• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.505-513
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• 2015

The present paper deals with the determination of displacement and thermal stresses in a semi-infinite circular cylinder defined as $0{\leq}r{\leq}b$, $0{\leq}z<{\infty}$, due to internal heat generation within it. A circular cylinder is considered having arbitrary initial temperature and subjected to time dependent heat flux at the fixed circular boundary (r = b) whereas the zero temperature at the lower surface (z = 0) of the semi-infinite circular cylinder. The governing heat conduction equation has been solved by using integral transform method. The results are obtained in series form in terms of Bessel functions. The results for displacement and stresses have been computed numerically and illustrated graphically.

• Bulletin of the Korean Chemical Society
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• v.35 no.2
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• pp.407-414
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• 2014

Polyacrylonitrile (PAN) copolymers with different methyl acrylate (MA) contents were synthesized via solution polymerization and used as precursors for high-performance PAN ultrafine fibrids. The chemical structures of the copolymers were characterized using Fourier-transform infrared spectroscopy and $^{13}C$ nuclear magnetic resonance spectroscopy. Their particle sizes and aspect ratios increased with increasing viscosity, and the degree of crystallinity increased with decreasing concentration of copolymer solution. In contrast, their peak temperature and heat of exotherm increased with decreasing concentration of the copolymer solution. The aromatization indices (AIs) of the fibrids increased with increasing heat-treatment time; however, the AIs decreased when the heat-treatment temperature was higher than the onset temperature of the copolymers. On the other hand, the crystal sizes of the fibrids decreased with increasing concentration of the copolymer solution when the MA content was held constant.

• Smart Structures and Systems
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• v.21 no.2
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• pp.163-170
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• 2018

The dynamic response of a finite length thermo-piezoelectric rod with variable material properties is investigated in the context of the fractional order theory of thermoelasticity. The rod is subjected to a moving heat source and fixed at both ends. The governing equations are formulated and then solved by means of Laplace transform together with its numerical inversion. The results of the non-dimensional temperature, displacement and stress in the rod are obtained and illustrated graphically. Meanwhile, the effects of the fractional order parameter, the velocity of heat source and the variable material properties on the variations of the considered variables are presented, and the results show that they significantly influence the variations of the considered variables.

• Advances in materials Research
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• v.7 no.3
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• pp.203-220
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• 2018

This investigation is focused on the study of effect of hall current in transversely isotropic magneto thermoelastic homogeneous medium with fractional order heat transfer and rotation. As an application the bounding surface is subjected to normal force. The research becomes more interesting due to interaction of Hall current with the effect of rotation as it has found various applications. Laplace and Fourier transform is used for solving field equations. The analytical expressions of temperature, displacement components, stress components and current density components are computed in the transformed domain. The effects of hall current and fractional order parameter at different values are represented graphically.

• Steel and Composite Structures
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• v.18 no.4
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• pp.909-924
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• 2015

This paper investigates the vibration phenomenon of a nanobeam subjected to a time-dependent heat flux. Material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel exponential distribution law in terms of the volume fractions of the metal and ceramic constituents. The upper surface of the functionally graded (FG) nanobeam is pure ceramic whereas the lower surface is pure metal. A nonlocal generalized thermoelasticity theory with dual-phase-lag (DPL) model is used to solve this problem. The theories of coupled thermoelasticity, generalized thermoelasticity with one relaxation time, and without energy dissipation can extracted as limited and special cases of the present model. An analytical technique based on Laplace transform is used to calculate the variation of deflection and temperature. The inverse of Laplace transforms are computed numerically using Fourier expansion techniques. The effects of the phase-lags (PLs), nonlocal parameter and the angular frequency of oscillation of the heat flux on the lateral vibration, the temperature, and the axial displacement of the nanobeam are studied.

• Structural Engineering and Mechanics
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• v.68 no.2
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• pp.215-226
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• 2018

In this article, the theory of fractional order two temperature generalized thermoelasticity is employed to study the wave propagation in a fiber reinforced anisotropic thermoelastic half space in the presence of moving internal heat source. The whole space is assumed to be under the influence of gravity. The surface of the half-space is subjected to an inclined load. Laplace and Fourier transform techniques are employed to solve the problem. Expressions for different field variables in the physical domain are derived by the application of numerical inversion technique. Physical fields are presented graphically to study the effects of gravity and heat source. Effects of time, reinforcement, fractional parameter and inclination of load have also been reported. Results of some earlier workers have been deduced from the present analysis.

