scholarly journals Three-dimensional generalized thermoelasticity with variable thermal conductivity

2020 ◽  
Vol 09 (01) ◽  
pp. 2050002
Author(s):  
Hamdy M. Youssef ◽  
Mowffaq Oreijah ◽  
Hunaydi S. Alsharif
Keyword(s):  
Thermal Conductivity ◽  
Thermal Loading ◽  
Fourier Transforms ◽  
Three Dimensional ◽  
Generalized Thermoelasticity ◽  
Variable Thermal Conductivity ◽  
Rectangular Pulse ◽  
Governing Equations ◽  
Three Dimensional Model ◽  
Double Fourier Transform

In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity is constructed. The resulting nondimensional governing equations, together with the Laplace and double Fourier transform techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free surface. The inverses of double Fourier transforms and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of thermal conductivity has significant effects on all the studied fields.

scholarly journals Numerical simulation of variable thermal conductivity on 3D flow of nanofluid over a stretching sheet

2020 ◽  
Vol 9 (1) ◽  
pp. 233-243 ◽  
Author(s):  
Nainaru Tarakaramu ◽  
P.V. Satya Narayana ◽  
Bhumarapu Venkateswarlu
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Variable Thermal Conductivity ◽  
Normal Velocity ◽  
Transfer Coefficients ◽  
Similarity Transformations ◽  
Frictional Coefficients ◽  
The Impact

AbstractThe present investigation deals with the steady three-dimensional flow and heat transfer of nanofluids due to stretching sheet in the presence of magnetic field and heat source. Three types of water based nanoparticles namely, copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are considered in this study. The temperature dependent variable thermal conductivity and thermal radiation has been introduced in the energy equation. Using suitable similarity transformations the dimensional non-linear expressions are converted into dimensionless system and are then solved numerically by Runge-Kutta-Fehlberg scheme along with well-known shooting technique. The impact of various flow parameters on axial and transverse velocities, temperature, surface frictional coefficients and rate of heat transfer coefficients are visualized both in qualitative and quantitative manners in the vicinity of stretching sheet. The results reviled that the temperature and velocity of the fluid rise with increasing values of variable thermal conductivity parameter. Also, the temperature and normal velocity of the fluid in case of Cu-water nanoparticles is more than that of Al2O3- water nanofluid. On the other hand, the axial velocity of the fluid in case of Al2O3- water nanofluid is more than that of TiO2nanoparticles. In addition, the current outcomes are matched with the previously published consequences and initiate to be a good contract as a limiting sense.

A Node-Dependent Kinematic Approach for Rotordynamics Problems

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Matteo Filippi ◽  
Enrico Zappino ◽  
Erasmo Carrera
Keyword(s):  
Dynamic Analysis ◽  
Computational Cost ◽  
Three Dimensional ◽  
Governing Equations ◽  
Three Dimensional Model ◽  
Flexible Supports ◽  
Out Of Plane ◽  
Kinematic Models ◽  
Carrera Unified Formulation ◽  
Kinematic Approach

This paper presents the dynamic analysis of rotating structures using node-dependent kinematics (NDK) one-dimensional (1D) elements. These elements have the capabilities to assume a different kinematic at each node of a beam element, that is, the kinematic assumptions can be continuously varied along the beam axis. Node-dependent kinematic 1D elements have been extended to the dynamic analysis of rotors where the response of the slender shaft, as well as the responses of disks, has to be evaluated. Node dependent kinematic capabilities have been exploited to impose simple kinematic assumptions along the shaft and refined kinematic models where the in- and out-of-plane deformations appear, that is, on the disks. The governing equations of the rotordynamics problem have been derived in a unified and compact form using the Carrera unified formulation. Refined beam models based on Taylor and Lagrange expansions (LEs) have been considered. Single- and multiple-disk rotors have been investigated. The effects of flexible supports have also been included. The results show that the use of the node-dependent kinematic elements allows the accuracy of the model to be increased only where it is required. This approach leads to a reduction of the computational cost compared to a three-dimensional model while the accuracy of the results is preserved.

