Transient Heat Conduction in Elliptical Plates and Cylinders

1959 ◽  
Vol 81 (1) ◽  
pp. 54-58 ◽  
Author(s):  
E. T. Kirkpatrick ◽  
W. F. Stokey
Keyword(s):  
Heat Conduction ◽  
Temperature Change ◽  
Outer Surface ◽  
Digital Computer ◽  
Numerical Evaluation ◽  
Initial Temperature ◽  
Transient Heat Conduction ◽  
Elliptical Cylinder ◽  
Mathieu Functions ◽  
Sudden Temperature Change

In 1945, N. W. McLachlan published the equations governing the problem of heat conduction in a long elliptical cylinder, including the solution for the case of a cylinder with a uniform initial temperature, subject to a sudden temperature change at the outer surface of the cylinder. This paper describes the numerical evaluation of McLachlan’s solution by the use of a digital computer and includes a table of the necessary zeros of the modified Mathieu functions. Tables of the temperatures in cylinders with eccentricities of 0.6, 0.7, 0.8, and 0.9 are given.

The Inverse Problem in Transient Heat Conduction

1964 ◽  
Vol 31 (3) ◽  
pp. 369-375 ◽  
Author(s):  
E. M. Sparrow ◽  
A. Haji-Sheikh ◽  
T. S. Lundgren
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Heat Conduction ◽  
Numerical Calculation ◽  
Initial Temperature ◽  
Transient Heat Conduction ◽  
Analytical Treatment ◽  
Initial Temperature Distribution ◽  
Plane Slab ◽  
Long Cylinder

A general theory is devised for determining the temperature and heat flux at the surface of a solid when the temperature at an interior location is a prescribed function of time. The theory is able to accommodate an initial temperature distribution which varies arbitrarily with position throughout the solid. Detailed analytical treatment is extended to the sphere, the plane slab, and the long cylinder; and it is additionally shown that the semi-infinite solid is a particular case of the general formulation. The accuracy of the method is demonstrated by a numerical example. In addition, a numerical calculation procedure is devised which appears to provide smooth, nonoscillatory results.

Transient Heat Conduction Between a Sphere and a Surrounding Medium of Different Thermal Properties

1964 ◽  
Vol 17 (3) ◽  
pp. 420 ◽  
Author(s):  
JR Philip
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Initial Temperature ◽  
Surrounding Medium ◽  
Transient Heat Conduction ◽  
Infinite Medium ◽  
Ice Crystals ◽  
Evaporation Of Droplets

The paper treats the redistribution of heat between a sphere and an infinite medium of different thermal properties and different initial temperature. The problem is relevant to two geophysical questions: the cooling of laccoliths, and the psychrometry of the growth and evaporation of droplets and ice crystals.

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.

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