was set at 25 °C. The neutral temperature was slightly decreased when changing warmer temperature set-points. Building-related symptom reports were found in this study that the number of votes reduced continuously when the temperature was warmer. The symptoms that occurred by a cooler condition had the number of votes more than ones that occurred by a warmer condition. In sum, for this green office, there is a possibility to adjust a higher temperature set-point to +1 °C (24 °C) in terms of reducing cold sensitivity, discomfort, and symptoms. All results could support the policy of changing a warmer temperature of this office to become “a better green building”.

Keywords: Thermal environment, green office, temperature set-point, comfort.

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Authors: Z. Pavlík, J. Kočí, M. Pavlíková, R. Černý

Abstract:

Combined experimental and computational analysis of hygrothermal performance of an interior thermal insulation system applied on a brick wall is presented in the paper. In the experimental part, the functionality of the insulation system is tested at simulated difference climate conditions using a semi-scale device. The measured temperature and relative humidity profiles are used for the calibration of computer code HEMOT that is finally applied for a long-term hygrothermal analysis of the investigated structure.

Keywords: Additional thermal insulation, hygrothermal analysis, semi-scale testing, long-term computational analysis

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Authors: Azizollah Khormali, Seyyed Shahab Tabatabaee Moradi, Dmitry Petrakov

Abstract:

One of the most important parameters in petroleum reservoirs is the pressure distribution along the reservoir, as the pressure varies with the time and location. A popular method to determine the pressure distribution in a reservoir in the unsteady state regime of flow is applying Darcy’s equation and solving this equation numerically. The numerical simulation of reservoirs is based on these numerical solutions of different partial differential equations (PDEs) representing the multiphase flow of fluids. Pressure profile has obtained in a one dimensional system solving Darcy’s equation explicitly. Changes of pressure profile in three situations are investigated in this work. These situations include section length changes, step time changes and time approach to infinity. The effects of these changes in pressure profile are shown and discussed in the paper.

Keywords: Explicit solution, Numerical simulation, Petroleum reservoir, Pressure distribution.

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Authors: F. Soleymani, M. Sharifi

Abstract:

Most of the nonlinear equation solvers do not converge always or they use the derivatives of the function to approximate the root of such equations. Here, we give a derivative-free algorithm that guarantees the convergence. The proposed two-step method, which is to some extent like the secant method, is accompanied with some numerical examples. The illustrative instances manifest that the rate of convergence in proposed algorithm is more than the quadratically iterative schemes.

Keywords: Non-linear equation, iterative methods, derivative-free, convergence.

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Authors: A.Tajaddini

Abstract:

In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.

Keywords: Bisymmetric matrices, Paige’s algorithms, Least square.

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Authors: S. M. Sohel Murshed, C. A. Nieto de Castro, M. J. V. Lourenço, J. França, A. P. C. Ribeiro, S. I. C.Vieira, C. S. Queirós

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Ionanofluids are a new and innovative class of heat transfer fluids which exhibit fascinating thermophysical properties compared to their base ionic liquids. This paper deals with the findings of thermal conductivity and specific heat capacity of ionanofluids as a function of a temperature and concentration of nanotubes. Simulation results using ionanofluids as coolants in heat exchanger are also used to access their feasibility and performance in heat transfer devices. Results on thermal conductivity and heat capacity of ionanofluids as well as the estimation of heat transfer areas for ionanofluids and ionic liquids in a model shell and tube heat exchanger reveal that ionanofluids possess superior thermal conductivity and heat capacity and require considerably less heat transfer areas as compared to those of their base ionic liquids. This novel class of fluids shows great potential for advanced heat transfer applications.

Keywords: Heat transfer, Ionanofluids, Ionic liquids, Nanotubes, Thermal conductivity.

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Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

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In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: Feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation.

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Authors: Marco Morini, Nicolandrea Calabrese, Dario Chello

Abstract:

Despite the international commitment of Algeria towards the development of energy efficiency and renewable energy in the country, the internal energy demand has been continuously growing during the last decade due to the substantial increase of population and of living conditions, which in turn has led to an unprecedented expansion of the residential building sector. The RTB (Thermal Building Regulation) is the technical document that establishes the calculation framework for the thermal performance of buildings in Algeria, setting up minimum obligatory targets for the thermal performance of new buildings. An update of this regulation is due in the coming years and this paper discusses some proposals in this regard, with the aim to improve the energy efficiency of the building sector, particularly with regard to social housing. In particular, it proposes a methodology for drafting an energy performance label of new Algerian residential buildings, moving from the results of the thermal compliance verification and sizing of technical systems as defined in the RTB. Such an energy performance label – whose calculation method is briefly described in the paper – aims to raise citizens' awareness of the benefits of energy efficiency. It can represent the first step in a process of integrating technical installations into the calculation of the energy performance of buildings in Algeria.

