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.

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.

Estimation of transient wall and flow temperature distributions in a circular duct using an inverse approach

2007 ◽  
Vol 221 (11) ◽  
pp. 1353-1361
Author(s):  
S D Masouros ◽  
K Mathioudakis
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Forced Convection ◽  
Convection Heat Transfer ◽  
Convection Heat ◽  
Convection Heat Transfer Coefficient ◽  
Circular Duct ◽  
Inverse Approach ◽  
Forced Convection Heat Transfer

Inverse methods have become a useful tool for estimating parameters that cannot be measured or calculated directly in engineering applications. Parameters characterizing unsteady heat convection in circular duct flows are associated with numerous uncertainties. This fact renders the inverse approach appropriate for the determination of these parameters. An inverse problem for transient turbulent thermally developing and thermally developed forced-convection flow in a circular duct is formulated and discussed, and a simplified direct thermal model is presented. Parameters of the model are estimated by solving a minimization problem, using temperature data from the wall surface and/or the flow. A multivariable optimization algorithm is employed for this purpose. Furthermore, a model for the forced-convection heat-transfer coefficient is proposed and its effect on the results is discussed. The validity of the proposed method is assessed using data from two different circular duct flows. The method is shown to provide a good prediction capability in computationally demanding transient heat-data sequences of different duct flows, both in terms of duct and of flow characteristics. Results show that a hyperbolic axial distribution of the forced-convection heat-transfer coefficient in the developing region of the flow is essential for good adaptation of the method to the test data.

scholarly journals Analytical solution of transient temperature in continuous wave end-pumped laser slab: Reduction of temperature distribution and time of thermal response

2017 ◽  
Vol 21 (3) ◽  
pp. 1223-1230 ◽  
Author(s):  
Khalid Shibib ◽  
Mohammad Munshid ◽  
Mohammed Hamza
Keyword(s):  
Temperature Distribution ◽  
Analytical Solution ◽  
Response Time ◽  
Continuous Wave ◽  
Integral Transform ◽  
Convection Heat Transfer ◽  
Thermal Response ◽  
Transient Temperature ◽  
Transform Method ◽  
Thermal Response Time

An analytical solution of transient 3-D heat equation based on integral transform method is derived. The result are compared with numerical solution, and good agreements are obtained. Minimization of response time and temperature distribution through a laser slab are tested. It is found that the increasing in the lateral convection heat transfer coefficient can significantly reduce the response time and the temperature distribution while no effect on response time is observed when changing pumping profile from Gaussian to top hat beam in spite of the latter reduce the temperature distribution, also it is found that dividing the pumping power between two slab ends might reduce the temperature distribution and it has no effect on thermal response time.

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