In recent decades active infrared thermography gained vital importance in the field of non-destructive testing and evaluation. It is non-invasive, non-ionizing, reliable, quantitative and qualitative ...imaging modality for estimation of properties of surface and subsurface abnormalities in various biomaterials. Recently introduced non-periodic thermal excitation schemes for the active infrared thermography gained attention in thermal imaging community by providing a solution to overcome the constrains associated with the traditional pulse and lock-in infrared thermography methods. Among these thermographic methods, digitized frequency modulated thermal wave imaging is one of the imaging modality which supports the principle of pulse compression to overcome constrains associated with traditional methods. This work proposes an analytical solution for digitized frequency modulated thermal wave imaging, which is used for estimation of osteoporosis stages in multilayer human bone model. In order to validate the proposed analytical approach, the results obtained from the analytical approach has been compared with the numerically obtained results from a commercially available simulator (COMSOL Multiphysics) by taking correlation coefficient as a figure of merit.
We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities, where initially one medium has temperature ...0 and the other has temperature 1. Under the assumptions that one medium is bounded and the interface is of class $ C^{2, \alpha} $, we show that if the interface is stationary isothermic, then it must be a sphere. The method of moving planes due to Serrin is directly utilized to prove the result.
This paper aims to systematically assess the local radial basis function collocation method, structured with multiquadrics (MQs) and polyharmonic splines (PHSs), for solving steady and transient ...diffusion problems. The boundary value test involves a rectangle with Dirichlet, Neuman, and Robin boundary conditions, and the initial value test is associated with the Dirichlet jump problem on a square. The spectra of the free parameters of the method, i.e., node density, timestep, shape parameter, etc., are analyzed in terms of the average error. It is found that the use of MQs is less stable compared to PHSs for irregular node arrangements. For MQs, the most suitable shape parameter is determined for multiple cases. The relationship of the shape parameter with the total number of nodes, average error, node scattering factor, and the number of nodes in the local subdomain is also provided. For regular node arrangements, MQs produce slightly more accurate results, while for irregular node arrangements, PHSs provide higher accuracy than MQs. PHSs are recommended for use in diffusion problems that require irregular node spacing.
Nanoscale phonon transport within silicon structures subjected to internal heat generation was explored. A Monte Carlo simulation was used. The simulation procedures differed from the current ...existing methods in which phonons below a predefined “reference temperature” were not accounted to reduce memory storage and computational resources. Results indicated that the heat diffusion equation significantly underestimates temperature distribution at nanoscales in the presence of an external heat source. Discussions on temperature distribution inside silicon thin film when heated by a pulsed laser, an electron beam or due to near-field thermal radiation effects were also provided.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
•A mathematical model for micro thermoelectric cooler behaviour is proposed.•The modelling is based on the hyperbolic heat diffusion equation.•The solution is derived analytically by splitting up the ...original problem into three simpler problems.•The solution of each problem is based on a modified Separation of Variables method.•The semi-infinite body solution is used to eliminate numerical oscillations in the temperature solutions at early times.
The ultrafast thermal behaviour of a micro thermoelectric cooler under the hyperbolic heat conduction model is analysed. An important step forward is taken in that the instantaneous application of the electric current is modelled by means of the Heaviside function. Two terms of internal heat generation derive from this model: the former is time-independent, whereas the latter is time-dependent through Dirac’s delta function. A modified Separation of Variables method is used to solve analytically the governing equations. Also, the initial linear problem is split up into three sub-problems through the principle of superposition. In order to eliminate the numerical oscillations in the temperature profiles at early times in correspondence of the wave fronts, the semi-infinite hyperbolic body model is considered. The performance (COP) of the device is evaluated and then compared with that derived from the parabolic case. An increase of about 27% is observed at early times.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Recently, a number of studies have assimilated land surface temperature (LST) within a variational data assimilation (VDA) framework to estimate turbulent heat fluxes. These VDA models have mainly ...considered soil and vegetation as a combined source (CS) and have not accounted for the difference between soil and canopy temperatures and turbulent exchange rates, although soil and canopy can exhibit very different behaviors. Hence, in this study the contribution of soil and canopy to the LST and turbulent heat fluxes is taken into account separately by developing a dual‐source (DS) VDA model. The unknown model parameters are the neutral bulk heat transfer coefficient (that scales the sum of turbulent heat fluxes) and the evaporative fractions for soil and canopy (which represent partitioning among the turbulent fluxes over soil and vegetation). The model as developed has been tested with area‐averaged measurements of turbulent heat fluxes obtained from the First International Satellite Land Surface Climatology Project Field Experiment (FIFE) during the summers of 1987 and 1988. The results show that the predicted turbulent heat fluxes match well with observations. For FIFE 1987 (1988), the half‐hourly latent heat flux estimates from the new model have a root‐mean square‐error (RMSE) of 57.4 Wm−2 (66.8 Wm−2), which represents a significant improvement over the previous study.
