Mathematical model and sensor development for measuring energy transfer from wildland fires

2014 ◽  
Vol 23 (7) ◽  
pp. 995 ◽  
Author(s):  
Erik A. Sullivan ◽  
André G. McDonald
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Finite Length ◽  
Scale Model ◽  
Transient Temperature ◽  
High Heat Flux ◽  
Length Scale ◽  
Infinite Length ◽  
Wildland Fires ◽  
Loss Cone

Current practices for measuring high heat flux in scenarios such as wildland forest fires use expensive, thermopile-based sensors, coupled with mathematical models based on a semi-infinite-length scale. Although these sensors are acceptable for experimental testing in laboratories, high error rates or the need for water cooling limits their applications in field experiments. Therefore, a one-dimensional, finite-length scale, transient-heat conduction model was developed and combined with an inexpensive, thermocouple-based rectangular sensor, to create a rapidly deployable, non-cooled sensor for testing in field environments. The proposed model was developed using concepts from heat conduction and with transient temperature boundary conditions, to avoid complicated radiation and convection conditions. Constant heat flux and tree-burning tests were respectively conducted using a mass loss cone calorimeter and a propane-fired radiant panel to validate the proposed analytical model and sensor as well as test the sensor in a simulated forest fire setting. The sensor was mounted directly beside a commercial Schmidt–Boelter gauge to provide data for comparison. The proposed heat flux measurement method provided results similar to those obtained from the commercial heat flux gauge to within one standard deviation. This suggests that the use of a finite-length scale model, coupled with an inexpensive thermocouple-based sensor, is effective in estimating the intense heat loads from wildland fires.

Mass Nature of Heat and Its Applications I: Motion of Thermomass Fluid and General Heat Conduction Law

2010 ◽  
Author(s):  
Zeng-Yuan Guo ◽  
Bing-Yang Cao
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Gas Flow ◽  
Short Pulse ◽  
Rest Mass ◽  
Inertial Force ◽  
High Heat Flux ◽  
Phase Lag ◽  
Energy Relation ◽  
Inertial Terms

The concept of thermomass is defined as the equivalent mass of thermal energy according to the Einstein’s mass-energy relation. Hence, the phonon gas in dielectrics can be regarded a weighty, compressible fluid. Heat conduction in the medium, where the rest mass lattices or molecules acts the porous framework, resembles the gas flow through the porous medium. Newton mechanics has been applied to establish the equation of state and the equation of motion for the phonon gas as in fluid mechanics, since the drift velocity of a phonon gas is normally much less than the speed of light. The momentum equation of the thermomass gas, including the driving, inertial and resistant forces, is a damped wave equation, which is in fact the general conduction law. This is because it reduces to the CV (Cattaneo-Vernotte) model or the single phase-lag model as the heat flux related inertial terms are neglected, and reduces to Fourier’s heat conduction law as all inertial terms are neglected. Therefore, the underlying physics of Fourier’s heat conduction law is the balance between the driving force and the resistant force of the heat motion, and Fourier’s law will break down when the inertial force is comparable to the resistant force, for instance, in the case of ultra-short pulse laser heating or heat conduction in carbon nanotubes at ultra-high heat flux.

Mesoscopic Heat Conduction and Onset of Periodicity

2003 ◽  
Author(s):  
Kal Renganathan Sharma
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Time Domain ◽  
Heat Conduction Equation ◽  
Higher Order ◽  
Heat Propagation ◽  
Conduction Equation ◽  
Transient Temperature ◽  
Higher Order Terms ◽  
Fourier Heat Conduction

Mesoscopic approach deals with study that considers temporal fluctuations which is often averaged out in a macroscopic approach without going into the molecular or microscopic approach. Transient heat conduction cannot be fully described by Fourier representation. The non-Fourier effects or finite speed of heat propagation effect is accounted for by some investigators using the Cattaneo and Vernotte non-Fourier heat conduction equation: q=−k∂T/∂x−τr∂q/∂t(1) A generalized expression to account for the non-Fourier or thermal inertia effects suggested by Sharma (5) as: q=−k∂T/∂x−τr∂q/∂t−τr2/2!∂2q/∂t2−τr3/3!∂3q/∂t3−…(2) This was obtained by a Taylor series expansion in time domain. Manifestation of higher order terms in the modified Fourier’w law as periodicity in the time domain is considered in this study. When a CWT is maintained at one end of a medium of length L where L is the distance from the isothermal wall beyond which there is no appreciable temperature change from the initial condition during the duration of the study the transient temperature profile is obtained by the method of Laplace transforms. The space averaged heat flux is obtained and upon inversion from Laplace domain found to be a constant for the the case obeying Fourier’s law; 1 − exp(−τ) using the Cattaneo and Vernotte non-Fourier heat conduction equation, and upon introduction of the second derivative in time of the heat flux the expression becomes, 1 − exp(−τ)(Sin(τ) + Cos(τ)). Thus the periodicity in time domain is lost when the higher order terms in the generalized Fourier expression is neglected.