Keywords: building, energy certification, energy efficiency, social housing, international cooperation, Mediterranean Region

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Authors: Hosein Shokohmand, Mahmood Hosein Zare, Abdorreza Qolibeik

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In this paper, the effects of thermodynamic, hydrodynamic and geometric of an air cooled condenser on COP of vapor compression cycle are investigated for a fixed condenser facing surface area. The system is utilized with a scroll compressor, modeled based on thermodynamic and heat transfer equations employing Matlab software. The working refrigerant is R134a whose thermodynamic properties are called from Engineering Equation Software. This simulation shows that vapor compression cycle can be designed by different configurations and COPs, economical and optimum working condition can be obtained via considering these parameters.

Keywords: Vapor compression cycle, air cooled condenser, COP, heat exchanger, thermal modeling.

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Authors: J. Hroudova, J. Zach

Abstract:

The majority of contemporary insulation materials commonly used in the building industry is made from non-renewable raw materials; furthermore, their production often brings high energy costs. A long-term trend as far as sustainable development is concerned has been the reduction of energy and material demands of building material production. One of the solutions is the possibility of using easily renewable natural raw material sources which are considerably more ecological and their production is mostly less energy-consuming compared to the production of normal insulations (mineral wool, polystyrene). The paper describes the results of research focused on the development of thermal and acoustic insulation materials based on natural fibres intended for floor constructions. Given the characteristic open porosity of natural fibre materials, the hygrothermal behaviour of the developed materials was studied. Especially the influence of relative humidity and temperature on thermal insulation properties was observed.

Keywords: Green thermal and acoustic insulating materials, natural fibres, technical hemp, flax, floor construction.

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Authors: Nopparat Pochai

Abstract:

Smoke discharging is a main reason of air pollution problem from industrial plants. The obstacle of a building has an affect with the air pollutant discharge. In this research, a mathematical model of the smoke dispersion from two sources and one source with a structural obstacle is considered. The governing equation of the model is an isothermal mass transfer model in a viscous fluid. The finite element method is used to approximate the solutions of the model. The triangular linear elements have been used for discretising the domain, and time integration has been carried out by semi-implicit finite difference method. The simulations of smoke dispersion in cases of one chimney and two chimneys are presented. The maximum calculated smoke concentration of both cases are compared. It is then used to make the decision for smoke discharging and air pollutant control problems on industrial area.

Keywords: Air pollution, Smoke dispersion, Finite element method, Stream function, Vorticity equation, Convection-diffusion equation, Semi-implicit method

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Authors: M. Jalali Azizpour, S.Norouzi H. Mohammadi Majd

Abstract:

In this paper, the babbitting of a bearing in boiler feed pump of an electromotor has been studied. These bearings have an important role in reducing the shut down times in the pumps, compressors and turbines. The most conventional method in babbitting is casting as a melting method. The comparison between thermal spray and casting methods in babbitting shows that the thermal spraying babbitt layer has better performance and tribological behavior. The metallurgical and tribological analysis such as SEM, EDS and wet chemical analysis has been made in the Babbitt alloys and worn surfaces. Two type of babbitt materials: tinbase and lead-base babbitt was used. The benefits of thermally sprayed babbitt layers are completely clear especially in large bearings.

Keywords: Thermal spray, Babbitting, Bonding, Bearing, BFP, CWP

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Authors: Michael Tupý, Jaroslav Císař, Pavel Mokrejš, Dagmar Měřínská, Alice Tesaříková-Svobodová

Abstract:

It is the worldwide problem that the recycled PVB is not recycled and it is wildly stored in landfills. However, PVB has similar chemical properties such as PVC. Moreover, both of these polymers are plasticized. Therefore, the study of thermal properties of plasticized PVC and the recycled PVB obtained by recycling of windshields is carried out. This work has done in order to find nondegradable processing conditions applicable for both polymers. Tested PVC contained 38% of plasticizer diisononyl phthalate (DINP) and PVB was plasticized with 28% of triethylene glycol, bis(2-ethylhexanoate) (3GO). The thermal and thermo-oxidative decomposition of both vinyl polymers are compared by calorimetric analysis and by tensile strength analysis.

Keywords: Poly(vinyl chloride), Poly(vinyl butyral), Recycling, Reprocessing, Thermal analysis, Decomposition.

