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In the present work, an optimization technique is applied for inverse boundary design problem of radiative convective heat transfer of laminar duct flow by numerical method. The main goal is to verify how the solution of inverse problem is affected by the spectral behavior of the boundary surfaces.

Yeram S. Touloukian

The conjugate gradient method is used to find the unknown temperature distribution over the heater surface to satisfy the prescribed temperature and heat flux distributions over the design surface. The bottom boundary surface including design surface is diffuse-spectral, while the top wall heater surface behaves as gray one. The variation of emissivity with respect to the wavelength is approximated by considering a set of spectral bands with constant emissivity and then the radiative transfer equation is solved by the discrete ordinates method for each band.

The performance of the present method is evaluated by comparing the results with those obtained by considering a diffuse-gray design surface. Finally an attempt is made to investigate the spectral behavior of the design surface on the calculated temperature distribution over the heater surface.

Infrared Thermography – Physical Basics

Rousse, D. There is clear correlation between the surface of a body and the intensity and spectral composition of its emitted radiation. By determining its radiation intensity the temperature of an object can thereby be determined in a non-contact way. Infrared radiation is that part of the electromagnetic spectrum that is immediately adjacent to the red light of approx. In this respect, the wavelength range of up to approx. In the second half of the 19th century, it became known that heat radiation and other electromagnetic waves, such as visible light or radio waves, were similar in nature.


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By the midth century, intensive and successful work on the military use of infrared technology facilitated the building of first infrared viewers. With some distance in time and technology, also the first thermographic devices for non-military application available in the 60s. Parallel to this, however, in considerably larger diversification of available devices, pyrometry developed to become a wide-spread approach in industrial temperature measuring.

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The bodies occurring in real life show very diverse radiation properties. Therefore, it has proved worthwhile to initially consider the simplified laws of a model body of ideal radiation properties to be then applied to actually occurring objects.

Thermography Theory - Physical basics | InfraTec GmbH

It distinguishes itself by the fact that, of all bodies of equal temperature, it shows the largest possible emitted radiation. This representation shows that the spectral composition varies with the object temperature.


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  7. Furthermore, it must be noted that, at each wavelength, radiation intensity increases with rising temperature. Due to its abstract nature, however, it is not directly applicable in this form to many practical calculations. But a variety of further correlations can be derived from it, two of which shall briefly be mentioned in the following.

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    So by means of integrating, for example, the spectral radiation intensity across all wavelengths, the value of the entire radiation emitted by the body is obtained. Due to its simple mathematical correlation, it is well suited for rough estimates, particularly when calculating the heat balance of objects as well as interrelations of total radiation pyrometers.

    However, the spectral measuring range of most measuring devices is usually strongly limited and, therefore, this equation is inapplicable to this purpose. The lower the temperature of the object to be measured the further its radiation maximum shifts towards larger wavelengths.

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    The level of transmittance of air is strongly dependent on wavelength. Ranges of high attenuation alternate with ranges of high transmittance shaded , the so-called "atmospheric windows".

    While transmittance in the range of The black body as a radiometric model is indispensable when considering principal correlations. Since real objects that are to be measured deviate more or less strongly from that model, it may become necessary to take this influence into account in measurements. Having a value of 1, the black body has the highest possible emittance, which is additionally dependent on wavelength.

    Contrary to this, the emittance of real objects to be measured may show more or less strong dependence on wavelength.