Heat Flux Estimation in a Nonlinear Inverse Heat Conduction Problem With Moving Boundary

2009 ◽  
Author(s):  
Hosein Molavi ◽  
Ali Hakkaki-Fard ◽  
Alireza Pourshaghaghy ◽  
Mehdi Molavi ◽  
Ramin K. Rahmani
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Measurement Errors ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Adjoint Problem ◽  
Inverse Heat Conduction Problem ◽  
Transient Temperature ◽  
Nonlinear Heat Conduction ◽  
Mechanical Removal

Estimation of heat flux in the nonlinear heat conduction problem becomes more challenging when the material at the boundary loses its mass due to phase change, chemical erosion, oxidation, or mechanical removal. In this paper, a new gradient-type method with adjoint problem is employed to predict the unknown time-varying heat flux at the receding surface in the nonlinear heat conduction problem. Particular features of this novel approach are discussed and examined. Results obtained by the new method for several test cases are benchmarked and analyzed using the numerical experiments with the simulated exact and noisy measurements. Exceedingly reliable estimation on the heat flux can be obtained from the knowledge of the transient temperature recordings, even in the case with measurement errors. In order to evaluate the performance characteristics of the present inverse scheme, simulations are conducted to analyze the effects of this technique with regard to conjugate gradient method with adjoint problem and variable metric method with adjoint problem. The obtained results show that the present inverse scheme distinguishably accelerates the convergence rate, which approve the well capability of the method for this type of heat conduction problems.

Analytical Solution of Hyperbolic Heat Conduction Equation for a Finite Slab With Arbitrary Boundaries, Initial Condition, and Stationary Heat Source

2008 ◽  
Author(s):  
Hossein Shokouhmand ◽  
Seyed Reza Mahmoudi ◽  
Kaveh Habibi
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Transient Temperature ◽  
Hyperbolic Heat Conduction ◽  
High Heat Flux ◽  
Adequate Model ◽  
Finite Slab

This paper presents an analytical solution of the hyperbolic heat conduction equation for a finite slab that sides are subjected to arbitrary heat source, boundary, and initial conditions. In the mathematical model used in this study, the heating on both sides treated as an apparent heat source while sides of the slab assumed to be insulated. Distribution of the apparent heat source for a problem with arbitrary heating on two boundaries is solved. The solution obtained by separation of variable method using appropriate Fourier series. Being a Sturm-Liouville problem in x-direction, suitable orthogonal functions can be allocated to hyperbolic heat conduction equation depending on the type of boundary conditions. Despite ease of proposed method, very few works has been done to solve hyperbolic heat conduction problems using this method by authors. The main feature of the method is straightforward formulation. In the analysis of heat conduction involving extremely short times, the parabolic heat conduction equation breaks down. By increasing the applications of the fast heat sources such as laser pulse for annealing of semiconductors and high heat flux applications, the need for adequate model of heat conduction has arisen. The hyperbolic heat conduction equation eliminates the paradox of an infinite speed of propagation of thermal disturbances which contradicts with Einstein’s theory of relativity. Moreover, it describes the highly transient temperature distribution in a finite medium more accurately.

The Model of Non-Fourier Heat Conduction in a Kind of Two-Phase Medium With Great Different Heat Conductivity

2008 ◽  
Author(s):  
Wen-Qiang Lu ◽  
Junfeng Lu
Keyword(s):  
Heat Flux ◽  
Relaxation Time ◽  
Heat Conduction ◽  
Heat Conductivity ◽  
Rapid Heating ◽  
Relaxation Times ◽  
High Heat Flux ◽  
Phase Lag ◽  
Two Phase ◽  
Fourier Heat Conduction

The model of non-Fourier heat conduction in a kind of two-phase mediums with great different heat conductivity is deduced by the idea and mathematics of dual phase lag. It is pointed out that the relaxation times to establish heat flux and temperature gradient include both kinds in this model: the relaxation time appeared under the conditions of applied high heat flux and rapid heating, the relaxation time introduced by the non-equilibrium heat exchange between the two-phase mediums. It is very important to distinguish the both kinds of relaxation times for analyzing and explaining the experimental phenomena of non-Fourier heat conduction in this kind of two-phase mediums.