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Authors: Limin Zhao, Xingfa Gu, C. Tao Yu

Abstract:

one of the significant factors for improving the accuracy of Land Surface Temperature (LST) retrieval is the correct understanding of the directional anisotropy for thermal radiance. In this paper, the multiple scattering effect between heterogeneous non-isothermal surfaces is described rigorously according to the concept of configuration factor, based on which a directional thermal radiance model is built, and the directional radiant character for urban canopy is analyzed. The model is applied to a simple urban canopy with row structure to simulate the change of Directional Brightness Temperature (DBT). The results show that the DBT is aggrandized because of the multiple scattering effects, whereas the change range of DBT is smoothed. The temperature difference, spatial distribution, emissivity of the components can all lead to the change of DBT. The “hot spot" phenomenon occurs when the proportion of high temperature component in the vision field came to a head. On the other hand, the “cool spot" phenomena occur when low temperature proportion came to the head. The “spot" effect disappears only when the proportion of every component keeps invariability. The model built in this paper can be used for the study of directional effect on emissivity, the LST retrieval over urban areas and the adjacency effect of thermal remote sensing pixels.

Keywords: Directional thermal radiance, multiple scattering, configuration factor, urban canopy, hot spot effect

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Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study presents an inverse analysis for predicting the thermal conductivities and the heat flux of a high-temperature metallurgical reactor simultaneously. Once these thermal parameters are predicted, the time-varying thickness of the protective phase-change bank that covers the inside surface of the brick walls of a metallurgical reactor can be calculated. The enthalpy method is used to solve the melting/solidification process of the protective bank. The inverse model rests on the Levenberg-Marquardt Method (LMM) combined with the Broyden method (BM). A statistical analysis for the thermal parameter estimation is carried out. The effect of the position of the temperature sensors, total number of measurements and measurement noise on the accuracy of inverse predictions is investigated. Recommendations are made concerning the location of temperature sensors.

Keywords: Inverse heat transfer, phase change, metallurgical reactor, Levenberg–Marquardt method, Broyden method, bank thickness.

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Authors: K. Touafek, A. Khelifa, E. H. Khettaf, A. Embarek

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Hybrid photovoltaic thermal (PV/T) solar system comprises a solar collector which is disposed on photovoltaic solar cells. The disadvantage of a conventional photovoltaic cell is that its performance decreases as the temperature increases. Indeed, part of the solar radiation is converted into electricity and is dissipated as heat, increasing the temperature of the photovoltaic cell with respect to the ambient temperature. The objective of this work is to study experimentally and implement a hybrid prototype to evaluate electrical and thermal performance. In this paper, an experimental study of two new configurations of hybrid collectors is exposed. The results are given and interpreted. The two configurations of absorber studied are a new combination with tubes and galvanized tank, the other is a tubes and sheet.

Keywords: Experimental, Photovoltaic, Solar, Temperature.

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Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new method for solving the matrix equation AXB=F . The new method can be considered as a generalized form of the well-known global full orthogonalization method (Gl-FOM) for solving multiple linear systems. Hence, the method will be called extended Gl-FOM (EGl- FOM). For implementing EGl-FOM, generalized forms of block Krylov subspace and global Arnoldi process are presented. Finally, some numerical experiments are given to illustrate the efficiency of our new method.

Keywords: Matrix equations, Iterative methods, Block Krylovsubspace methods.

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Authors: Amr Sayed, Y. Hiroshi, T. Goto, N. Enteria, M. M. Radwan, M. Abdelsamei Eid

Abstract:

Climate considerations are essential dimensions in the assessment of thermal comfort and indoor environments inside Egyptian housing. The primary aim of this paper is to analyze the indoor environment of new housing in the new city of Assiut in the Southern Upper Egypt zone, in order to evaluate its thermal environment and determine the acceptable indoor operative temperatures. The psychrometric charts for ASHRAE Standard 55 and ACS used in this study would facilitate an overall representation of the climate in one of the hottest months in the summer season. This study helps to understand and deal with this problem and work on a passive cooling ventilation strategy in these contexts in future studies. The results that demonstrated the indoor temperature is too high, ranges between 31°C to 40°C in different natural ventilation strategies. This causes the indoor environment to be far from the optimum comfort operative temperature of ACS except when using air conditioners. Finally, this study is considered a base for developing a new system using natural ventilation with passive cooling strategies.

Keywords: Adaptive comfort standard (ACS), indoor environment, thermal comfort, ventilation.

