Method of analysis of asymmetrical thermal field in a double insulated wire

2017 ◽  
Vol 36 (4) ◽  
pp. 1075-1088
Author(s):  
Jerzy Golebiowski ◽  
Marek Zareba
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Transfer Coefficient ◽  
Axial Symmetry ◽  
Thermal Field ◽  
Scalar Fields ◽  
Content Type ◽  
Steady State Current ◽  
The Wire

Purpose The purpose of this article is investigating the impact of the spatially variable heat transfer coefficient on the thermal field in the double insulated wire. Design/methodology/approach The effect of the air boundary layer was modelled by means of changing the total heat transfer coefficient on the external perimeter of the wire. This leads to an elliptical boundary problem with Hankel’s condition dependent on the angular coordinate. The eigenfunctions of the problem were determined analytically. On the other hand, the unknown coefficients of eigenfunctions and the constants were calculated numerically by solving a respective system of algebraic equations. The steady state current rating was determined with an iterative method. Findings By means of the presented method, the thermal field distribution deprived of axial symmetry in the double insulated wire was determined. The obtained results have good physical interpretation and were verified with the finite element method (by means of NISA v. 16 software). The determined values of the steady-state current rating were compared with those calculated by means of the equivalent heat transfer coefficient method and the International Electrotechnical Commission (IEC) standard. Research limitations/implications The method is applied to analyse scalar fields in layered cylindrical structures. This could be expanded to the case of a wire of any number of insulation layers. What is more, one could also consider heat sources without axial symmetry and located within the external area. Originality/value The analytical method of determining a thermal field deprived of axial symmetry in heterogeneous cylindrical system (the wire composed of three different materials) was developed.

scholarly journals Transient Thermal Field Analysis in ACCC Power Lines by the Green’s Function Method

Energies ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 280
Author(s):  
Jerzy Gołębiowski ◽  
Marek Zaręba
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Thermal Field ◽  
Continuity Condition ◽  
Field Analysis ◽  
Parabolic Differential Equations ◽  
Steady State Current ◽  
Core Line ◽  
Transient Thermal

The paper investigates the dynamics of the thermal field of the ACCC (aluminum conductor composite core) line. The system was heated by solar radiation and current flow. Conductor cooling was modeled using the total heat transfer coefficient as the sum of convective and radiative components. The temperature increase generated by the current is described by a system of parabolic differential equations with an appropriate set of boundary, initial and continuity condition. The mentioned boundary-initial problem was solved by a modified Green’s method, adapted to the layered structure of the system. For this purpose, Green’s functions, as the kernels of integral operators inverse to differential ones, were determined. Aluminum resistivity and heat transfer coefficient change significantly with temperature. For this reason, the solution to the problem is presented in the form of a lower and upper estimation of the heating curve and local time constant. A steady-state current rating was also determined. The results are presented graphically and verified by other methods (power balance and finite element). The physical interpretation of the presented solution is also given.

Parallel analysis of thermal field in a layered DC cable part I

2013 ◽  
Vol 24 (1) ◽  
pp. 58-72 ◽  
Author(s):  
Jerzy Golebiowski ◽  
Robert Piotr Bycul
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Finite Difference ◽  
Transfer Coefficient ◽  
Parallel Algorithm ◽  
Conjugate Gradient ◽  
Thermal Field ◽  
Initial Boundary ◽  
Content Type ◽  
Time Decomposition

Purpose – The paper aims to propose a parallel algorithm in order to increase speed and efficiency of an analysis of transient thermal field in layered DC cables. Design/methodology/approach – Initial-boundary problem of thermal field was discretized by means of implicit finite difference method in cylindrical coordinates. A two-stage time decomposition method was applied to introduce parallel computations. An assumed duration of the transient state was decomposed. The system of algebraic equations was being solved with the use of a conjugate gradient method (with diagonal preconditioning) in all time intervals simultaneously. Findings – A method for solving (with the use of parallel computing system) the transient heat conduction equation in a DC cable consisting of arbitrary number of material layers was given. The dependence of the convective heat transfer coefficient on the location on the perimeter of the cable and on its surface temperature (which introduced non-linearity in the boundary condition) was taken into account. The influence of the determined field on the efficiency of the heat source was also taken into consideration in the model. Research limitations/implications – The main limitation is induced by cylindrical and coaxial structure of the consecutive layers of the system. Thermal field is generated by direct current flow only. The length of the fragment of the cable under consideration should be much greater than its diameter. Practical implications – The time-spatial distribution of thermal field in the cross-section of the cable can be used for analysis of its reliability and for determination of important characteristics and parameters of the system. Originality/value – A parallel algorithm of solving initial-boundary parabolic problem was proposed as a result of synthesis of three methods (finite difference, time decomposition and conjugate gradient). An algorithm of minimization of disturbances of the solution introduced at the division points was given. Equations approximating real distribution of heat transfer coefficient from the surface of the cable were proposed.

