Heat Conduction in an Energy-Generating Slab Subject to a Nonuniform Heat Transfer Coefficient

1995 ◽  
Vol 117 (1) ◽  
pp. 219-222 ◽  
Author(s):  
G. F. Jones ◽  
E. V. McAssey ◽  
B. W. Yang
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Transfer Coefficient

scholarly journals An Analytical Solution for Transient Heat Conduction in a Composite Slab with Time-Dependent Heat Transfer Coefficient

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Ryoichi Chiba
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Differential Equations ◽  
Transfer Coefficient ◽  
Transient Heat Conduction ◽  
External Boundary ◽  
Composite Slab ◽  
Composite Slabs

An analytical solution is derived for one-dimensional transient heat conduction in a composite slab consisting of n layers, whose heat transfer coefficient on an external boundary is an arbitrary function of time. The composite slab, which has thermal contact resistance at n-1 interfaces, as well as an arbitrary initial temperature distribution and internal heat generation, convectively exchanges heat at the external boundaries with two different time-varying surroundings. To obtain the analytical solution, the shifting function method is first used, which yields new partial differential equations under conventional types of external boundary conditions. The solution for the derived differential equations is then obtained by means of an orthogonal expansion technique. Numerical calculations are performed for two composite slabs, whose heat transfer coefficient on the heated surface is either an exponential or a trigonometric function of time. The numerical results demonstrate the effects of temporal variations in the heat transfer coefficient on the transient temperature field of composite slabs.

Analytical Solution of Nonequilibrium Heat Conduction in Porous Medium Incorporating a Variable Porosity Model With Heat Generation

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
M. Nazari ◽  
F. Kowsary
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Transfer Coefficient ◽  
Heat Generation ◽  
Conductivity Ratio ◽  
Variable Porosity ◽  
Porosity Model

This paper is concerned with the conduction heat transfer between two parallel plates filled with a porous medium with uniform heat generation under a nonequilibrium condition. Analytical solution is obtained for both fluid and solid temperature fields at constant porosity incorporating the effects of thermal conductivity ratio, porosity, and a nondimensional heat transfer coefficient at pore level. The two coupled energy equations for the case of variable porosity condition are transformed into a third order ordinary equation for each phase, which is solved numerically. This transformation is a valuable solution for heat conduction regime for any distribution of porosity in the channel. The effects of the variable porosity on temperature distribution are shown and compared with the constant porosity model. For the case of the exponential decaying porosity distribution, the numerical results lead to a correlation incorporating conductivity ratio and interstitial heat transfer coefficient.

Application of Inverse Heat Conduction Problems in the Slab Solidification Process

2013 ◽  
Vol 395-396 ◽  
pp. 1135-1141
Author(s):  
Yang Yu ◽  
Xiao Chuan Luo ◽  
Yuan Wang
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Transfer Coefficient ◽  
Surface Heat ◽  
Cooling Zone ◽  
Inverse Heat Conduction ◽  
Surface Heat Transfer ◽  
Surface Heat Transfer Coefficient ◽  
Inverse Heat Conduction Problems

The surface heat transfer coefficient is obtained by the calculation of water-flowing in the second cooling zone of continuous casting; the parameters of this formula are determined by the engineering experiment methods. This paper adopts a new method-numerical calculation method to obtain these parameters. Firstly, the paper uses the method of solving inverse heat conduction problems to calculate the surface heat flux and the surface heat transfer coefficient. Secondly, by using the least square method, the parameters in the formula between the surface heat transfer coefficient and water-flowing are identified. Finally, a plant steel data is used to do some simulation experiments. The results of this simulation prove this numerical method feasibility and effectiveness.

Influence of the Finite Element Model on the Inverse Determination of the Heat Transfer Coefficient Distribution over the Hot Plate Cooled by the Laminar Water Jets / Wpływ Modelu Metody Elementów Skonczonych Na Współczynnika Wymiany Ciepła Wyznaczany Z Rozwiazania Odwrotnego Procesu Laminarnego Chłodzenia Płyty Metalowej

2013 ◽  
Vol 58 (1) ◽  
pp. 105-112 ◽  
Author(s):  
B. Hadała ◽  
Z. Malinowski ◽  
T. Telejko ◽  
A. Szajding
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Transfer Coefficient ◽  
Shape Functions ◽  
Strip Surface ◽  
Coefficient Distribution ◽  
Laminar Jets ◽  
The Heat Transfer Coefficient

The industrial hot rolling mills are equipped with systems for controlled cooling of hot steel products. In the case of strip rolling mills the main cooling system is situated at run-out table to ensure the required strip temperature before coiling. One of the most important system is laminar jets cooling. In this system water is falling down on the upper strip surface. The proper cooling rate affects the final mechanical properties of steel which strongly dependent on microstructure evolution processes. Numerical simulations can be used to determine the water flux which should be applied in order to control strip temperature. The heat transfer boundary condition in case of laminar jets cooling is defined by the heat transfer coefficient, cooling water temperature and strip surface temperature. Due to the complex nature of the cooling process the existing heat transfer models are not accurate enough. The heat transfer coefficient cannot be measured directly and the boundary inverse heat conduction problem should be formulated in order to determine the heat transfer coefficient as a function of cooling parameters and strip surface temperature. In inverse algorithm various heat conduction models and boundary condition models can be implemented. In the present study two three dimensional finite element models based on linear and non-linear shape functions have been tested in the inverse algorithm. Further, two heat transfer boundary condition models have been employed in order to determine the heat transfer coefficient distribution at the hot plate cooled by laminar jets. In the first model heat transfer coefficient distribution over the cooled surface has been approximated by the witch of Agnesi type function with the expansion in time of the approximation parameters. In the second model heat transfer coefficient distribution over the cooled plate surface has been approximated by the surface elements serendipity family with parabolic shape functions. The heat transfer coefficient values at surface element nodes have been expanded in time by the cubic-spline functions. The numerical tests have shown that in the case of heat conduction model based on linear shape functions inverse solution differs significantly from the searched boundary condition. The dedicated finite element heat conduction model based on non-linear shape functions has been developed to ensure inverse determination of heat transfer coefficient distribution over the cooled surface in the time of cooling. The heat transfer coefficient model based on surface elements serendipity family is not limited to a particular form of the heat flux distribution. The solution has been achieved for measured temperatures of the steel plate cooled by 9 laminar jets.

Sign in / Sign up

Export Citation Format

Share Document