An Exact Solution for Transient Anisotropic Heat Conduction in Composite Cylindrical Shells

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Hossein Rahmani ◽  
Mahmood Norouzi ◽  
Alireza Komeili Birjandi ◽  
Amir Komeili Birjandi
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Cylindrical Shells ◽  
Cylindrical Vessel ◽  
Conductive Heat ◽  
Composite Shells ◽  
Fiber Angle ◽  
Present Solution ◽  
Composite Cylindrical Shells

Abstract In this study, an analytical solution is proposed for the problem of transient anisotropic conductive heat transfer in composite cylindrical shells. The composite shells are considered to have directional heat transfer properties, which is due to the existence of fibers which can be winded in any direction. The composite shells usually show high conductivity in the direction parallel to fiber direction and low conductivity in other two orthogonal directions. To solve the heat transfer partial differential equation, finite Fourier transform and separation of variables method are used. The present solution is used to find the temperature distribution in a composite cylindrical vessel for which the composite material is graphite/epoxy and the vessel is prone to an external heat flux and also ambient flow. The analytical solution is verified perfectly by the data obtained from a second-order finite difference solution. The solution is used to investigate the effects of values of fiber angle and material conductivity coefficients on temperature distribution of the composite cylindrical vessel. The results show the important role of fiber angle values on the temperature distribution of vessel.

Prediction of Weld Bead Parameters, Transient Temperature Distribution & HAZ Width of Submerged Arc Welded Structural Steel Plates

2012 ◽  
Vol 326-328 ◽  
pp. 405-409 ◽  
Author(s):  
Aniruddha Ghosh ◽  
Somnath Chattopadhyaya ◽  
N.K. Singh
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Welding Process ◽  
Weld Bead ◽  
Transient Temperature ◽  
Conductive Heat ◽  
Transient Temperature Distribution ◽  
Haz Width ◽  
Submerged Arc

In submerged arc welding process, concept on temperature distribution is essential in order to control HAZ dimensions and get the required bead size and quality. In this paper, an analytical solution for moving heat source with Gaussian distribution of inside volume of central conicoidal shape is derived. Heat transfer in welded plates during welding is assumed to be conductive heat transfer of a semi infinite body. With the help of this analytical solution, transient temperature distribution, HAZ width, weld bead dimensions are estimated. Good agreements between predicted and experimental values are achieved.

A New Exact Analysis for Anisotropic Conductive Heat Transfer in Truncated Composite Spherical Shells

2019 ◽  
Vol 35 (5) ◽  
pp. 677-691
Author(s):  
M. Norouzi ◽  
H. Rahmani ◽  
A. K Birjandi
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Integral Transformation ◽  
Internal Heat ◽  
Heat Radiation ◽  
Fiber Direction ◽  
Conductive Heat ◽  
Spherical Shells ◽  
Transform Method ◽  
Fiber Angle

ABSTRACTIn the present paper, a general analytical solution is proposed for anisotropic heat conduction through truncated composite spherical shells. The solution is so important in designing the spherical vessels which are usually used to store the CNG, LNG, LPG and other petroleum condensates. Herein, it is supposed that the fiber angle of composite laminate is in range of zero to 90 degrees. Heat convection with ambient flow, an external heat radiation, and a possible internal heat generation are modeled within the heat transfer equation. The exact solution is derived using the complex finite Fourier transform method. The particular solution of transferred equation is found based on the Green’s function and Sturm-Liouville theories. Finally, an inverse integral transformation is applied to form the final analytical solution in physical space. Defining four materials differing in the value of conductivity coefficient in fiber direction, the effects of used composite material and fiber angle on temperature distribution of the spherical shell are investigated in detail.

A Comparison Between 2-D and 3-D Conduction Shape Factors

2003 ◽  
Author(s):  
Devashish Shrivastava ◽  
Robert Roemer
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Cross Section ◽  
Three Dimensional ◽  
Cylindrical Vessel ◽  
Shape Factors ◽  
Axial Conduction ◽  
Power Deposition ◽  
Tissue Matrix

Conduction shape factors are frequently used in a variety of heat transfer applications to evaluate heat transfer from one three-dimensional body to another three-dimensional body. Previous investigators have used conduction shape factors derived using the 2-D cross-section of the 3-D geometries for non-heating conditions as approximations to 3-D conduction shape factors with heating and no-heating present. This paper investigates the suitability of neglecting the axial conduction and power deposition in deriving expressions for conduction shape factors for the case of a single, cylindrical vessel imbedded concentrically in a cylindrical, uniformly heated tissue matrix. It is shown that 1) conduction shape factors are functions of the deposited power and the temperature distribution and 2) the magnitudes of conduction shape factors are affected significantly by axial conduction.