Key Points
A variational data assimilation model is developed to estimate heat fluxes
Accounts for the difference between soil and vegetation temperature and fluxes
Dual‐source model improves estimation compared to previous combined source mode
We report the heat diffusion on flexible active-matrix organic light-emitting diode (AMOLED) displays. Two-dimensional heat diffusion is used for the heat conduction and convection analysis, ...generated on the surface of a flexible AMOLED display. The heat diffusion parameters and the time constant are studied in terms of the driving conditions of a 6-inch flexible AMOLED display. The temperature distribution on the screen is obtained by applying heat diffusion using the finite difference method (FDM) with an FPGA driving board. We can predict temperature more precisely by calculating temperature changes according to the images. The proposed method improves the accuracy of predicting the temperature. The average and standard deviation of the temperature error (TER) are ∼0.5°C and ∼0.5°C for the proposed method, respectively. For the conventional method, the values are ∼4.5°C and ∼0.7°C, respectively, neglecting the increase in temperature based on the images. This method can be used in compensation technology for OLEDs and thin film transistors (TFTs) that require accurate temperature distribution on the screen.
Key Points
LST is assimilated to heat diffusion equation to estimate evaporation.
Evaporation estimations are used to study the surface control on evaporation.
Dependence of EF‐soil moisture ...relationship on vegetation cover is examined.
A variational data assimilation model is developed to estimate surface energy fluxes from remotely sensed land surface temperature (LST). Components of the surface energy balance (sensible, latent, and ground heat fluxes) have different degrees of efficiency in dissipating available energy. LST is the state variable of the surface energy balance (SEB). Land surface models that capture the exchange and storage of energy in the soil and vegetation media use LST as a prognostic variable. Sequences of LST measurements implicitly contain information on partitioning of available energy among the components of SEB. In this study, we focus on the estimation of the sum of the turbulent fluxes as well as the partitioning among them. Two dimensionless parameters are used to characterize the sum and the partitioning. Using LST observations from a constellation of satellites, these parameters are mapped over a large region. The remotely sensed LST is assimilated to the heat diffusion equation within the SEB framework. In addition, a model error term is added to the SEB equation such that the variational data assimilation scheme includes model uncertainty as well as observation error. The framework is tested over the Southern Great Plains region. The mapped results of the surface evaporation estimation are used to study the surface control on evaporation. Independent mapped soil moisture estimates from an airborne microwave campaign are used. The dependence of the evaporation control‐soil moisture relationship on vegetation cover and plant functional types over large regions is examined in this first and exploratory study.
Full text
Available for:
BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
Two different strategies are provided to generate solutions to the three-dimensional heat diffusion equation. The first strategy is inspired by the well-known one-dimensional heat polynomial, which ...consists of an infinite set of polynomials, which are solutions to the one-dimensional heat diffusion equation. The second strategy is based on an exponential type function. None of the solutions presented here can be obtained by the method of separation of variables. The mathematical developments proving that, indeed, the particular solutions generated with both strategies satisfy the three-dimensional heat diffusion equation are presented. The analytical solutions are validated by generating the corresponding numerical solutions with the method of finite differences. When comparing both analytical and numerical solutions, it is found that they are identical. In addition, as part of the results, it is found that there are exponential solutions that reproduce the behavior of polynomial solutions. Finally, an example of the use of heat polynomials in engineering applications is provided.
In this study, we combine heat diffusion equation and modified Hodgkin-Huxley axonal model to investigate how an action potential is generated during infrared neural stimulation. The effects of ...temporal and spatial distribution of heat induced by infrared pulsed lasers on variation of electrical membrane capacitance are investigated. These variations can lead to depolarize the membrane and generate an action potential. We estimate the threshold values of laser light parameters such as energy density, pulse duration, and repetition rate are needed to trigger an action potential. In order to do it, we present an analytic solution to heat diffusion equation. Then, the analytic results are verified by experimental results. Furthermore, the modified Hodgkin-Huxley axonal model is applied to simulate the generation of action potential during infrared neural stimulation by taking into account the temperature dependence of electrical membrane capacitance. Results show that the threshold temperature increase induced by a train infrared pulse laser can be smaller if repetition rate is higher. These results also indicate that temperature rise time and axon diameter influence on threshold temperature increase. To verify threshold values estimated by the presented method, we use a train infrared pulsed laser (
λ
= 1450 nm with repetition rate of 3.8 Hz, pulse duration of 18 ms and energy density of 5 J/cm
2
) to optically pace an adult rat heart, and we are able to successfully pace the rat heart during an open-heart surgery. The presented method can be used to estimate threshold values of laser parameters required for generating an action potential, and it can provide an insight to how the temperature changes lead to neural stimulation during INS.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
PDF
