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.

Analytic Model for Non-Steady State Heat Transfer of Powder Pressing Roller

2005 ◽  
Vol 475-479 ◽  
pp. 3227-3230
Author(s):  
H.J. Chang ◽  
Heung Nam Han ◽  
M.W. Moon ◽  
Kwang Hee Lee ◽  
Kyu Hwan Oh
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Transfer Coefficient ◽  
Hot Pressing ◽  
Analytic Model ◽  
Contact Heat ◽  
Contact Heat Transfer ◽  
Steady State Heat ◽  
Steady State Heat Transfer

An analysis for non steady state heat transfer of a hot pressing roller was suggested in 1-dimensional model. The surface temperature on hot pressing roller was predicted by using surface contact heat transfer coefficient calculated with induced analytic solution. We calculated the size of iron powder, influencing on surface contact heat transfer coefficient. Since coarse iron powder has reduced heat transfer coefficient during contacting on roll surface with smaller contact area, temperature on roller surface has been expected to decrease. This predicted temperature by the analytic model was fairly reasonable in comparison with experimental data and finite element model.

Effect of Buried Depth on Steady-State Heat-Transfer Characteristics for Pipeline-Flow Assurance

SPE Journal ◽  
2014 ◽  
Vol 19 (06) ◽  
pp. 1162-1168 ◽  
Author(s):  
Dong-Wook Oh ◽  
Jang Min Park ◽  
Kong Hoon Lee ◽  
Erich Zakarian ◽  
Jungho Lee
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Transfer Coefficient ◽  
Oil And Gas ◽  
Heat Transfer Characteristics ◽  
Buried Pipes ◽  
Overall Heat Transfer Coefficient ◽  
Steady State Heat ◽  
Steady State Heat Transfer

Summary Pipeline embedment into the seabed is a key consideration for offshore oil and gas developments with high-temperature fluids. To date, the mechanism of steady-state heat transfer from partially and fully buried pipes has been modeled predominantly through analytical and numerical approaches. The current study focuses on making detailed measurements of heat-transfer characteristics. A laboratory-scale experimental apparatus imitating a subsea pipeline partially or fully buried into the seabed is created. Hot flow of hydrocarbons inside oil and gas offshore pipelines and the cold external flow of seawaters are simulated by means of 70°C and 5°C water flows from two separate water tanks, respectively. The experiments are carried out for seven different burial depths representing a range of various burial configurations, from fully exposed to fully buried pipes. The temperatures measured on the external surface of the pipe are analyzed, and the overall heat-transfer coefficient of the pipe is calculated. The effect of burial depth on the overall heat-transfer coefficient is compared with analytical formulae.

scholarly journals STEADY-STATE HEAT TRANSFER IN A PLATE WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY (AN EXACT SOLUTION)

2019 ◽  
Vol 18 (2) ◽  
pp. 85
Author(s):  
A. Miguelis ◽  
R. Pazetto ◽  
R. M. S. Gama
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Transfer Problem ◽  
Internal Heat ◽  
Temperature Dependent ◽  
State Heat ◽  
Kirchhoff Transformation ◽  
Steady State Heat ◽  
Steady State Heat Transfer

This work presents the solution of the steady-state heat transfer problem in a rectangular plate with an internal heat source in a context in which the thermal conductivity depends on the local temperature. This generalization of one of the most classical heat transfer problems is carried out with the aid of the Kirchhoff transformation and employs only well known tools, as the superposition of solutions and the Fourier series. The obtained results illustrate how the usual procedures may be extended for solving more realistic physical problems (since the thermal conductivity of any material is temperature-dependent). A general formula for evaluating the Kirchhoff transformation as well as its inverse is presented too. This work has a strong didactical contribution since such analytical solutions are not found in any classical heat transfer book. In addition, the main idea can be used in a lot of similar problems.

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.

