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The purpose of this paper is to study the transient waves caused by a line heat source with a stable internal heat source inside isotropic homogenous thermoelastic perfectly conducting half‐space permeate into a uniform magnetic field. The formulation is applied under three theories of generalized thermoelasticity Lord‐Shulman (L‐S) theory with one relaxation time, Green‐Lindsay (G‐L) theory with two relaxation times, as well as the classical dynamical coupled theory. The problem is reduced to the solution of three differential equations by introducing the elastic and thermoelastic potentials.

The normal mode analysis is used to obtain the expressions. Numerical results are given and illustrated graphically. Comparisons are made with the results predicted by the three theories in the presence and absence of magnetic field and the internal heat source.

The results are graphically described for the medium of copper. We can conclude that the magnetic field has a great effect on the displacement components and this effect produces the same trend under the three theories. The results show that the relaxation times have salient effect to the distribution of displacement at small values of time.

The present theoretical results may provide interesting information for experimental scientists /researchers/seismologist working on this subject.

In this paper a numerical simulation, based on finite difference techniques, has been developed in order to analyse turbulent natural and mixed convection of air in internal flows. The study has been restricted to two‐dimensional cavities with the possibility of inlet and outlet ports, and with internal heat sources. Turbulence is modelled by means of two‐equation k‐ε turbulence models, both in the simplest form using wall functions and in the more general form of low‐Reynolds‐number k‐ε models. The couple time average governing equations (continuity, momentum, energy, and turbulence quantities) are solved in a segregated manner using the SIMPLEX method. An implicit control volume formulation of the differential equations has been employed. Some illustrative numerical results are presented to study the influence of geometry and boundary conditions in cavities. A comparison of different k‐ε turbulence models has also been presented.

This paper aims to investigate the transient disturbances created by an internal line heat source that suddenly starts moving uniformly inside a visco‐elastic half‐space.

Generalised theory of thermo‐elasticity with relaxation time proposed by Lord‐Shulman is applied. The material of the semi‐infinite medium is an isotropic visco‐elastic solid of Kelvin‐Voight type. Fourier and Laplace transform techniques are used.

Applying the Fourier and Laplace transform techniques, expressions for displacement components in the transformed domain are found. These expressions prove the existence of three waves – a modified thermal wave, a visco‐elastic wave of defused nature and a transverse visco‐elastic wave.

Surface displacement components were evaluated on the boundary for only a short time.

The paper provides numerical results that are illustrated graphically to highlight the variations of surface displacement components with distance for different values of time, source depth and velocity of the source.

Briefly reviews previous literature by the author before presenting an original 12 step system integration protocol designed to ensure the success of companies or countries in their efforts to develop and market new products. Looks at the issues from different strategic levels such as corporate, international, military and economic. Presents 31 case studies, including the success of Japan in microchips to the failure of Xerox to sell its invention of the Alto personal computer 3 years before Apple: from the success in DNA and Superconductor research to the success of Sunbeam in inventing and marketing food processors: and from the daring invention and production of atomic energy for survival to the successes of sewing machine inventor Howe in co‐operating on patents to compete in markets. Includes 306 questions and answers in order to qualify concepts introduced.

The study of instability due to the effects of Maxwell–Cattaneo law and internal heat source/sink on Casson dielectric fluid horizontal layer is an open question. Therefore, in this paper, the impact of internal heat generation/absorption on Rayleigh–Bénard convection in a non-Newtonian dielectric fluid with Maxwell–Cattaneo heat flux is investigated. The horizontal layer of the fluid is cooled from the upper boundary, while an isothermal boundary condition is utilized at the lower boundary.

The Casson fluid model is utilized to characterize the non-Newtonian fluid behavior. The horizontal layer of the fluid is cooled from the upper boundary, while an isothermal boundary condition is utilized at the lower boundary. The governing equations are non-dimensionalized using appropriate dimensionless variables and the subsequent equations are solved for the critical Rayleigh number using the normal mode technique (NMT).

Results are presented for two different cases namely dielectric Newtonian fluid (DNF) and dielectric non-Newtonian Casson fluid (DNCF). The effects of Cattaneo number, Casson fluid parameter, heat source/sink parameter on critical Rayleigh number and wavenumber are analyzed in detail. It is found that the value Rayleigh number for non-Newtonian fluid is higher than that of Newtonian fluid; also the heat source aspect decreases the magnitude of the Rayleigh number.

The effect of Maxwell–Cattaneo heat flux and internal heat source/sink on Rayleigh-Bénard convection in Casson dielectric fluid is investigated for the first time.

A numerical study of a two‐dimensional turbulent flow in a partially open rectangular cavity such as a room is carried out. The turbulent flow is induced by the energy input due to a localized heat source positioned on the floor of the cavity. This flow is of interest in enclosure fires where the flow in the cavity interacts with the environment through the opening or vents. The focus is on the stable, thermal stratification that arises in the room and on the influence of the opening height. A finite‐difference method is employed for the solution of the problem, using a low Reynolds number k — ε turbulence model for the turbulent flow calculations. This model is particularly suitable for flows in which the possibility for relaminarization exists. It was found that, for high Grashof numbers and for relatively small opening heights, particularly for doorway openings, a strong stable thermal stratification is generated within the cavity, with a cooler, essentially uniform, layer underlying a warmer, linearly stratified, upper layer. As a consequence, turbulence is suppressed and the flow in the upper region of the cavity becomes laminar with turbulence confined to locations such as the fire plume above the source and the shear layer at the opening. The penetration distance and the height of the interface are both found to decrease with a reduction in the opening height. The Nusselt number for heat transfer from the source is seen to be affected to a small extent by the opening height. The basic trends are found to agree with those observed in typical compartment fires. Comparisons with results available in the literature on turbulent buoyancy‐driven enclosure flows indicate good agreement, lending support to this model and the numerical scheme.

