A new front surface heat flux calibration method for a 1-D nonlinear thermal system with a time-varying back boundary condition

2017 ◽  
Vol 105 (1) ◽  
pp. 157-187 ◽  
Author(s):  
Y. Y. Chen ◽  
J. I. Frankel ◽  
M. Keyhani
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Surface Heat Flux ◽  
Front Surface ◽  
Calibration Method ◽  
Surface Heat ◽  
Thermal System ◽  
Time Varying ◽  
Flux Calibration

Heat Transfer During Liquid Contact on Superheated Surfaces

1995 ◽  
Vol 117 (3) ◽  
pp. 693-697 ◽  
Author(s):  
J. C. Chen ◽  
K. K. Hsu
Keyword(s):  
Heat Flux ◽  
Atmospheric Pressure ◽  
Surface Heat Flux ◽  
Temperature Data ◽  
Surface Heat ◽  
Transient Temperature ◽  
Time Varying ◽  
Wall Superheat ◽  
Hot Surface ◽  
Better Than

Several boiling regimes are characterized by intermittent contacts of vapor and liquid at the superheated wall surface. A microthermocouple probe was developed capable of detecting transient surface temperatures with a response time better than 1 ms. The transient temperature data were utilized to determine the time-varying heat flux under liquid contacts. The instantaneous surface heat flux was found to vary by orders of magnitude during the milliseconds of liquid residence at the hot surface. The average heat flux during liquid contact was found to range from 105 to 107 W/m2 for water at atmospheric pressure, as wall superheat was varied from 50 to 450°C.

Small and Large Time Solutions for Surface Temperature, Surface Heat Flux, and Energy Input in Transient, One-Dimensional Conduction

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
A. S. Lavine ◽  
T. L. Bergman
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Surface Temperature ◽  
Surface Heat Flux ◽  
Energy Input ◽  
Approximate Solutions ◽  
Surface Heat ◽  
Dimensionless Time ◽  
Flux Boundary Condition ◽  
Dimensionless Energy

This paper addresses one-dimensional transient conduction in simple geometries. It is well known that the transient thermal responses of various objects, or of an infinite medium surrounding such objects, collapse to the same behavior as a semi-infinite solid at small dimensionless time. At large dimensionless time, the temperature reaches a steady state (for a constant surface temperature boundary condition) or increases linearly with time (for a constant heat flux boundary condition). The objectives of this paper are to bring together existing small and large time solutions for transient conduction in simple geometries, put them into forms that will promote their usage, and quantify the errors associated with the approximations. Approximate solutions in the form of simple algebraic expressions are derived (or compiled from existing solutions) for use at both small and large times. In particular, approximate solutions, which are accurate for Fo<0.2 and which bridge the gap between the large Fo (single-term) approximation and the semi-infinite solid solution (valid only at very small Fo), are presented. Solutions are provided for the surface temperature when there is a constant surface heat flux boundary condition, or for the surface heat flux when there is a constant surface temperature boundary condition. These results are provided in terms of a dimensionless heat transfer rate. In addition, the dimensionless energy input is given for the constant surface temperature cases. The approximate expressions may be used with good accuracy over the entire Fourier number range to rapidly estimate important features of the transient thermal response. With the use of the approximations, it is now a trivial matter to calculate the dimensionless heat transfer rate and dimensionless energy input, using simple closed-form expressions.

Transient Convective Heat Transfer in Planar Stagnation Flows With Time-Varying Surface Heat Flux and Temperature

1992 ◽  
Vol 114 (1) ◽  
pp. 85-93 ◽  
Author(s):  
D. A. Zumbrunnen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Steady State ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Governing Equation ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Time Varying ◽  
Rapid Transients

Impinging flows are used in a variety of applications where effective and localized heat transfer is mandated by short residence times or by space constraints, as in cooling materials moving along a conveyor or removing heat dissipated within microelectronic circuitry. A wide selection of heat transfer correlations is available for steady-state conditions. However, instantaneous heat transfer coefficients can differ significantly from steady-state values when temporal variations occur in the surface heat flux or surface temperature. Under these conditions, the temperatures of fluid layers near the surface are affected preferentially due to their proximity to the temporal variation. A theoretical model is formulated to assess the importance of a time-varying surface heat flux or temperature on convective heat transfer in a steady, planar stagnation flow. A governing equation for the transient heat transfer response is formulated analytically from the boundary layer equations for momentum and energy conservation in the fluid. Numerical solutions to the governing equation are determined for ramp and sinusoidal changes in the surface heat flux or temperature. Results indicate that the time response is chiefly governed by the velocity gradient in the free stream and to a lesser extent by the Prandtl number. Departures from steady-state Nusselt numbers are larger for more rapid transients and smaller or comparable in size to the magnitude of the imposed variation at the surface.

