Analytical Solution of the Problem of Heat Conduction of a Semi-Bounded Body with an Envelope and Its Application to Control and Identification of Heat Transfer Processes

2006 ◽  
Vol 37 (2) ◽  
pp. 183-189
Author(s):  
N. M. Lazuchenkov ◽  
D. N. Lazuchenkov
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Transfer Processes ◽  
Bounded Body

scholarly journals Modeling methodology of locally non-equilibrium heat conductivity processes

Vestnik IGEU ◽  
2020 ◽  
pp. 65-71
Author(s):  
A.V. Eremin
Keyword(s):  
Mathematical Modeling ◽  
Heat Transfer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Equation ◽  
Exact Analytical Solution ◽  
Separation Of Variables ◽  
Infinite Plate ◽  
Transfer Processes ◽  
Non Equilibrium

With the development of laser technologies and the ability to carry out processing steps under extreme conditions (ul-trahigh temperatures, pressures and their gradients), the interest in studying the processes that occur under locally non-equilibrium conditions has grown significantly. The key directions for the description of locally non-equilibrium pro-cesses include thermodynamic, kinetic and phenomenological ones. The locally non-equilibrium transfer equations can also be derived from the Boltzmann equation by using the theory of random walks and molecular-kinetic methods. It should be noted that some options of locally non-equilibrium processes lead to conflicting results. This study aims to develop a method for mathematical modeling of locally nonequilibrium heat conduction processes in solids, which allows determining their temperature with high accuracy during fast and high-intensity heat transfer processes. As applied to heat transfer processes in solids, a generalized heat equation that takes into account the relaxation properties of materials is formulated. The exact analytical solution is obtained using the Fourier method of separation of variables. The methodology for mathematical modeling of locally non-equilibrium transfer processes based on modified conservation laws has been developed. The generalized differential heat equation which allows performing N-fold relaxation of the heat flow and temperature in the modified heat balance equation has been formulated. For the first time, an exact analytical solution to the unsteady heat conduction problem for an infinite plate was obtained taking into account many-fold relaxation. The analysis of the solution to the boundary value problem of locally nonequilibrium heat conduction enabled to conclude that it is impossible to instantly has establish a boundary condition of the first kind. It has been demonstrated that each of the following terms in the relaxed heat equation has an ever smaller effect on the heat transfer process. The obtained results can be used by the scientific and technical personnel of organizations and higher educational institutions in the study of fuel ignition processes, the development of laser processing of materials, the design of highly efficient heat transfer equipment and the description of fast-flowing heat transfer processes.

scholarly journals An Analytical Solution for Transient Heat Conduction in a Composite Slab with Time-Dependent Heat Transfer Coefficient

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Ryoichi Chiba
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Differential Equations ◽  
Transfer Coefficient ◽  
Transient Heat Conduction ◽  
External Boundary ◽  
Composite Slab ◽  
Composite Slabs

An analytical solution is derived for one-dimensional transient heat conduction in a composite slab consisting of n layers, whose heat transfer coefficient on an external boundary is an arbitrary function of time. The composite slab, which has thermal contact resistance at n-1 interfaces, as well as an arbitrary initial temperature distribution and internal heat generation, convectively exchanges heat at the external boundaries with two different time-varying surroundings. To obtain the analytical solution, the shifting function method is first used, which yields new partial differential equations under conventional types of external boundary conditions. The solution for the derived differential equations is then obtained by means of an orthogonal expansion technique. Numerical calculations are performed for two composite slabs, whose heat transfer coefficient on the heated surface is either an exponential or a trigonometric function of time. The numerical results demonstrate the effects of temporal variations in the heat transfer coefficient on the transient temperature field of composite slabs.

Analytical Solution of Nonequilibrium Heat Conduction in Porous Medium Incorporating a Variable Porosity Model With Heat Generation

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
M. Nazari ◽  
F. Kowsary
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Transfer Coefficient ◽  
Heat Generation ◽  
Conductivity Ratio ◽  
Variable Porosity ◽  
Porosity Model

This paper is concerned with the conduction heat transfer between two parallel plates filled with a porous medium with uniform heat generation under a nonequilibrium condition. Analytical solution is obtained for both fluid and solid temperature fields at constant porosity incorporating the effects of thermal conductivity ratio, porosity, and a nondimensional heat transfer coefficient at pore level. The two coupled energy equations for the case of variable porosity condition are transformed into a third order ordinary equation for each phase, which is solved numerically. This transformation is a valuable solution for heat conduction regime for any distribution of porosity in the channel. The effects of the variable porosity on temperature distribution are shown and compared with the constant porosity model. For the case of the exponential decaying porosity distribution, the numerical results lead to a correlation incorporating conductivity ratio and interstitial heat transfer coefficient.