This paper aims to analyze the behavior of the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet in the presence of the viscous dissipation and heat source effects.

The governing partial differential equations are converted into ordinary differential equations by similarity transformations before being solved numerically using the bvp4c function built in Matlab software. Effects of suction/injection parameter and heat source parameter on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented in the forms of tables and graphs. A temporal stability analysis will be conducted to verify which solution is stable for the dual solutions exist for the shrinking case.

The analysis indicates that the skin friction coefficient and the local Nusselt number as well as the velocity and temperature were influenced by suction/injection parameter. In contrast, only the local Nusselt number, which represents heat transfer rate at the surface, was affected by heat source effect. Further, numerical results showed that dual solutions were found to exist for the certain range of shrinking case. Then, the stability analysis is performed, and it is confirmed that the first solution is linearly stable and has real physical implication, while the second solution is not.

In practice, the study of the steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet in the presence of heat source effect is very crucial and useful. The problems involving fluid flow over stretching or shrinking surfaces can be found in many industrial manufacturing processes such as hot rolling, paper production and spinning of fibers. Owing to the numerous applications, the study of stretching/shrinking sheet was subsequently extended by many authors to explore various aspects of skin friction coefficient and heat transfer in a fluid. Besides that, the study of suction/injection on the boundary layer flow also has important applications in the field of aerodynamics and space science.

Although many studies on viscous fluid has been investigated, there is still limited discoveries found on the heat source and suction/injection effects. Indeed, this paper managed to obtain the second (dual) solutions and stability analysis is performed. The authors believe that all the results are original and have not been published elsewhere.

The purpose of this paper is to apply the meshless method of fundamental solutions (MFS) to the two‐dimensional time‐dependent heat equation in order to locate an unknown internal inclusion.

The problem is formulated as an inverse geometric problem, using non‐invasive Dirichlet and Neumann exterior boundary data to find the internal boundary using a non‐linear least‐squares minimisation approach. The solver will be tested when locating a variety of internal formations.

The method implemented was proven to be both stable and reasonably accurate when data were contaminated with random noise.

Owing to limited computational time, spatial resolution of internal boundaries may be lower than some similar case investigations.

This research will have practical implications to the modelling and monitoring of crystalline deposit formations within the nuclear industry, allowing development of future designs.

Similar work has been completed in regards to the steady state heat equation, however to the best of the authors' knowledge no previous work has been completed on a time‐dependent inverse inclusion problem relating to the heat equation, using the MFS. Preliminary results presented here will have value for possible future design and monitoring within the nuclear industry

To develop a numerical technique for solving the inverse source problem associated with the constant coefficients convection‐diffusion equation.

The proposed numerical technique is based on the boundary element method (BEM) combined with an iterative sequential quadratic programming (SQP) procedure. The governing convection‐diffusion equation is transformed into a Helmholtz equation and the ill‐conditioned system of equations that arises after the application of the BEM is solved using an iterative technique.

The iterative BEM presented in this paper is well‐suited for solving inverse source problems for convection‐diffusion equations with constant coefficients. Accurate and stable numerical solutions were obtained for cases when the number of sources is correctly estimated, overestimated, or underestimated, and with both exact and noisy input data.

The proposed numerical method is limited to cases when the Péclet number is smaller than 100. Future approaches should include the application of the BEM directly to the convection‐diffusion equation.

Applications of the results presented in this paper can be of value in practical applications in both heat and fluid flow as they show that locations and strengths for an unknown number of point sources can be accurately found by using boundary measurements only.

The BEM has not as yet been employed for solving inverse source problems related with the convection‐diffusion equation. This study is intended to approach this problem by combining the BEM formulation with an iterative technique based on the SQP method. In this way, the many advantages of the BEM can be applied to inverse source convection‐diffusion problems.

The aim of this paper is to present a Eulerian–Lagrangian model of aircraft ground deicing that avoids the scale’s dispersion problem caused by the great distance between the spray nozzle and the surface to be deiced. Verification is done using the case of a hot particle liquid spray impinging on a horizontal flat plate. The impinged particles flow outwards radially from the impingement zone and form a hot film wall. The computed wall heat distribution is verified. In the end, an inclination spray’s angle study is presented.

The problem is divided into two regions. First, a 3D region is created for the evolution of the Lagrangian particles spray. A second 2D region is provided for the formation of a liquid film. The two regions exchange mass, momentum and energy through an interface. Heat losses are modelled through particles and liquid-film cooling and evaporation, particles splash and heat transfer to a fixed temperature plate.

For a chamber pressure of 1 bar, the predicted spray penetration is within 10 per cent of the experimental results. For this study case, the heat transfer is maximized with an inclination angle of approximately 30° of the spray.

The model presented makes it possible to simulate the impingement and heat transfer of a large-scale liquid spray with a reasonable computational cost. To the best of the authors’ knowledge, this model is a first attempt of the computational fluid dynamics simulation of ground deicing.