scholarly journals A problem in the theory of heat conduction

1921 ◽  
Vol 100 (704) ◽  
pp. 226-240 ◽  
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Hollow Cylinder ◽  
Main Difficulty ◽  
Uniform Temperature ◽  
External Temperature ◽  
The Law

The first problem discussed in this paper is as follows :— “A long hollow cylinder is immersed in a medium of uniform temperature, and at a certain instant, is brought suddenly to a temperature above that of the medium, for example, by the passage through it of a stream of heated liquid. It is maintained at that temperature, and the temperature distribution in the outside medium at any instant, and the rate of leakage of heat from the cylinder, are required.” The main difficulty arises from the fact that the law of temperature on the surface of separation is arbitrary—we shall suppose, in the first instance, that it is constant. Solutions for the external temperature distribution are apparently known only when the surface has a given initial distribution, which is left to adjust itself without further direct supply of heat.

Heat Conduction in an Eccentrically Hollow, Infinitely Long Cylinder With Internal Heat Generation

1961 ◽  
Vol 83 (4) ◽  
pp. 510-512 ◽  
Author(s):  
M. R. El-Saden
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Hollow Cylinder ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Theoretical Solution ◽  
Steady Temperature ◽  
Special Case ◽  
Long Cylinder

This paper discusses the steady temperature distribution in an infinitely long, eccentrically hollow cylinder with uniform rate of internal heat generation. An exact theoretical solution is presented. The result is applied to the special case of no internal heat generation, and the rate of heat conduction is obtained.

IMPACT OF EXTERNAL TEMPERATURE DISTRIBUTION ON THE TURBULENT AND THERMAL FIELDS IN A VERTICAL UNIFORMLY HEATED CHANNEL

2018 ◽  
Author(s):  
Martin Thebault ◽  
Stephanie Giroux-Julien ◽  
Victoria Timchenko ◽  
Christophe Menezo ◽  
John Reizes
Keyword(s):  
Temperature Distribution ◽  
External Temperature ◽  
Thermal Fields ◽  
Heated Channel

An analytical solution of a two-dimensional temperature field in a hollow cylinder under a time periodic boundary condition using Fourier series

2009 ◽  
Vol 223 (8) ◽  
pp. 1889-1901 ◽  
Author(s):  
G Atefi ◽  
M A Abdous ◽  
A Ganjehkaviri ◽  
N Moalemi
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Separation Of Variables ◽  
Two Dimensional

The objective of this article is to derive an analytical solution for a two-dimensional temperature field in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface, while the inner surface is insulated. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Because of the time-dependent term in the boundary condition, Duhamel's theorem is used to solve the problem for a periodic boundary condition. The periodic boundary condition is decomposed using the Fourier series. This condition is simulated with harmonic oscillation; however, there are some differences with the real situation. To solve this problem, first of all the boundary condition is assumed to be steady. By applying the method of separation of variables, the temperature distribution in a hollow cylinder can be obtained. Then, the boundary condition is assumed to be transient. In both these cases, the solutions are separately calculated. By using Duhamel's theorem, the temperature distribution field in a hollow cylinder is obtained. The final result is plotted with respect to the Biot and Fourier numbers. There is good agreement between the results of the proposed method and those reported by others for this geometry under a simple harmonic boundary condition.

scholarly journals Understanding the thermal problem of variable gradient functionally graded plate based on hybrid numerical method under linear heat source

2021 ◽  
Vol 13 (5) ◽  
pp. 168781402110178
Author(s):  
Jianhui Tian ◽  
Guoquan Jing ◽  
Xingben Han ◽  
Guangchu Hu ◽  
Shilin Huo
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Heat Source ◽  
Numerical Method ◽  
Functionally Graded ◽  
Thermal Problem ◽  
Linear Heat ◽  
Hybrid Numerical Method ◽  
Linear Heat Source ◽  
Gradient Parameter

The thermal problem of functionally graded materials (FGM) under linear heat source is studied by a hybrid numerical method. The accuracy of the analytical method and the efficiency of the finite element method are taken into account. The volume fraction of FGM in the thickness direction can be changed by changing the gradient parameters. Based on the weighted residual method, the heat conduction equation under the third boundary condition is established. The temperature distribution of FGM under the action of linear heat source is obtained by Fourier transform. The results show that the closer to the heat source it is, the greater the influence of the heat source is and the influence of the heat source is local. The temperature change trend of the observation points is consistent with the heat source, showing a linear change. The results also show that the higher the value of gradient parameter is, the higher the temperature of location point is. The temperature distribution of observation points is positively correlated with gradient parameter. When the gradient parameter value exceeds a certain value, it has a little effect on the temperature change in the model and the heat conduction in the model tends to be pure metal heat conduction, the optimal gradient parameters combined the thermal insulation property of ceramics and the high strength toughness of metals are obtained.

scholarly journals Shape Effect on the Temperature Field during Microwave Heating Process

