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.

Numerical investigation of laminar forced convection for a non-Newtonian nanofluids flowing inside an elliptical duct under convective boundary condition

2019 ◽  
Vol 29 (1) ◽  
pp. 334-364 ◽  
Author(s):  
Haroun Ragueb ◽  
Kacem Mansouri
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Fluid Flow ◽  
Transfer Coefficient ◽  
Convective Boundary Condition ◽  
Bulk Temperature ◽  
Convective Boundary ◽  
Content Type ◽  
The Heat Transfer Coefficient

PurposeThe purpose of this study is to investigate the thermal response of the laminar non-Newtonian fluid flow in elliptical duct subjected to a third-kind boundary condition with a particular interest to a non-Newtonian nanofluid case. The effects of Biot number, aspect ratio and fluid flow behavior index on the heat transfer have been examined carefully.Design/methodology/approachFirst, the mathematical problem has been formulated in dimensionless form, and then the curvilinear elliptical coordinates transform is applied to transform the original elliptical shape of the duct to an equivalent rectangular numerical domain. This transformation has been adopted to overcome the inherent mathematical deficiency due to the dependence of the ellipsis contour on the variables x and y. The yielded problem has been successfully solved using the dynamic alternating direction implicit method. With the available temperature field, several parameters have been computed for the analysis purpose such as bulk temperature, Nusselt number and heat transfer coefficient.FindingsThe results showed that the use of elliptical duct enhances significantly the heat transfer coefficient and reduces the duct’s length needed to achieve the thermal equilibrium. For some cases, the reduction in the duct’s length can reach almost 50 per cent compared to the circular pipe. In addition, the analysis of the non-Newtonian nanofluid case showed that the addition of nanoparticles to the base fluid improves the heat transfer coefficient up to 25 per cent. The combination of using an elliptical duct and the addition of nanoparticles has a spectacular effect on the overall heat transfer coefficient with an enhancement of 50-70 per cent. From the engineering applications view, the results demonstrate the potential of elliptical duct in building light-weighted compact shell-and-tube heat exchangers.Originality/valueA complete investigation of the heat transfer of a fully developed laminar flow of power law fluids in elliptical ducts subject to the convective boundary condition with application to non-Newtonian nanofluids is addressed.

Inverse BEM Method to Identify Surface Temperatures and Heat Transfer Coefficient Distributions at Inaccessible Surfaces

2005 ◽  
Author(s):  
Alain J. Kassab ◽  
Eduardo A. Divo ◽  
Minking K. Chyu ◽  
Frank J. Cunha
Keyword(s):  
Heat Transfer ◽  
Inverse Problem ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Field Variable ◽  
Quadratic Functional ◽  
Two Dimensional ◽  
Additional Information ◽  
Coefficient Distribution ◽  
The Heat Transfer Coefficient

The purpose of the inverse problem considered in this study is to resolve heat transfer coefficient distributions by solving a steady-state inverse problem. Temperature measurements at interior locations supply the additional information that renders the inverse problem solvable. A regularized quadratic functional is defined to measure the deviation of computed temperatures from the values under current estimates of the heat transfer coefficient distribution at the surface exposed to convective heat transfer. The inverse problem is solved by minimizing this functional using a parallelized genetic algorithm (PGA) as the minimization algorithm and a two-dimensional multi-region boundary element method (BEM) heat conduction code as the field variable solver. Results are presented for a regular rectangular geometry and an irregular geometry representative of a blade trailing edge and demonstrate the success of the approach in retrieving accurate heat transfer coefficient distributions.

Thermal Resistance in a Rectangular Flux Channel With Nonuniform Heat Convection in the Sink Plane

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
M. Razavi ◽  
Y. S. Muzychka ◽  
S. Kocabiyik
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Thermal Resistance ◽  
Transfer Coefficient ◽  
Least Squares ◽  
Least Squares Method ◽  
Separation Of Variables ◽  
Plane Boundary ◽  
The Heat Transfer Coefficient