Design and Testing of a Carbon Foam Based Supercooler for High Heat Flux Cooling in Optoelectronic Packages

2009 ◽  
Author(s):  
Walter W. Yuen ◽  
Jianping Tu ◽  
Wai-Cheong Tam ◽  
Dan Blumenthal
Keyword(s):  
Heat Flux ◽  
Heated Surface ◽  
Local Maximum ◽  
Carbon Foam ◽  
High Heat ◽  
Maximum Temperature ◽  
Transient Temperature ◽  
High Heat Flux ◽  
Periodic Heating ◽  
Heating Region

The feasibility of using carbon foam as a heat sink and heat spreader in optoelectronic packages is assessed. A “supercooler” is designed, fabricated and tested to verify its cooling capability under high heat flux conditions in a typical optoelectronic package. The supercooler uses carbon foam as a primary heat transfer material. Water is soaked into the carbon foam and under evacuated pressure, boiling is initiated under the heating region to provide enhanced cooling. Experiments were conducted for a heat flux of up to 400 W/cm2 deposited over a heating area of 0.5 mm × 5 mm. Two dimensional transient temperature distributions were recorded using a high speed infrared camera. Data were obtained for steady heating, as well as periodic heating with frequency up to 8 hz. Results show that the supercooler is very efficient in dissipating heat away from the heating region. Data obtained under 8 hz periodic heating with a peak power input of 10W, for example, showed that the temperature of the heated surface rises quickly to a local maximum of 15 to 20 °K above the ambient. The heated surface is then cooled uniformly back to a near ambient condition (with a maximum temperature of less than 5 °K above ambient) during the cooling half of the cycle (less than 0.0625 sec after the heating is turned off). The average cooling rate during the cooling period exceeds 170 °K/s. A numerical model, based on COMSOL, is developed to interpret the experimental data and to provide insights on the relevant physics responsible for the rapid cooling. Numerical data are presented to demonstrate how the supercooler can be further improved and adopted for other applications.

Heat Flux Estimation in a Nonlinear Inverse Heat Conduction Problem With Moving Boundary

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
Hosein Molavi ◽  
Ramin K. Rahmani ◽  
Alireza Pourshaghaghy ◽  
Ebrahim Sharifi Tashnizi ◽  
Ali Hakkaki-Fard
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Measurement Errors ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Adjoint Problem ◽  
Inverse Heat Conduction Problem ◽  
Transient Temperature ◽  
Nonlinear Heat Conduction ◽  
Mechanical Removal

The estimation of heat flux in the nonlinear heat conduction problem becomes more challenging when the material at the boundary loses its mass due to phase change, chemical erosion, oxidation, or mechanical removal. In this paper, a new gradient-type method with an adjoint problem is employed to predict the unknown time-varying heat flux at the receding surface in the nonlinear heat conduction problem. Particular features of this novel approach are discussed and examined. Results obtained by the new method for several test cases are benchmarked and analyzed using numerical experiments with simulated exact and noisy measurements. Exceedingly reliable estimation on the heat flux can be obtained from the knowledge of the transient temperature recordings, even in the case with measurement errors. In order to evaluate the performance characteristics of the present inverse scheme, simulations are conducted to analyze the effects of this technique with regard to the conjugate gradient method with an adjoint problem and variable metric method with an adjoint problem. The results obtained show that the present inverse scheme distinguishably accelerates the convergence rate, which approve the well capability of the method for this type of heat conduction problems.

Novel 2D Transient Heat Conduction Calculation in a Cooled Rotor: Ventilation Preheating — Blowdown Flux

2008 ◽  
Author(s):  
J. P. Solano ◽  
G. Paniagua ◽  
A. de la Loma
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Short Duration ◽  
Data Reduction ◽  
Transient Heat Conduction ◽  
Element Model ◽  
Wall Heat Flux ◽  
Transient Temperature ◽  
Blow Down ◽  
Cross Sectional

An alternative to classical data reduction techniques for thin film gauges in short duration facilities is presented. A finite element model of the two-dimensional unsteady heat conduction equation is solved in the cross-sectional area of a metallic airfoil bounded with a polyamide sheet, on which thermal sensors are deposited. As a result, the transient temperature field in the multilayered substrate and the experimental wall heat flux distribution are derived. The methodology allows for capuring all 2D heat conduction effects that are irremediably neglected with the 1D data reduction technique. The application of this technique in a compression tube facility allows an exact evaluation of the initial wall heat flux into cooled rotor blades. During the spinning up period, the rotor of this type of fully rotating transient facilities is spun up to nearly its nominal speed (from 0 RPM to 6200 RPM) resulting in preheating due to drag losses. The long duration of this experiment (∼450 s) and the magnitude of the wall temperature increase result in significant 2D conduction effects that are not accounted for using the 1D approach. In addition, short duration experiments confirm the existence of 2D effects at smaller time scales (∼0.5 s), as well as the influence of the initial non-uniform temperature distribution in the rotor blade. The resulting flux with such an initial condition appears to be the superposition of the wall heat flux at the end of the spinning up before the test and the flux due to the blow-down itself.

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