2018 ◽  
Vol 2018 ◽  
pp. 1-24 ◽  
Author(s):  
Zhijun Zhang ◽  
Tianyi Su ◽  
Shiwei Zhang
Keyword(s):  
Electromagnetic Field ◽  
Heat Conduction ◽  
Temperature Distribution ◽  
Microwave Cavity ◽  
Heating Process ◽  
Shape Effect ◽  
Power Absorption ◽  
Sample Shape ◽  
Distribution Uniformity ◽  
Microwave Process

Aiming at improving the food quality during microwave process, this article mainly focused on the numerical simulation of shape effect, which was evaluated by microwave power absorption capability and temperature distribution uniformity in a single sample heated in a domestic microwave oven. This article only took the electromagnetic field and heat conduction in solid into consideration. The Maxwell equations were used to calculate the distribution of microwave electromagnetic field distribution in the microwave cavity and samples; then the electromagnetic energy was coupled as the heat source in the heat conduction process in samples. Quantitatively, the power absorption capability and temperature distribution uniformity were, respectively, described by power absorption efficiency (PAE) and the statistical variation of coefficient (COV). In addition, we defined the comprehensive evaluation coefficient (CEC) to describe the usability of a specific sample. In accordance with volume or the wave numbers and penetration numbers in the radial and axial directions of samples, they can be classified into different groups. And according to the PAE, COV, and CEC value and the specific need of microwave process, an optimal sample shape and orientation could be decided.

Non-uniform temperature distribution of the main reflector of a large radio telescope under solar radiation

2021 ◽  
Vol 21 (11) ◽  
pp. 293
Author(s):  
Shan-Xiang Wei ◽  
De-Qing Kong ◽  
Qi-Ming Wang
Keyword(s):  
Temperature Field ◽  
Temperature Distribution ◽  
Solar Radiation ◽  
Radio Telescope ◽  
Thermal Imaging ◽  
Uniform Temperature ◽  
Large Radio Telescope ◽  
Uniform Temperature Distribution ◽  
Uniform Temperature Field ◽  
Main Reflector

Abstract The non-uniform temperature distribution of the main reflector of a large radio telescope may cause serious deformation of the main reflector, which will dramatically reduce the aperture efficiency of a radio telescope. To study the non-uniform temperature field of the main reflector of a large radio telescope, numerical calculations including thermal environment factors, the coefficients on convection and radiation, and the shadow boundary of the main reflector are first discussed. In addition, the shadow coverage and the non-uniform temperature field of the main reflector of a 70-m radio telescope under solar radiation are simulated by finite element analysis. The simulation results show that the temperature distribution of the main reflector under solar radiation is very uneven, and the maximum of the root mean square temperature is 12.3°C. To verify the simulation results, an optical camera and a thermal imaging camera are used to measure the shadow coverage and the non-uniform temperature distribution of the main reflector on a clear day. At the same time, some temperature sensors are used to measure the temperature at some points close to the main reflector on the backup structure. It has been verified that the simulation and measurement results of the shadow coverage on the main reflector are in good agreement, and the cosine similarity between the simulation and the measurement is above 90%. Despite the inevitable thermal imaging errors caused by large viewing angles, the simulated temperature field is similar to the measured temperature distribution of the main reflector to a large extent. The temperature trend measured at the test points on the backup structure close to the main reflector without direct solar radiation is consistent with the simulated temperature trend of the corresponding points on the main reflector with the solar radiation. It is credible to calculate the temperature field of the main reflector through the finite element method. This work can provide valuable references for studying the thermal deformation and the surface accuracy of the main reflector of a large radio telescope.

Embedded resistive heating in composite scarf repairs

2016 ◽  
Vol 51 (18) ◽  
pp. 2575-2583 ◽  
Author(s):  
Mahdi Ashrafi ◽  
Brandon P Smith ◽  
Santosh Devasia ◽  
Mark E Tuttle
Keyword(s):  
Temperature Distribution ◽  
Outer Surface ◽  
Thermal Gradient ◽  
Thermal Damage ◽  
Electrical Current ◽  
Tensile Tests ◽  
Resistance Heating ◽  
Uniform Temperature ◽  
Uniform Temperature Distribution ◽  
Bond Strengths

Composite scarf repairs were cured using heat generated by passing an electrical current through a woven graphite-epoxy prepreg embedded in the bondline. Resistance heating using the embedded prepreg resulted in a more uniform temperature distribution in the bondline while preventing any potential thermal damage to the surface of the scarf repairs. In contrast, conventional surface heating methods such as heat blankets or heat lamps lead to large through thickness thermal gradient that causes non-uniform temperature in the bondline and overheating the outer surface adjacent to the heater. Composite scarf repair specimens were created using the proposed embedded heating approach and through the use of a heat blanket for circular and rectangular scarf configurations. Tensile tests were performed for rectangular scarf specimens, and it was shown that the bond strengths of all specimens were found to be comparable. The proposed embedded curing technique results in bond strengths that equal or exceed those achieved with external heating and avoids overheating the surface of the scarf repairs.

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