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.

scholarly journals A Review of Peridynamics (PD) Theory of Diffusion Based Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Migbar Assefa Zeleke ◽  
Mesfin Belayneh Ageze
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Transfer Processes ◽  
Recent Developments ◽  
Nonlocal Nature

The study of heat conduction phenomena using peridynamic (PD) theory has a paramount significance on the development of computational heat transfer. This is because PD theory has got an interesting feature to deal with the inherent nonlocal nature of heat transfer processes. Since the revolutionary work on PD theory by Silling (2000), extensive investigations have been devoted to PD theory. This paper provides a survey on the recent developments of PD theory mainly focusing on diffusion based peridynamic (PD) formulation. Both the bond-based and state-based PD formulations are revisited, and numerical examples of two-dimensional problems are presented.

Analytical Solution of the Problem of Conjugate Heat Transfer between a Gasdynamic Boundary Layer and Anisotropic Strip

2020 ◽  
pp. 44-59
Author(s):  
V.F. Formalev ◽  
S.A. Kolesnik ◽  
B.A. Garibyan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Conjugate Heat Transfer ◽  
Heat Fluxes ◽  
The Body ◽  
Conductivity Tensor

The paper focuses on the problem of conjugate heat transfer between the thermal-gas-dynamic boundary layer and the anisotropic strip in conditions of aerodynamic heating of aircraft. Under the assumption of an incompressible flow which takes place in the shock layer behind the direct part of the shock wave, we found a new analytical solution for the components of the velocity vector, temperature distribution, and heat fluxes in the boundary layer. The obtained heat fluxes at the interface between the gas and the body are included as boundary conditions in the problem of anisotropic heat conduction in the body. The study introduces an analytical solution to the second initial-boundary value problem of heat conduction in an anisotropic strip with arbitrary boundary conditions at the interfaces, with heat fluxes which are obtained by solving the problem of a thermal boundary layer used at the interface. An analytical solution to the conjugate problem of heat transfer between a boundary layer and an anisotropic body can be effectively used to control, e.g. to reduce, heat fluxes from the gas to the body if the strip material chosen is such that the longitudinal component of the thermal conductivity tensor is many times larger than the transverse component of the thermal conductivity tensor. Such adjustment is possible due to an increase in body temperature in the longitudinal direction, and, consequently, a decrease in the heat flow from the gas to the body, as well as due to a favorable change in the physical characteristics of the gas. Results of numerical experiments are obtained and analyzed

scholarly journals ORIGINATION AND PROPAGATION OF TEMPERATURE SOLITONS WITH WAVE HEAT TRANSFER IN THE BOUNDED AREA DURING ADDITIVE TECHNOLOGICAL PROCESSES

2019 ◽  
Vol 16 (33) ◽  
pp. 505-515
Author(s):  
V. F. FORMALEV ◽  
S. A. KOLESNIK ◽  
E. L. KUZNETSOVA ◽  
L. N. RABINSKIY
Keyword(s):  
Heat Transfer ◽  
Forward Direction ◽  
The Body ◽  
Solid Surfaces ◽  
Initial Time ◽  
Transfer Processes ◽  
Bounded Area ◽  
Power Radiation ◽  
High Power Radiation ◽  
Bounded Body

Within this work, based on analyses of problems on wave heat transfer in bounded bodies, the theory of thermally isolated waves (solitons) is developed to investigate the heat transfer processes in the initial time vicinity and in the vicinity of the bounded body, that is the time scales are commensurate with the relaxation time (nanoseconds), and the scales of the spatial variable are measured in nanometers. A new analytical solution of the wave heat transfer based on the heat conduction equation of hyperbolic type under the action of a series of solitons was received, based on which the interaction of individual solitons with each other, absorption and reflection of the solitons from the body boundaries was analyzed. Analysis of a large number of results made clear that thermal solitons reflect not as mechanical ones, since first there is absorption of the soliton thermal energy by the heat-insulated boundary on the heat-insulated walls, and then the energy is rejected by the thermal conductivity in the opposite direction. It was found that the temperature gradient inside the soliton is negative in the forward direction and positive in the reflected direction. The results of the paper can be used in thermal interaction of high-power radiation with solid surfaces, as well as in the problems of quantum mechanics.

Heat Conduction Across Corrugated Thermal Interface

2007 ◽  
Author(s):  
Bozhi Yang ◽  
Wenjun Liu
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
High Performance ◽  
Fem Simulation ◽  
Expansion Method ◽  
Thermal Interface Material ◽  
Thermal Interface ◽  
Eigenfunction Expansion Method ◽  
First Time

This paper presents the analytical solution of the heat conduction across a corrugated thermal interface material with rectangular straight fin arrangement. Domain decomposition and eigenfunction expansion method were used to study the thermal diffusion in such geometry for the first time. The temperature field solved from the analytical method agrees well with FEM simulation. The total heat transfer rate across the corrugated interface and thermal boundary resistance were derived analytically also. Results have shown that the effective thermal resistance across the interface can be significantly reduced with the corrugated TIM geometry. The analytical solution in the paper can provide insight into geometry effect on the heat transfer enhancement, and is a very useful complement to experimental work and numerical simulation in designing high-performance corrugated thermal interface.

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