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Authors: Marziyeh Halimi, Roushanak Lotfikar, Simin Mansouri Borojeni

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In this paper we considered the Neumann problem for the fourth order differential equation. First we define the weighted Sobolev space 2 Wα and generalized solution for this equation. Then we consider the existence and uniqueness of the generalized solution, as well as give the description of the spectrum and of the domain of definition of the corresponding operator.

Keywords: Neumann problem, weighted Sobolev spaces, generalized solution, spectrum of linear operators.2000 mathematic subject classification: 34A05, 34A30.

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Authors: H. Taheri Shahraiyni, B. Ataie Ashtiani

Abstract:

Flow movement in unsaturated soil can be expressed by a partial differential equation, named Richards equation. The objective of this study is the finding of an appropriate implicit numerical solution for head based Richards equation. Some of the well known finite difference schemes (fully implicit, Crank Nicolson and Runge-Kutta) have been utilized in this study. In addition, the effects of different approximations of moisture capacity function, convergence criteria and time stepping methods were evaluated. Two different infiltration problems were solved to investigate the performance of different schemes. These problems include of vertical water flow in a wet and very dry soils. The numerical solutions of two problems were compared using four evaluation criteria and the results of comparisons showed that fully implicit scheme is better than the other schemes. In addition, utilizing of standard chord slope method for approximation of moisture capacity function, automatic time stepping method and difference between two successive iterations as convergence criterion in the fully implicit scheme can lead to better and more reliable results for simulation of fluid movement in different unsaturated soils.

Keywords: Finite Difference methods, Richards equation, fullyimplicit, Crank-Nicolson, Runge-Kutta.

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Authors: Z. El Felsoufi, L. Azrar

Abstract:

This paper studies a mathematical model based on the integral equations for dynamic analyzes numerical investigations of a non-uniform or multi-material composite beam. The beam is subjected to a sub-tangential follower force and elastic foundation. The boundary conditions are represented by generalized parameterized fixations by the linear and rotary springs. A mathematical formula based on Euler-Bernoulli beam theory is presented for beams with variable cross-sections. The non-uniform section introduces non-uniformity in the rigidity and inertia of beams and consequently, more complicated equilibrium who governs the equation. Using the boundary element method and radial basis functions, the equation of motion is reduced to an algebro-differential system related to internal and boundary unknowns. A generalized formula for the deflection, the slope, the moment and the shear force are presented. The free vibration of non-uniform loaded beams is formulated in a compact matrix form and all needed matrices are explicitly given. The dynamic stability analysis of slender beam is illustrated numerically based on the coalescence criterion. A realistic case related to an industrial chimney is investigated.

Keywords: Chimney, BEM and integral equation formulation, non uniform cross section, vibration and Flutter.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special non-empty closed convex set and utilizing M¨onch fixed point theory, we investigate the existence of solution for a class of fourth-order singular differential equation in Banach space, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

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Authors: Changqiao Wu, Guoqing Ding, Xin Chen

Abstract:

In this paper, ways of modeling dynamic measurement systems are discussed. Specially, for linear system with single-input single-output, it could be modeled with shallow neural network. Then, gradient based optimization algorithms are used for searching the proper coefficients. Besides, method with normal equation and second order gradient descent are proposed to accelerate the modeling process, and ways of better gradient estimation are discussed. It shows that the mathematical essence of the learning objective is maximum likelihood with noises under Gaussian distribution. For conventional gradient descent, the mini-batch learning and gradient with momentum contribute to faster convergence and enhance model ability. Lastly, experimental results proved the effectiveness of second order gradient descent algorithm, and indicated that optimization with normal equation was the most suitable for linear dynamic models.

Keywords: Dynamic system modeling, neural network, normal equation, second order gradient descent.

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Authors: Promise A. Azor, Avievie Igodo, Esabai M. Ase

Abstract:

The paper merged the return of premium clause and voluntary contributions to investigate retirees’ investment plan in a defined contributory (DC) pension scheme with a portfolio comprising of a risk-free asset and a risky asset whose price process is described by geometric Brownian motion (GBM). The paper considers additional voluntary contributions paid by members, charge on balance by pension fund administrators and the mortality risk of members of the scheme during the accumulation period by introducing return of premium clause. To achieve this, the Weilbull mortality force function is used to establish the mortality rate of members during accumulation phase. Furthermore, an optimization problem from the Hamilton Jacobi Bellman (HJB) equation is obtained using dynamic programming approach. Also, the Legendre transformation method is used to transform the HJB equation which is a nonlinear partial differential equation to a linear partial differential equation and solves the resultant equation for the value function and the optimal distribution plan under logarithm utility function. Finally, numerical simulations of the impact of some important parameters on the optimal distribution plan were obtained and it was observed that the optimal distribution plan is inversely proportional to the initial fund size, predetermined interest rate, additional voluntary contributions, charge on balance and instantaneous volatility.