Exact Solution of Unsteady Conductive Heat Transfer in Cylindrical Composite Laminates

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
M. Norouzi ◽  
S. M. Rezaei Niya ◽  
M. H. Kayhani ◽  
M. Shariati ◽  
M. Karimi Demneh ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Exact Solution ◽  
Temperature Distribution ◽  
Composite Laminates ◽  
Exact Analytical Solution ◽  
Conductive Heat Transfer ◽  
Orthotropic Materials ◽  
Conductive Heat ◽  
Multilayer Composite ◽  
Unsteady Temperature

This paper presents an exact analytical solution for unsteady conductive heat transfer in a cylindrical multilayer composite laminate. Here, it is supposed that fibers have been wound around the cylinder in each lamina. In order to find the exact solution, the Laplace transformation is applied on anisotropic heat conduction equation to convert the time scale of problem to frequency scale and the separation of variable method is used to solve the resulted partial differential equations. The effect of fibers arrangements of multilayer cylindrical laminates and thermal boundary conditions on unsteady conductive heat transfer of these orthotropic materials is studied based on the exact solution that is presented in the current investigation. The analytical results illustrated that the unsteady temperature distribution in any multilayer composite laminates is in a state between the temperature distribution in single layer laminates with fibers’ angle equal to 0 deg and 90 deg.

Numerical Simulations and Experimental Characterization of Heat Transfer From a Periodic Impingement of Droplets

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Mario F. Trujillo ◽  
Jorge Alvarado ◽  
Eelco Gehring ◽  
Guillermo S. Soriano
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Temperature Distribution ◽  
Numerical Simulations ◽  
Droplet Impact ◽  
Numerical Comparison ◽  
Temperature Profiles ◽  
Conductive Heat ◽  
Radial Temperature ◽  
The Impact

In this combined experimental and simulation investigation, a stream of HFE-7100 droplets striking a prewetted surface under constant heat flux was studied. An implicit free surface capturing technique based on the Volume-of-Fluid (VOF) approach was employed to simulate this process numerically. Experimentally, an infrared thermography technique was used to measure the temperature distribution of the surface consisting of a 100 nm ITO layer on a ZnSe substrate. The heat flux was varied to investigate the heat transfer behavior of periodic droplet impingement at the solid–liquid interface. In both experiments and simulations, the morphology of the impact zone was characterized by a quasi-stationary liquid impact crater. Comparison of the radial temperature profiles on the impinging surface between the experiments and numerical simulations yielded reasonable agreement. Due to the strong radial flow emanating from successive droplet impacts, the temperature distribution inside the crater region was found to be significantly reduced from its saturated value. In effect, the heat transfer mode in this region was governed by single phase convective and conductive heat transfer, and was mostly affected by the HFE-7100 mass flow rates or the number of droplets. At higher heat fluxes, the minimum temperature, and its gradient with respect to the radial coordinate, increased considerably. Numerical comparison between average and instantaneous temperature profiles within the droplet impact region showed the effect of thermal mixing produced by the liquid crowns formed during successive droplet impact events.

scholarly journals Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Te-Wen Tu ◽  
Sen-Yung Lee
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Analytical Solution ◽  
Transfer Coefficient ◽  
Time Dependent ◽  
Physical Parameters ◽  
Expansion Theorem ◽  
Present Solution ◽  
Hollow Cylinders

An analytical solution for the heat transfer in hollow cylinders with time-dependent boundary condition and time-dependent heat transfer coefficient at different surfaces is developed for the first time. The methodology is an extension of the shifting function method. By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. The transformed system is thus solved by series expansion theorem. Limiting cases of the solution are studied and numerical results are compared with those in the literature. The convergence rate of the present solution is fast and the analytical solution is simple and accurate. Also, the influence of physical parameters on the temperature distribution of a hollow cylinder along the radial direction is investigated.

Exact Analytical Solution for Unsteady Heat Conduction in Fiber-Reinforced Spherical Composites Under the General Boundary Conditions

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
A. Amiri Delouei ◽  
M. Norouzi
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Laplace Transformation ◽  
Exact Analytical Solution ◽  
Function Technique ◽  
Conductive Heat ◽  
Fiber Reinforced ◽  
Legendre Series

The current study presents an exact analytical solution for unsteady conductive heat transfer in multilayer spherical fiber-reinforced composite laminates. The orthotropic heat conduction equation in spherical coordinate is introduced. The most generalized linear boundary conditions consisting of the conduction, convection, and radiation heat transfer is considered both inside and outside of spherical laminate. The fibers' angle and composite material in each lamina can be changed. Laplace transformation is employed to change the domain of the solutions from time into the frequency. In the frequency domain, the separation of variable method is used and the set of equations related to the coefficients of Fourier–Legendre series is solved. Meromorphic function technique is utilized to determine the complex inverse Laplace transformation. Two functional cases are presented to investigate the capability of current solution for solving the industrial unsteady problems in different arrangements of multilayer spherical laminates.

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