In this paper, thermal resistance of a 2D flux channel with nonuniform convection coefficient in the heat sink plane is studied using the method of separation of variables and the least squares technique. For this purpose, a two-dimensional flux channel with discretely specified heat flux is assumed. The heat transfer coefficient at the sink boundary is defined symmetrically using a hyperellipse function which can model a wide variety of different distributions of heat transfer coefficient from uniform cooling to the most intense cooling in the central region. The boundary condition along the edges is defined with convective cooling. As a special case, the heat transfer coefficient along the edges can be made negligible to simulate a flux channel with adiabatic edges. To obtain the temperature profile and the thermal resistance, the Laplace equation is solved by the method of separation of variables considering the applied boundary conditions. The temperature along the flux channel is presented in the form of a series solution. Due to the complexity of the sink plane boundary condition, there is a need to calculate the Fourier coefficients using the least squares method. Finally, the dimensionless thermal resistance for a number of different systems is presented. Results are validated using the data obtained from the finite element method (FEM). It is shown that the thick flux channels with variable heat transfer coefficient can be simplified to a flux channel with the same uniform heat transfer coefficient.

scholarly journals Distributed parameter modeling and thermal analysis of a spiral water wall in a supercritical boiler

2013 ◽  
Vol 17 (5) ◽  
pp. 1337-1342 ◽  
Author(s):  
Shu Zheng ◽  
Zixue Luo ◽  
Huaichun Zhou
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Supercritical Pressure ◽  
Distributed Parameter ◽  
Water Wall ◽  
Coefficient Distribution ◽  
Distributed Parameter Model ◽  
The Heat Transfer Coefficient

In this paper, a distributed parameter model for the evaporation system of a supercritical spiral water wall boiler is developed based on a 3-D temperature field. The mathematical method is formulated for predicting the heat flux and the metal-surface temperature. The results show that the influence of the heat flux distribution is more obvious than that of the heat transfer coefficient distribution in the spiral water wall tube, and the peak of the heat transfer coefficient decreases with an increment of supercritical pressure. This distributed parameter model can be used for a 600 MW supercritical-pressure power plant.

Implementation of the Axially Symmetrical and Three Dimensional Finite Element Models to the Determination of the Heat Transfer Coefficient Distribution on the Hot Plate Surface Cooled by the Water Spray Nozzle

2012 ◽  
Vol 504-506 ◽  
pp. 1055-1060 ◽  
Author(s):  
Zbigniew Malinowski ◽  
Tadeusz Telejko ◽  
Beata Hadala ◽  
Agnieszka Cebo-Rudnicka
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Three Dimensional ◽  
Spray Nozzle ◽  
Water Spray ◽  
Coefficient Distribution ◽  
The Heat Transfer Coefficient ◽  
Material Temperature

Plate and strip hot rolling lines are equipped with water cooling systems used to control the deformed material temperature. This system has a great importance in the case of thermal - mechanical deformation of steel which is focused on formation a proper microstructure and mechanical properties. The desired rate of cooling is achieved by water spray or laminar cooling applied to the hot surface of a strip. The water flow rate and pressure can be changed in a wide range and it will result in a very different heat transfer from the cooled material to the cooling water. The suitable cooling rate and the deformed material temperature can be determined based on numerical simulations. In this case thermal boundary conditions have to be specified on the cooled surface. The determination of the heat transfer coefficient distribution in the area of the water spray nozzle would improve numerical simulations significantly. In the paper an attempt is made to determine the heat transfer coefficient distribution on the hot plate surface cooled by the water spray nozzle. In the inverse method direct axially symmetrical and three dimensional solutions to the plate temperature field have been implemented. The computation time and the achieved accuracy have been compared for five cases. The studied cases differed in the maximum value of the heat transfer coefficient in nozzle spray axis and its distribution in the cooling time.

The Effect of Free-Stream Turbulence on Gas Turbine Blade Heat Transfer

1989 ◽  
Vol 111 (4) ◽  
pp. 497-501 ◽  
Author(s):  
V. Krishnamoorthy ◽  
S. P. Sukhatme
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Gas Turbine ◽  
Free Stream ◽  
Flux Boundary Condition ◽  
Number Range ◽  
Free Stream Turbulence ◽  
Coefficient Distribution ◽  
The Heat Transfer Coefficient

This paper describes the results of systematic investigations undertaken to study the effect of free-stream turbulence on the heat transfer coefficient distribution around gas turbine rotor blades and nozzle guide vanes. The heat transfer coefficient distribution around the blade surface was obtained under a uniform heat flux boundary condition. Experiments were conducted in the Reynolds number range 2.0–8.1 × 105 (exit Mach number range 0.182 to 0.600) with the free-stream turbulence level in the range 1.0–21.3 percent. A new type of active turbulence generator was used for generating high turbulence levels. Correlations were obtained for the effect of free-stream turbulence on the local heat transfer coefficient in the laminar, transitional, and turbulent boundary layer regions.

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