Heat Transfer Coefficient Measurements on the Film-Cooled Pressure Surface of a Transonic Airfoil

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Paul M. Kodzwa ◽  
John K. Eaton
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Transfer Coefficient ◽  
Film Cooling ◽  
Wide Band ◽  
Heat Fluxes ◽  
Pressure Surface ◽  
Lift Off ◽  
Transonic Airfoil

This paper presents isoenergetic temperature and steady-state film-cooled heat transfer coefficient measurements on the pressure surface of a modern, highly cambered transonic airfoil. A single passage model simulated the idealized two-dimensional flow path between blades in a modern transonic turbine. This set up offered a simpler construction than a linear cascade but produced an equivalent flow condition. Furthermore, this model allowed the use of steady-state, constant surface heat fluxes. We used wide-band thermochromic liquid crystals (TLCs) viewed through a novel miniature periscope system to perform high-accuracy (±0.2 °C) thermography. The peak Mach number along the pressure surface was 1.5, and maximum turbulence intensity was 30%. We used air and carbon dioxide as injectant to simulate the density ratios characteristic of the film cooling problem. We found significant differences between isoenergetic and recovery temperature distributions with a strongly accelerated mainstream and detached coolant jets. Our heat transfer data showed some general similarities with lower-speed data immediately downstream of injection; however, we also observed significant heat transfer attenuation far downstream at high blowing conditions. Our measurements suggested that the momentum ratio was the most appropriate variable to parameterize the effect of injectant density once jet lift-off occurred. We noted several nonintuitive results in our turbulence effect studies. First, we found that increased mainstream turbulence can be overwhelmed by the local augmentation of coolant injection. Second, we observed complex interactions between turbulence level, coolant density, and blowing rate with an accelerating mainstream.

Identification of three-dimensional transient temperature fields in thick-walled elements using the inverse method

2018 ◽  
Vol 28 (1) ◽  
pp. 138-150 ◽  
Author(s):  
Magdalena Jaremkiewicz
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Inverse Method ◽  
Thermal Stresses ◽  
Computing Time ◽  
Transient Temperature ◽  
Content Type ◽  
Inner Surface ◽  
The Heat Transfer Coefficient

Purpose The purpose of this paper is to propose a method of determining the transient temperature of the inner surface of thick-walled elements. The method can be used to determine thermal stresses in pressure elements. Design/methodology/approach An inverse marching method is proposed to determine the transient temperature of the thick-walled element inner surface with high accuracy. Findings Initially, the inverse method was validated computationally. The comparison between the temperatures obtained from the solution for the direct heat conduction problem and the results obtained by means of the proposed inverse method is very satisfactory. Subsequently, the presented method was validated using experimental data. The results obtained from the inverse calculations also gave good results. Originality/value The advantage of the method is the possibility of determining the heat transfer coefficient at a point on the exposed surface based on the local temperature distribution measured on the insulated outer surface. The heat transfer coefficient determined experimentally can be used to calculate thermal stresses in elements with a complex shape. The proposed method can be used in online computer systems to monitor temperature and thermal stresses in thick-walled pressure components because the computing time is very short.

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.

SURFACE HEATER FABRICATION USING MICRO-LITHOGRAPHY FOR TRANSPIRATION COOLING HEAT TRANSFER COEFFICIENT MEASUREMENTS

2021 ◽  
pp. 1-23
Author(s):  
Zheng Min ◽  
Sarwesh Narayan Parbat ◽  
Qing-Ming Wang ◽  
Minking K. Chyu
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Transfer Coefficient ◽  
Film Cooling ◽  
Target Surface ◽  
Transpiration Cooling ◽  
Cooling Effectiveness ◽  
Blowing Ratio ◽  
Adiabatic Cooling

Abstract Transpiration cooling is able to provide more uniform coolant coverage than film cooling to effectively protect the component surface from contacting the hot gas. Due to numerous coolant ejection outlets within a small area at the target surface, the experimental thermo-fluid investigation on transpiration cooing becomes a significant challenge. Two classic methods to investigate film cooling, the steady-state foil heater method and the transient thermography technique, both fail for transpiration cooling because the foil heater would block numerous coolant outlets, and the semi-infinite solid conduction model no longer holds for porous plates. In this study, a micro-lithography method to fabricate a silver coil pattern on top of the additively manufactured polymer porous media as the surface heater was proposed. The circuit was deliberately designed to cover the solid surface in a combination of series connection and parallel connection to ensure the power in each unit cell area at the target surface was identical. With uniform heat flux generation, the steady-state tests were conducted to obtain distributions of a pair of parameters, adiabatic cooling effectiveness, and heat transfer coefficient (HTC). The results showed that the adiabatic cooling effectiveness could reach 0.65 with a blowing ratio lower than 0.5. Meanwhile, the heat transfer coefficient ratio (hf/h0) of transpiration cooling was close to 1 with a small blowing ratio at 0.125. A higher HTC ratio was observed for smaller pitch-to-diameter cases due to more turbulence intensity generated at the target surface.

