Fourier analysis of thermal diffusive waves

Anwar, Muhammad Sabieh; Alam, Junaid; Wasif, Muhammad; Ullah, Rafi; Shamim, Sohaib; Zia, Wasif

doi:10.1119/1.4881608

Cited by 5 publications

(2 citation statements)

References 11 publications

(18 reference statements)

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“…Here, we show that thermal problems, which depend on a scalar temperature field, are a much simpler setting in which to explore such connections. In addition, the central physical quantity in such problems, the thermal diffusivity α, is often interesting on its own, and techniques for measuring diffusivity continue to be developed and play important roles in experimental physics research [7][8][9] and in teaching physics [10][11][12][13]. The cited pedagogical articles focus on time-domain response, which is complementary to the frequency-domain approach taken here [13].…”

Section: Introductionmentioning

confidence: 99%

When geometry is irrelevant for heat diffusion: the transition from lumped-element to field formulations

Frick¹,

Gupta²,

Bechhoefer³

2018

Eur. J. Phys.

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Thermal systems are an attractive setting for exploring the connections between the lumped-element approximations of elementary circuit theory and the partial-differential field equations of mathematical physics. In a calculation suitable for an undergraduate course in mathematical physics, we show that the response function between an oscillating heater and temperature probe has a smooth crossover between a low-frequency, ‘lumped-element’ regime where the system behaves as a whole and a high-frequency regime dominated by the spatial dependence of the temperature field. Undergraduates can also easily (and cheaply) explore these ideas experimentally in a typical advanced laboratory course. Because the characteristic frequencies are low, ≈0.03 Hz, measuring the response frequency by frequency is slow and challenging; to speed up the measurements, we introduce a useful, if underappreciated, experimental technique based on a multisine power signal that sums carefully chosen harmonic components with random phases. Strikingly, a simple model assuming a one-dimensional, finite rod predicts a temperature response in the frequency domain that closely approximates experimental measurements from an irregular, blob-shaped object. A spherical model gives similar results. Thus, the frequency response of this irregular thermal system has surprisingly little sensitivity to its geometry, an example of—and justification for—the toy models so beloved of physicists.

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Section: Introductionmentioning

confidence: 99%

When geometry is irrelevant for heat diffusion: the transition from lumped-element to field formulations

Frick¹,

Gupta²,

Bechhoefer³

2018

Eur. J. Phys.

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“…In most basic textbooks in electricity, the use of time-dependent voltage source to drive a circuit is reduced to a sinusoidal driving 1 . This is of paramount importance to introduce the concept of filtering in Fourier space 2 , a technique that appears in many other fields of physics 3 including wave optics 4 . Such time-dependent circuits also provide an opportunity to train the students on solving linear differential equations, and gives the opportunity to discuss the mechanical equivalent of an inductance, a capacitor or a resistor.…”

mentioning

confidence: 99%

Shortcut to stationary regimes: A simple experimental demonstration

Faure

Ciliberto

Trizac

et al. 2019

American Journal of Physics

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We introduce a reverse engineering approach to drive a RC circuit. This technique is implemented experimentally 1) to reach a stationary regime associated to a sinusoidal driving in very short amount of time, 2) to ensure a fast discharge of the capacitor, and 3) to guarantee a fast change of stationary regime associated to different driving frequencies. This work can be used as a simple experimental project dedicated to the computer control of a voltage source. Besides the specific example addressed here, the proposed method provides an original use of simple linear differential equation to control the dynamical quantities of a physical system, and has therefore a certain pedagogical value.

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Heat conduction in carrots studied with an IR-camera

Hänisch

Ziese

2021

Eur. J. Phys.

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Heat conduction and diffusion are important phenomena for the understanding of many physical, chemical and biological processes. In physics education these topics are an area to effectively relate the complexity of the mathematical description with modern experimental techniques that enable students to conduct their own research projects. In this work an infrared (IR) camera was used to image temperature profiles of carrot cross-sections after boiling. Using modelling of the spatial and temporal evolution of the heat conduction process it was possible to extract a value of the thermal diffusivity of D = (2.3 ± 0.2) × 10−7 m2 s−1. From this a thermal conductivity κ = (0.9 ± 0.1) W m−1 K−1 was calculated. The heat transfer coefficients between water and carrot of h W = (333 ± 50) W m−2 K−1 and between air and carrot of h A = (7 ± 1) W m−2 K−1 were determined. This experiment could be potentially used as an experiment in the general physics or in the advanced physics laboratory in the second or third year.

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Fourier analysis of thermal diffusive waves

Cited by 5 publications

References 11 publications

When geometry is irrelevant for heat diffusion: the transition from lumped-element to field formulations

When geometry is irrelevant for heat diffusion: the transition from lumped-element to field formulations

Shortcut to stationary regimes: A simple experimental demonstration

Heat conduction in carrots studied with an IR-camera

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