• Progress in Superconductivity and Cryogenics
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• v.8 no.1
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• pp.59-64
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• 2006

A closed-loop cryogenic cooling system for high field magnets is presented. This design is motivated by our recent development of cooling system for 21 tesla Fourier Transform ion Cyclotron Resonance (FT-ICR) superconducting magnets without any replenishment of cryogen. The low temperature superconducting magnets are immersed in a subcooled 1.8 K bath, which is connected hydraulically to the 4.2 K reservoir through a narrow channel. Saturated liquid helium is cooled by Joule-Thomson heat exchanger and flows through the JT valve, isenthalpically dropping its pressure to approximately 1 6 kPa, corresponding saturation temperature of 1.8 K. Helium gas exhausted from pump is now recondensed by two-stage cryocooler located after vapor purify system. The amount of cryogenic Heat loads and required mass flow rate through closed-loop are estimated by a relevant heat transfer analysis, from which dimensions of JT heat exchanger and He II heat exchanger are determined. The detailed design of cryocooler heat exchanger for helium recondensing is performed. The effect of cryogenic loads, especially superfluid heat leak through the gap of weight load relief valve, on the dimensions of cryogenic system is also investigated.

• Structural Engineering and Mechanics
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• v.69 no.6
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• pp.607-614
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• 2019

The present investigation has focus on the study of deformation due to thermomechanical sources in a thick circular plate. The thick circular plate is homogeneous, transversely isotropic with two temperatures and without energy dissipation. The upper and lower surfaces of the thick circular plate are traction free. The Laplace and Hankel transform has been used for finding the general solution to the field equations. The analytical expressions of stresses, conductive temperature and displacement components are computed in the transformed domain. However, the resulting quantities are obtained in the physical domain by using numerical inversion technique. Numerically simulated results are illustrated graphically. The effects of two temperatures by considering different values of temperature parameters are shown on the various components. Some particular cases are also figured out from the present investigation.

• Journal of the Korean Society for Heat Treatment
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• v.8 no.2
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• pp.101-112
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• 1995

A study was made to examine the effects of heat-treatment on the microstructures of Cu-bearing HSLA steels. The details of microstructures were studied by using optical microscopy(OM), transmission electron microscopy(TEM) and hardness test. The as-rolled microstructure of HSLA-A consists of ferrite (${\alpha}$) whereas that of HSLA-B consists of needle-shaped phase. The difference in microstructure can be ascribed to the different amount of Ni, Mn, Mo, Cu which affect the hardenability. The austenite grain size is very small up to $1000^{\circ}C$ owing to the Nb-precipitates. As the austenitizing temperature increases above $1000^{\circ}C$, the austenite grain grows rapidly. There are two hardness peaks in the hardness versus temperature curve, at $500^{\circ}C$ and at $675^{\circ}C$ (HSLA-A), $725^{\circ}C$ (HSLA-B). The peak at $500^{\circ}C$ result from the formation of Cu-precipitates and second hardness peak is created due to the formation of M-A constituents. The hardriess decrease in HSLA-B steel with ageing temperature is small because of the higher amounts of Cu than HSLA-A steel. The fine, round ${\varepsilon}$-Cu precipitates grow with ageing temperature and finally transform into rod shape.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.607-623
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• 2024

This article studies the effects of heat generation/absorption and thermal radiation on the unsteady magnetohydrodynamic (MHD) Casson fluid flow past a vertical plate through rotating porous medium with constant temperature and mass diffusion. It is assumed that the plate temperature and concentration level are raised uniformly. For finding the exact solution, a set of non-dimensional partial differential equations is solved analytically using the Laplace transform technique. The influence of various non-dimensional parameters on the velocity are discussed, including the effects of the magnetic parameter M, heat generation/absorption Q, thermal radiation parameter R, Prandtl number Pr, Schmidt number Sc, permeability of porous medium parameter, Casson fluid parameter γ, on velocity, temperature, and concentration profiles, which are discussed through several figures. It is found that velocity, temperature, and concentration profiles in the case of heat generation parameter Q, Casson fluid parameter γ, thermal Grashof number Gr, mass Grashof number Gc, Permeability Porous medium parameter K, and time t have retarding effects. It is also seen that the magnetic field M, Thermal Radiation parameter R, Prandtl field Pr, Schmidt number Sc have reverse effects on it.