scholarly journals Heat transfer aspects of condensation during vapour phase soldering on aligned PCB-based surfaces

2020 ◽  
Vol 32 (4) ◽  
pp. 247-252 ◽  
Author(s):  
Daniel Straubinger ◽  
István Bozsóki ◽  
Balazs Illes ◽  
Oliver Krammer ◽  
David Bušek ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Vertical Wall ◽  
Initial Pressure ◽  
Vapour Phase ◽  
Circuit Board ◽  
Pressure Measurements ◽  
Transfer Coefficients ◽  
Content Type

Purpose The paper aims to present an investigation on heat transfer in a vapour phase soldering (VPS) oven, focusing on the differences of horizontally and vertically aligned Printed Circuit Board (PCB) surfaces. The investigation can help develop a better understanding of the process and provide information for future modelling of the process. Design/methodology/approach For the investigations, flame retardant grade 4 (FR4) PCB plates and sealed plate–based boxes were immersed into saturated vapour of an experimental oven. The temperature and resulting heat transfer coefficients were analysed according to the sample boxes and the surface orientations. In addition, the boxes’ vapour consumption was investigated with pressure measurements. Findings The horizontal top- and bottom-side heating shows very similar results. In addition, the sides of a box were heated in a manner similar to the top and the bottom sides, but there was a slight increase in the heat transfer coefficient because of the vertical wall alignment. The pressure measurements reveal the dynamic changes in vapour after immersion of the boxes. Practical implications The findings may help to show differences on different surface orientations, pointing to more precise, explicit and multiphysics simulation results. Originality/value The experiments present an aspect of heat transfer coefficient differences in VPS ovens, also highlighting the effect of initial pressure drop inside the workspace of an oven.

Casing Convective Heat Transfer Coefficient and Reference Freestream Temperature Determination Near an Axial Flow Turbine Rotor

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
C. Camci ◽  
B. Gumusel
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Transfer Coefficient ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Convective Heat Transfer Coefficient ◽  
Axial Flow ◽  
Reference Temperature ◽  
Steady State Heat Transfer

The present study explains a steady-state method of measuring convective heat transfer coefficient on the casing of an axial flow turbine. The goal is to develop an accurate steady-state heat transfer method for the comparison of various casing surface and tip designs used for turbine performance improvements. The freestream reference temperature, especially in the tip gap region of the casing, varies monotonically from the rotor inlet to rotor exit due to work extraction in the stage. In a heat transfer problem of this nature, the definition of the freestream temperature is not as straightforward as constant freestream temperature type problems. The accurate determination of the convective heat transfer coefficient depends on the magnitude of the local freestream reference temperature varying in axial direction, from the rotor inlet to exit. The current study explains a strategy for the simultaneous determination of the steady-state heat transfer coefficient and freestream reference temperature on the smooth casing of a single stage rotating turbine facility. The heat transfer approach is also applicable to casing surfaces that have surface treatments for tip leakage control. The overall uncertainty of the method developed is between 5% and 8% of the convective heat transfer coefficient.

Steady State Heat Transfer Within a Nanoscale Spatial Domain

2012 ◽  
Vol 134 (7) ◽  
Author(s):  
Kirill V. Poletkin ◽  
Vladimir Kulish
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Transfer Coefficient ◽  
Spatial Domain ◽  
Thermal Waves ◽  
Steady State Heat ◽  
Steady State Heat Transfer ◽  
The Heat Transfer Coefficient

In this paper, we study the steady state heat transfer process within a spatial domain of the transporting medium whose length is of the same order as the distance traveled by thermal waves. In this study, the thermal conductivity is defined as a function of a spatial variable. This is achieved by analyzing an effective thermal diffusivity that is used to match the transient temperature behavior in the case of heat wave propagation by the result obtained from the Fourier theory. Then, combining the defined size-dependent thermal conductivity with Fourier’s law allows us to study the behavior of the heat flux at nanoscale and predict that a decrease of the size of the transporting medium leads to an increase of the heat transfer coefficient which reaches its finite maximal value, contrary to the infinite value predicted by the classical theory. The upper limit value of the heat transfer coefficient is proportional to the ratio of the bulk value of the thermal conductivity to the characteristic length of thermal waves in the transporting medium.

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