Mathematical Model of the Cooling of a Plastic, Thermoformed Part

2010 ◽  
Author(s):  
Thomas M. Aidich ◽  
Tien-Chien Jen ◽  
Yi-Hsin Yen
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Boundary Condition ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Surface Temperature ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Cooling Cycle ◽  
Transient Conduction

This paper presents research into the mechanism involved in the cooling of a plastic thermoformed part after it is formed onto a mold. The intent of this research is to develop a simple and practical mathematical model useful to small thermoforming companies without a large engineering staff that describes the transient heat conduction of the cooling process. The model should also be able to predict the temperature distribution within the thickness of the part during the cooling. This mathematical model, which began with simplified boundary conditions, was then compared to experimental cooling data and modified accordingly to properly fit that data and the actual boundary conditions of the cooling part. The research began by examining the cooling of a series of high molecular weight polyethylene thermoformed side panels for plastic, portable restrooms. These parts where chosen for this preliminary research because of their very simple, flat geometric shape that lends them to being modeled as simple plane walls in transient conduction. The shape of the parts also leads to near constant thickness over the vast majority of the part. Using the model of a plane wall in transient conduction, the governing partial differential equation was solved for two possible boundary conditions on the mold side of the part: constant imposed surface temperature and constant imposed surface heat flux. These two solutions were then compared to experimental data gathered on the temperature profile of the free surface of the part during a production environment. After the experimental data and simple mathematical models were compared the necessary changes to the assumed mold side boundary condition was made to adjust the mathematical model to the experimental data. The research found that the use of simple boundary conditions at the mold side of the part is incorrect. Neither the constant imposed surface temperature nor the imposed surface heat flux boundary conditions fit the data. Initial analysis of the experimental data showed that a time of 30 seconds into the cooling cycle an apparent change in that boundary condition occurs for the part and mold used to gather the data. Further analysis showed that the boundary condition begins as a constant surface heat flux and then changes to an imposed surface temperature that decays exponentially to the initial mold surface temperature. Using this boundary condition, a revised mathematical was developed that match the experimental data very well. The error of the new model compared to the experimental was less than 1.5% for all times during the cooling cycle.

scholarly journals Transient liquid crystal thermography using a time varying surface heat flux

2021 ◽  
Vol 179 ◽  
pp. 121718
Author(s):  
Julian Schmid ◽  
Michele Gaffuri ◽  
Alexandros Terzis ◽  
Peter Ott ◽  
Jens von Wolfersdorf
Keyword(s):  
Heat Flux ◽  
Liquid Crystal ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Time Varying ◽  
Liquid Crystal Thermography

Analysis of significant measures for thermal conductivity

2020 ◽  
pp. 35-42
Author(s):  
Yuri P. Zarichnyak ◽  
Vyacheslav P. Khodunkov
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Surface Heat Flux ◽  
Heat Flux Density ◽  
Measurement Method ◽  
Conductivity Measurement ◽  
Surface Heat ◽  
Measuring Instrument ◽  
New Class ◽  
Achievable Accuracy

The analysis of a new class of measuring instrument for heat quantities based on the use of multi-valued measures of heat conductivity of solids. For example, measuring thermal conductivity of solids shown the fallacy of the proposed approach and the illegality of the use of the principle of ambiguity to intensive thermal quantities. As a proof of the error of the approach, the relations for the thermal conductivities of the component elements of a heat pump that implements a multi-valued measure of thermal conductivity are given, and the limiting cases are considered. In two ways, it is established that the thermal conductivity of the specified measure does not depend on the value of the supplied heat flow. It is shown that the declared accuracy of the thermal conductivity measurement method does not correspond to the actual achievable accuracy values and the standard for the unit of surface heat flux density GET 172-2016. The estimation of the currently achievable accuracy of measuring the thermal conductivity of solids is given. The directions of further research and possible solutions to the problem are given.

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