Response of ramp-type heating in a monoclinic generalized thermoelastic material

2020 ◽  
Vol 16 (6) ◽  
pp. 1373-1384
Author(s):  
Leena Rani ◽  
Sushant Shekhar
Keyword(s):  
Half Space ◽  
Thermal Loading ◽  
Fourier Transforms ◽  
Generalized Thermoelasticity ◽  
Normal Displacement ◽  
Linear Temperature ◽  
Content Type ◽  
Wide Range ◽  
Eigen Value ◽  
Thermally Conducting

PurposeThe two-dimensional deformation of a homogeneous, thermally conducting, monoclinic material has been studied by using Laplace and Fourier transforms technique. A linear temperature ramping function is used to more realistically model: thermal loading of the half-space surface. The general solution obtained is applied to a specific problem of a half-space subjected to ramp-type heating and loading. The displacements, stresses and temperature distribution so obtained in the physical domain are computed numerically and illustrated graphically. The comparison for Lord-Shulman (L-S), Green and Lindsay (G–L), Green and Naghdi (G–N) and Chandrasekharaiah and Tzou (CTU) theories have been shown graphically to estimate the effect of ramping parameter of heating for an insulated and temperature gradient boundaries.Design/methodology/approachThe design of the study is eigenvalue approachFindingsHomogeneous, thermally conducting monoclinic material has been taken under consideration to study the effect of linear temperature ramping parameter on temperature and normal displacement field. It is observed that magnitude of field quantities is large near the point of application of source for the non-dimensional values of time in all the four models. The numerical values for the field quantities are computed graphically for a wide range of values of finite pulse rise-time in the two situations t0 < t, t0 > t for generalized thermoelasticity theories.Originality/value(1) Governing equations for homogeneous, t0 thermally conducting, monoclinic material are described and solved. (2) Eigen value approach is used to solve the problem. (3) The effect of ramping parameter of heating has been studied for various models of the thermoelasticity to show the comparision between them.

MHD three-dimensional flow of Maxwell fluid with variable thermal conductivity and heat source/sink

2014 ◽  
Vol 24 (5) ◽  
pp. 1073-1085 ◽  
Author(s):  
T. Hayat ◽  
S.A. Shehzad ◽  
A. Alsaedi
Keyword(s):  
Thermal Conductivity ◽  
Differential Equations ◽  
Heat Source ◽  
Three Dimensional ◽  
Maxwell Fluid ◽  
Variable Thermal Conductivity ◽  
Three Dimensional Flow ◽  
Content Type ◽  
Dimensional Flow ◽  
Source Sink

Purpose – The purpose of this paper is to investigate the three-dimensional flow of Maxwell fluid with variable thermal conductivity in presence of heat source/sink. Design/methodology/approach – Similarity transformations are utilized to reduce the nonlinear partial differential equations into ordinary differential equations. The governing nonlinear problems are solved by homotopy analysis method. Findings – The paper found that the velocities decrease while temperature increases for higher Hartman number. It is also seen that the thermal boundary layer thickness and temperature are increased with an increase in variable thermal conductivity parameter and heat source/sink parameter. Practical implications – Heat transfer analysis with heat source/sink has pivotal role in many industrial applications like cooling of an infinite metallic plate in a cooling bath, drawing of plastic films, nuclear plants, gas turbines, various propulsion devices for missiles, space vehicles and processes occurring at high temperatures. Originality/value – This study discusses the magnetohydrodynamic three-dimensional flow of Maxwell fluid with variable thermal conductivity and heat source/sink. No such analysis exists in the literature yet.

Modeling the temperature shock of elastic elements using a one-dimensional model of thermal conductivity

2020 ◽  
pp. 2050060
Author(s):  
D. A. Belousova ◽  
V. V. Serdakova
Keyword(s):  
Thermal Conductivity ◽  
Three Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Temperature Shock ◽  
One Dimensional ◽  
Small Spacecraft ◽  
Proposed Model ◽  
Direct Approximation ◽  
Elastic Elements

This paper considers the task of evaluating micro-accelerations arising due to the temperature shock of large elastic elements when a small spacecraft leaves the Earth’s shadow. In this case, a one-dimensional model of thermal conductivity is used. Its solution was obtained by the method of direct approximation with the construction of difference schemes. It is shown that the accuracy of estimating micro-accelerations is commensurate with the accuracy of solving by a three-dimensional model of thermal conductivity. The proposed model allows reducing the time to obtain estimates and significantly simplifies the task at hand. The results of the work can be used in the formation of the dynamic characteristics of a small spacecraft for technological purposes.

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