A Finite Element Based Inverse Method for Two-Dimensional Heat Conduction Problems

2005 ◽  
Author(s):  
Kannan Subramanian ◽  
Harish P. Cherukuri
Keyword(s):  
Finite Element ◽  
Inverse Method ◽  
Rectangular Domain ◽  
Two Dimensions ◽  
Surface Heat ◽  
Heat Fluxes ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
One Dimensional ◽  
Surface Heat Fluxes

An inverse method for predicting surface heat fluxes as functions of time and space was developed and applied to several one-dimensional problems by Ling et al. [1]. The method is based on the Galerkin finite element method and takes advantage of the linearity between the computed temperatures and the instantaneous surface heat fluxes. In the present work, the method is extended to two-dimensions and applications are made to a rectangular domain and an axisymmetric domain. Several possibilities are considered for solution stabilization and the effect of these approximations on the flux predictions is analysed. Results from a study of the sensitivity of the fluxes to the temperature sensor locations are also presented.

Dynamic Calibration of a Coaxial Thermocouples for Short Duration Transient Measurements

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Rakesh Kumar ◽  
Niranjan Sahoo
Keyword(s):  
Heat Flux ◽  
Finite Element ◽  
Heat Conduction ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Heat Fluxes ◽  
Dynamic Calibration ◽  
One Dimensional ◽  
Surface Heat Fluxes ◽  
Heat Loads

Coaxial thermocouple sensors are suitable for measuring highly transient surface heat fluxes because the response times of these sensors are very small (∼0.1 ms). These robust sensors have the flexibility of mounting them directly on the surface of any geometry. So, they have been routinely used in ground-based impulse facilities as temperature sensors where rapid changes in heat loads are expected on aerodynamic models. Subsequently, the surface heat fluxes are predicted from the transient temperatures by appropriate one-dimensional heat conduction modeling for semi-infinite body. In this backdrop, the purpose of this work is to design and fabricate K-type coaxial thermocouples in-house and calibrate them under similar nature of heat loads by using simple laboratory instruments. Here, two methods of dynamic calibration of coaxial thermocouples have been discussed, where the known step loads are applied through radiation and conduction modes of heat transfer. Using appropriate one dimensional heat conduction modeling, the surface heat fluxes are predicted from the measured temperature histories and subsequently compared with the input heat loads. The recovery of surface heat flux from laser based calibration experiment under-predicts by 4% from its true input heat load. Similarly, recovery of surface heat flux from the conduction mode calibration experiments under-predicts 6% from its true input value. Further, finite-element based numerical study is performed on the coaxial thermocouple model to obtain surface temperatures with same heat loads as used in the experiments. The recovery of surface temperatures from finite element simulation is achieved within an accuracy of ±0.3% from the experiment.

Accounting for Sensor Errors in Estimation of Surface Heat Flux by an Inverse Method

2008 ◽  
Author(s):  
Jonathan W. Woolley ◽  
Keith A. Woodbury
Keyword(s):  
Inverse Method ◽  
Surface Heat ◽  
Heat Fluxes ◽  
Inverse Heat Conduction ◽  
Aluminum Casting ◽  
Detailed Model ◽  
Surface Heat Fluxes ◽  
Measuring Devices ◽  
Parent Domain ◽  
Sensor Errors

Thermocouples or other measuring devices are often embedded into a solid to provide data for an inverse calculation. It is well-documented that such installations will result in erroneous (biased) sensor readings, unless the thermal properties of the measurement wires and surrounding insulation can be carefully matched to those of the parent domain. Since this rarely can be done, or doing so is prohibitively expensive, an alternative is to account for the sensor dynamics with an appropriate model. In this paper we simulate a thermocouple embedded in a sand mold near the interface of a solidifying aluminum casting. The effect of sensor errors is accounted for by generating correction kernels from a detailed model of the embedded thermocouple. The corrected sensor readings are used in the inverse heat conduction solution. The magnitude of the effect is shown by comparing surface heat fluxes computed with measured temperatures to the heat fluxes computed with corrected temperatures.

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