Solutions of Fourier’s equation appropriate for experiments using thermochromic liquid crystal

This paper describes a new method to determine the heat transfer coefficient, ℎ, and the adiabatic-surface temperature, , from transient measurements of the surface temperature of a test piece. Maximum Likelihood Estimation (MLE) is used in conjunction with Fourier's 1D equation to determine the optimum values of ℎ and , and also their 95% confidence intervals, without having to measure the air temperature. Validation experiments are conducted in a small purpose-built wind tunnel, and a novel infra-red (IR) sensor is used to measure the surface temperature of the test piece. A mesh heater is used to generate either a step-change in the air temperature or a 'slow-transient' in which the air temperature -and consequently -increases slowly with time. Numerical simulations, using 'noisy data', show that the computations give accurate estimates of ℎ and for both the step-change and slow-transient cases. The values of ℎ and determined from the measurements in the wind-tunnel are in good agreement with empirical correlations for turbulent flow over a flat plate.An advantage of the new method is that it can be used for all transient experiments, even those slow transients that violate the assumption of a semi-infinite solid, an assumption that is used in most existing analysis methods. The new method, which was applied here to boundary-layer flow with one stream of fluid, could also be applied to 'three-temperature problems', like film cooling, which involve two streams of fluid. The significant advantage of using the method for these problems is that both ℎ and could be determined accurately from a single experiment.

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“…The effect of on the variation of with computed from Eq. (2.4) by Pountney et al (2012) is shown in Fig. 1.…”

Section: Analysis Of Transient Data 21 Analytical Solutions Of Fourimentioning

confidence: 93%

On the measurement and analysis of data from transient heat transfer experiments

Cho

Tang

Owen

et al. 2016

International Journal of Heat and Mass Transfer

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“…Better result could be achieved if the experimental time can be extended. This will enable more surface temperature history data to be analyzed [8].…”

Section: Fourier One-dimensional Heat Transfer With Semi-infinite Solmentioning

confidence: 99%

“…Figure 4 shows the measured air temperature and surface temperature history data. As mentioned earlier, the experimental data will be analysed using two methods, first is the two temperature solution method from [8] that uses the semi-infinite solid solution, and secondly by using Crank Nicolson finite difference method with adiabatic back face boundary condition.…”

Section: Heat Transfer Experimentsmentioning

confidence: 99%

“…The calculated heat transfer coefficient and also adiabatic wall temperature will be inaccurate if this semi-infinite solid condition is being violated. Most transient heat transfer cases require much longer experimental time to accurately calculate the heat transfer coefficient and adiabatic wall temperature [8]. The problem arises when the need for a longer experimental time violates the semiinfinite solid condition.…”

Section: Introductionmentioning

confidence: 99%

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Semi-infinite solid heat transfer limitation

Saiah¹,

Rafie²,

Romli³

et al. 2018

IJET

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One-dimensional semi-infinite heat transfer solution is a common solution for transient heat transfer experiments. This solution is valid for a short certain amount of time before the semi-infinite solid became invalid. Crank Nicolson solution has been chosen to address this issue. This paper reports the time limitation for semi-infinite solid solution and justify the usability of Crank Nicolson solution given the same boundary conditions. The flat plate heat transfer experiment has been conducted. With the same boundary conditions, at Fourier number 0.1, the resultant heat transfer coefficient and adiabatic wall temperature have shown a good agreement between the semi-infinite solid solution and the Crank Nicolson solution. Beyond this Fourier number, both solutions have given inaccurate results. The inaccurate results are due to unsuitable boundary conditions. Future work will involve modification of the back face boundary conditions to address the time limitation of the one-dimensional semi-infinite solid heat transfer solution.

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“…In a transient experiment, starting from an isothermal condition between the airflow and the wetted channel surfaces, a sudden change in the flow temperature is imposed to trigger the heat-transfer process. Then, the computation of the heat-transfer coefficient (HTC) relies on the one-dimensional Fourier's equation written for a semi-infinite solid using the surface and flow-temperature evolutions as boundary conditions [4]. Schultz et al [5] evaluated the maximum duration of a transient test within which a flat wall can be properly assumed as a semi-infinite solid.…”

Section: Introductionmentioning

confidence: 99%

Validation of the Transient Liquid Crystal Thermography Technique for Heat Transfer Measurements on a Rotating Cooling Passage

Lorenzon

Casarsa

2020

Energies

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The transient liquid crystal thermography can be a suitable tool to study heat-transfer performances on internal cooling schemes of gas turbine blades. One of the hot topics related to this methodology is about the level of reliability of the heat-transfer assessments in rotating tests where the fluid experiences time-dependent rotating effects. The present study contribution aims to experimentally validate by cross-comparison of the outcomes obtained by employing the transient technique with those from the steady-state liquid crystal thermography in which the rotational effects occur as time-stable by definition. Heat-transfer measurements have been conducted on a rib-roughened square cross-section channel, with an inlet Reynolds number equal to 20,000 and rotation number up to 0.2. Special attention has been paid to the definition of the more reliable calibration strategy for liquid crystals that are employed in the transient thermography and to the proper estimation of the heat losses in the post-processing of the steady-state experimental data. The results show great accordance between the indications provided by the two techniques both in static and rotating conditions, demonstrating the possibility to exploit the advantages of the transient liquid crystal thermography for the investigation of heat transfer into rotating cooling channels.

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Solutions of Fourier’s equation appropriate for experiments using thermochromic liquid crystal

Cited by 11 publications

References 13 publications

On the measurement and analysis of data from transient heat transfer experiments

On the measurement and analysis of data from transient heat transfer experiments

Semi-infinite solid heat transfer limitation

Validation of the Transient Liquid Crystal Thermography Technique for Heat Transfer Measurements on a Rotating Cooling Passage

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