Analytical Solution and Symbolic Computation for the Temperature Distribution of the Annular Fin under Fully Wet‐Surface Condition

2008 ◽  
Author(s):  
Sanoe Koonprasert ◽  
Rilrada Sangsawang
Keyword(s):  
Temperature Distribution ◽  
Analytical Solution ◽  
Symbolic Computation ◽  
Surface Condition ◽  
Annular Fin ◽  
Wet Surface

Fin Efficiency of an Annular Fin Composed of a Substrate Metallic Fin and a Coating Layer

2006 ◽  
Vol 128 (8) ◽  
pp. 851-854 ◽  
Author(s):  
Ping Tu ◽  
Hideo Inaba ◽  
Akihiko Horibe ◽  
Zhongmin Li ◽  
Naoto Haruki
Keyword(s):  
Thermal Conductivity ◽  
Numerical Calculation ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Layer Thickness ◽  
Coating Layer ◽  
Fin Efficiency ◽  
Analytical Results ◽  
Annular Fin ◽  
Coating Layer Thickness

An analytical solution to a composite annular fin made of a substrate metallic fin and a coating layer has been carried out. Useful expressions for calculating temperature distribution and fin efficiency have been derived. Comparing the analytical results to those of numerical calculation, the premise for the expressions is also explored. Theoretical analyzing results show that fin efficiency of a coated fin decreases with an increase of the coating layer thickness if the thermal conductivity of coating layer is much less than that of the substrate metallic fin. Whereas, the reverse influence of the coating layer thickness on the fin efficiency appears if the thermal conductivity of the coating layer is beyond the above range.

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 An Analytical Approach to Wet Cooling Towers Based on Functional Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Guo Qianjian ◽  
Xiaoni Qi ◽  
Zheng Wei ◽  
Peng Sun
Keyword(s):  
Functional Analysis ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Cooling Tower ◽  
Transfer Model ◽  
Cooling Towers ◽  
Contraction Mapping Theorem ◽  
Uniqueness Of The Solution ◽  
Linear Differential ◽  
Analytical Expressions

An analytical solution for computing the temperature distribution of air and water over the height through the cooling tower is so complex that finding the exact solution takes too much time. The purpose of this paper is to present efficient and accurate analytical expressions for the heat and mass transfer model in cooling towers. Based on the method of functional analysis, we derived an analytical solution for temperature distribution of water and air by using the method of solving linear differential equations. The error estimation, the existence, and uniqueness of the solution are given by using Banach contraction mapping theorem. The basic equation of the model on the basis of the additional assumptions on the cooling tower is solved, and the outlet parameters are also obtained.

Use of Lagrangian-Eulerian Computing Method for Systems with Phase Change at the Solution of Stefan Boundary Value Problem

2016 ◽  
Vol 685 ◽  
pp. 177-180
Author(s):  
Alexander S. Ogorodnikov ◽  
M.V. Troshin
Keyword(s):  
Temperature Distribution ◽  
Analytical Solution ◽  
Phase Change ◽  
Nonstationary Problem ◽  
Problem Solution ◽  
Infinite Plane ◽  
Two Dimensional ◽  
Planar Solidification ◽  
Change Material ◽  
Computing Method

The problem of a planar solidification of a material with an additional nonstationary radiant of heat on a semi-infinite plane has been solved. For a solution the condition of Stefan was used. Results have been compared with an analytical solution in case of the absence of an additional radiant of heat, as well as with a solution obtained by perturbations method. A more complicated two-dimensional nonstationary problem of a solidification of a liquid with interface free-boundary has been also solved. The purpose of this problem solution is to predict position of a material phase boundary, as well as the temperature distribution in a layer of PCM (Phase-Change Material) with boundary conditions of Dirichlet.

scholarly journals Two-Dimensional Analytical Solution of the Laminar Forced Convection in a Circular Duct with Periodic Boundary Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
M. R. Astaraki ◽  
N. Ghiasi Tabari
Keyword(s):  
Boundary Condition ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Periodic Function ◽  
Forced Convection ◽  
Solid Wall ◽  
Convection Heat Transfer ◽  
Axial Direction ◽  
Energy Balance Equation ◽  
Circular Duct

In the present study analytical solution for forced convection heat transfer in a circular duct with a special boundary condition has been presented, because the external wall temperature is a periodic function of axial direction. Local energy balance equation is written with reference to the fully developed regime. Also governing equations are two-dimensionally solved, and the effect of duct wall thickness has been considered. The temperature distribution of fluid and solid phases is assumed as a periodic function of axial direction and finally temperature distribution in the flow field, solid wall, and local Nusselt number, is obtained analytically.

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