Keywords: Legendre transform, logarithm utility, optimal distribution plan, return clause of premium, charge on balance, Weibull mortality function.

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Authors: M.Jalali Azizpour, S.Norouzi, D.Sajedipour, H.Mohammadi majd, S.A.Hosseini, H.Talebi, A.Ghamari

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In this paper, the bond strength of thermal spray coatings in high speed shafts has been studied. The metallurgical and mechanical studies has been made on the coated samples and shaft using optical microscopy, scanning electron microscopy (SEM).

Keywords: Thermal spray, Residual stress, Wear mechanism, HVOF, Gas compressor shafts

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Authors: Mohamed Ouzzane, Mahmoud Bady

Abstract:

Due to energy and environment context, research is looking for the use of clean and energy efficient system in cooling industry. In this regard, the ejector represents one of the promising solutions. The thermal ejector is a passive component used for thermal compression in refrigeration and cooling systems, usually activated by heat either waste or solar. The present study introduces a theoretical analysis of the cooling system which uses a gas ejector thermal compression. A theoretical model is developed and applied for the design and simulation of the ejector, as well as the whole cooling system. Besides the conservation equations of mass, energy and momentum, the gas dynamic equations, state equations, isentropic relations as well as some appropriate assumptions are applied to simulate the flow and mixing in the ejector. This model coupled with the equations of the other components (condenser, evaporator, pump, and generator) is used to analyze profiles of pressure and velocity (Mach number), as well as evaluation of the cycle cooling capacity. A FORTRAN program is developed to carry out the investigation. Properties of refrigerant R134a are calculated using real gas equations. Among many parameters, it is thought that the generator pressure is the cornerstone in the cycle, and hence considered as the key parameter in this investigation. Results show that the generator pressure has a great effect on the ejector and on the whole cooling system. At high generator pressures, strong shock waves inside the ejector are created, which lead to significant condenser pressure at the ejector exit. Additionally, at higher generator pressures, the designed system can deliver cooling capacity for high condensing pressure (hot season).

Keywords: Air cooling system, refrigeration, thermal ejector, thermal compression.

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Abstract:

The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: Curved stretching sheet, finite difference method, MHD, variable thermal conductivity.

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Authors: F. Taouche-Kheloui, O. Fedaoui-Akmoussi, K. Ait tahar, Li. Alex

Abstract:

Currently, the reduction of energy consumption, through the use of abundant and recyclable natural materials, for better thermal insulation represents an important area of research. To this end, the use of bio-sourced materials has been identified as one of the green sectors with a very high economic development potential for the future. Because of its role in reducing the consumption of fossil-based raw materials, it contributes significantly to the storage of atmospheric carbon, limits greenhouse gas emissions and creates new economic opportunities. This study constitutes a contribution to the elaboration and the experimental characterization of the thermal behavior of a sawdust-reduced mortar matrix. We have taken into account the influence of the size of the grain fibers of sawdust, hence the use of three different ranges and also different percentage in the different confections. The intended practical application consists of producing a light weight compound at a lower cost to ensure a better thermal and acoustic behavior compared to that existing in the field, in addition to the desired resistances. Improving energy performance, while reducing greenhouse gas emissions from the building sector, is amongst the objectives to be achieved. The results are very encouraging and highlight the value of the proposed design of organic-source mortar panels which have specific mechanical properties acceptable for their use, low densities, lower cost of manufacture and labor, and above all a positive impact on the environment.

Keywords: Mortar, sawdust waste, thermal, experimental, analysis.

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Authors: M.Eskandari-Ghadi, M.Mahmoodian

Abstract:

In this article an isotropic linear elastic half-space with a cylindrical cavity of finite length is considered to be under the effect of a ring shape time-harmonic torsion force applied at an arbitrary depth on the surface of the cavity. The equation of equilibrium has been written in a cylindrical coordinate system. By means of Fourier cosine integral transform, the non-zero displacement component is obtained in the transformed domain. With the aid of the inversion theorem of the Fourier cosine integral transform, the displacement is obtained in the real domain. With the aid of boundary conditions, the involved boundary value problem for the fundamental solution is reduced to a generalized Cauchy singular integral equation. Integral representation of the stress and displacement are obtained, and it is shown that their degenerated form to the static problem coincides with existing solutions in the literature.

Keywords: Cosine transform, Half space, Isotropic, Singular integral equation, Torsion

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