Inverse analysis for the determination of heat transfer coefficient

2013 ◽  
Vol 91 (12) ◽  
pp. 1034-1043 ◽  
Author(s):  
Ali Fguiri ◽  
Naouel Daouas ◽  
M-Sassi Radhouani ◽  
Habib Ben Aissia
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Source Strength ◽  
Hot Wire ◽  
Source Power ◽  
Heating Source ◽  
The Heat Transfer Coefficient

The parallel hot wire technique is considered an effective and accurate means of experimental measurement of thermal conductivity. However, the assumptions of infinite medium and ideal infinitely thin and long heat source lead to some restrictions in the applicability of this technique. To make an effective experiment design, a numerical analysis should be carried out a priori, which requires a precise specification of the heating source strength and the heat transfer coefficient on the external surface. In this work, a more accurate physical and mathematical modeling of an experimental setup based on the parallel hot wire method is considered to estimate the two above-mentioned parameters from noisy temperature histories measured inside the material. Based on a sensitivity analysis, the heating source strength is estimated first using early time measurements. With such estimated value, determination of the heat transfer coefficient using temperatures measured at later times is then considered. The Levenberg–Marquardt (LM) method is successfully applied using a single experiment for the inverse solution of the two present parameter estimation problems. Estimates of this gradient-based deterministic method are validated with a stochastic method (Kalman filter). The effects of the measurement location, the heating duration, the measurement time step, and the LM parameter on the estimates and their associated confidence bounds are investigated. Used in the traditional fitting procedure of the parallel hot wire technique, the estimated heating source power provides a reasonable agreement between fitted and exact values of the thermal conductivity and the thermal diffusivity.

Thermal Management of Time-Varying High Heat Flux Electronic Devices

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
T. David ◽  
D. Mendler ◽  
A. Mosyak ◽  
A. Bar-Cohen ◽  
G. Hetsroni
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Transfer Coefficient ◽  
Heat Sink ◽  
Heat Fluxes ◽  
Vapor Quality ◽  
Flow Loop ◽  
Pin Fin ◽  
The Heat Transfer Coefficient

The thermal characteristics of a laboratory pin-fin microchannel heat sink were empirically obtained for heat flux, q″, in the range of 30–170 W/cm2, mass flux, m, in the range of 230–380 kg/m2 s, and an exit vapor quality, xout, from 0.2 to 0.75. Refrigerant R 134a (HFC-134a) was chosen as the working fluid. The heat sink was a pin-fin microchannel module installed in open flow loop. Deviation from the measured average temperatures was 1.5 °C at q = 30 W/cm2, and 2.0 °C at q = 170 W/cm2. These results indicate that use of pin-fin microchannel heat sink enables keeping an electronic device near uniform temperature under steady state and transient conditions. The heat transfer coefficient varied significantly with refrigerant quality and showed a peak at an exit vapor quality of 0.55 in all the experiments. At relatively low heat fluxes and vapor qualities, the heat transfer coefficient increased with vapor quality. At high heat fluxes and vapor qualities, the heat transfer coefficient decreased with vapor quality. A noteworthy feature of the present data is the larger magnitude of the transient heat transfer coefficients compared to values obtained under steady state conditions. The results of transient boiling were compared with those for steady state conditions. In contrast to the more common techniques, the low cost technique, based on open flow loop was developed to promote cooling using micropin fin sinks. Results of this experimental study may be used for designing the cooling high power laser and rocket-born electronic devices.

scholarly journals A Linear Approach Suitable for a Class of Steady-State Heat Transfer Problems with Temperature-Dependent Thermal Conductivity

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
R. M. S. Gama ◽  
R. Pazetto
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Steady State ◽  
Robin Boundary Conditions ◽  
Temperature Dependent ◽  
Steady State Heat ◽  
Steady State Heat Transfer ◽  
Transfer Problems ◽  
Robin Boundary ◽  
Temperature Dependent Thermal Conductivity

This work presents an useful tool for constructing the solution of steady-state heat transfer problems, with temperature-dependent thermal conductivity, by means of the solution of Poisson equations. Specifically, it will be presented a procedure for constructing the solution of a nonlinear second-order partial differential equation, subjected to Robin boundary conditions, by means of a sequence whose elements are obtained from the solution of very simple linear partial differential equations, also subjected to Robin boundary conditions. In addition, an a priori upper bound estimate for the solution is presented too. Some examples, involving temperature-dependent thermal conductivity, are presented, illustrating the use of numerical approximations.

Sign in / Sign up

Export Citation Format

Share Document