One-dimensional transient heat conduction in a bilayer finite slab: A case study in the printing process

2017 ◽  
Vol 47 (2) ◽  
pp. 305-319
Author(s):  
Uditya Borah ◽  
Dipal Baruah
Keyword(s):  
Heat Conduction ◽  
Transient Heat Conduction ◽  
Printing Process ◽  
One Dimensional ◽  
Finite Slab

scholarly journals Electrocaloric devices part I: Analytical solution of one-dimensional transient heat conduction in a multilayer electrocaloric system

2020 ◽  
Vol 10 (06) ◽  
pp. 2050028
Author(s):  
Farrukh Najmi ◽  
Wenxian Shen ◽  
Lorenzo Cremaschi ◽  
Z.-Y. Cheng
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Initial Temperature ◽  
Transient Heat Conduction ◽  
Typical Structure ◽  
One Dimensional ◽  
Conduction Heat Transfer ◽  
Materials Used

The analytical solution is reported for one-dimensional (1D) dynamic conduction heat transfer within a multilayer system that is the typical structure of electrocaloric devices. Here, the multilayer structure of typical electrocaloric devices is simplified as four layers in which two layers of electrocaloric materials (ECMs) are sandwiched between two semi-infinite bodies representing the thermal sink and source. The temperature of electrocaloric layers can be instantaneously changed by external electric field to establish the initial temperature profile. The analytical solution includes the temperatures in four bodies as a function of both time and location and heat flux through each of the three interfaces as a function of time. Each of these analytical solutions includes five infinite series. It is proved that each of these series is convergent so that the sum of each series can be calculated using the first [Formula: see text] terms of the series. The formula for calculating the value of [Formula: see text] is presented so that the simulation of an electrocaloric device, such as the temperature distribution and heat transferred from one body to another can be performed. The value of [Formula: see text] is dependent on the thickness of electrocaloric material layers, the time of heat conduction, and thermal properties of the materials used. Based on a case study, it is concluded that the [Formula: see text] is mostly less than 20 and barely reaches more than 70. The application of the analytical solutions for the simulation of real electrocaloric devices is discussed.

Enhanced Explicit Scheme to Solve Transient Heat Conduction Problem

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
Ganesh Hegde ◽  
Madhu Gattumane
Keyword(s):  
Heat Conduction ◽  
Correction Factor ◽  
Truncation Error ◽  
Transient Heat Conduction ◽  
Explicit Scheme ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Time Step ◽  
One Dimensional ◽  
Partial Derivatives

Improvement in accuracy without sacrificing stability and convergence of the solution to unsteady diffusion heat transfer problems by computational method of enhanced explicit scheme (EES), has been achieved and demonstrated, through transient one dimensional and two dimensional heat conduction. The truncation error induced in the explicit scheme using finite difference technique is eliminated by optimization of partial derivatives in the Taylor series expansion, by application of interface theory developed by the authors. This theory, in its simple terms gives the optimum values to the decision vectors in a redundant linear equation. The time derivatives and the spatial partial derivatives in the transient heat conduction, take the values depending on the time step chosen and grid size assumed. The time correction factor and the space correction factor defined by step sizes govern the accuracy, stability and convergence of EES. The comparison of the results of EES with analytical results, show decreased error as compared to the result of explicit scheme. The paper has an objective of reducing error in the explicit scheme by elimination of truncation error introduced by neglecting the higher order terms in the expansion of the governing function. As the pilot examples of the exercise, the implementation is aimed at solving one-dimensional and two-dimensional problems of transient heat conduction and compared with the results cited in the referred literature.

One-Dimensional Transient Heat Conduction in Composite Living Perfuse Tissue

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
S. M. Becker
Keyword(s):  
Heat Conduction ◽  
Initial Conditions ◽  
Separation Of Variables ◽  
Composite Layer ◽  
Circulatory System ◽  
Transient Heat Conduction ◽  
Bioheat Equation ◽  
Perfusion Rate ◽  
One Dimensional ◽  
Perfuse Tissue

Modeling the conduction of heat in living tissue requires the consideration of sudden spatial discontinuities in property values as well as the presence of the body's circulatory system. This paper presents a description of the separation of variables method that results in a remarkably simple solution of transient heat conduction in a perfuse composite slab for which at least one of the layers experiences a zero perfusion rate. The method uses the natural analytic approach and formats the description so that the constants of integration of each composite layer are expressed in terms of those of the previous layer's eigenfunctions. This allows the solution to be “built” in a very systematic and sequential manner. The method is presented in the context of the Pennes bioheat equation for which the solution is developed for a system composed of any number of N layers with arbitrary initial conditions.

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