HEAT FLUX MEASUREMENT BY USING A HEAT PIPE BASED HEAT FLUXSENSOR

2018 ◽  
Vol 3 (11) ◽  
Author(s):  
Joses Jenish Smart ◽  
Antony Raja S ◽  
D.S. Robinson Smart ◽  
Lindon Robert Lee
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Steady State ◽  
Heat Pipe ◽  
Thermal Flux ◽  
Heat Flux Sensor ◽  
Heat Flow Rate ◽  
Sensing Element ◽  
Time Duration ◽  
Radiation Mode

Heat flux or thermal flux, sometimes also referred to as heat flux density or heat flow rate intensity is a flow of energy per unit area. In SI units, it is measured in [Wm-2]. Measurements of heat flux are usually derived from temperature measurements. Under a temperature gradient the two thermocouples will be at different temperature and so register a voltage. The heat flux is proportional to this differential voltage. An effective way of measuring the heat flux in furnaces, boilers, ovens and similar other systems for combined convection and radiation mode of heat transfer by a heat pipe based heat flux sensor is described in this proposal. A cylindrical sensing element made out of Copper it is exposed to the heat source. The sensing element is insulated in the cylindrical surface so that one-dimensional heat conduction is ensured in the sensing element. By applying the Fourier law of heat conduction, the heat flux received by the sensing element can be evaluated at steady state by measuring the temperature difference between the two specific points in the sensing element. Since the sensing element is connected thermally to the heat pipe, the whole system will reach steady state in relatively short time duration.

HEAT FLUX MEASUREMENT BY USING A HEAT PIPE BASED HEAT FLUXSENSOR

2018 ◽  
Vol 3 (10) ◽  
Author(s):  
Joses Jenish Smart ◽  
Antony Raja S ◽  
D.S. Robinson Smart ◽  
Lindon Robert Lee
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Steady State ◽  
Heat Pipe ◽  
Thermal Flux ◽  
Heat Flux Sensor ◽  
Heat Flow Rate ◽  
Sensing Element ◽  
Time Duration ◽  
Radiation Mode

Heat flux or thermal flux, sometimes also referred to as heat flux density or heat flow rate intensity is a flow of energy per unit area. In SI units, it is measured in [Wm-2]. Measurements of heat flux are usually derived from temperature measurements. Under a temperature gradient the two thermocouples will be at different temperature and so register a voltage. The heat flux is proportional to this differential voltage. An effective way of measuring the heat flux in furnaces, boilers, ovens and similar other systems for combined convection and radiation mode of heat transfer by a heat pipe based heat flux sensor is described in this proposal. A cylindrical sensing element made out of Copper it is exposed to the heat source. The sensing element is insulated in the cylindrical surface so that one-dimensional heat conduction is ensured in the sensing element. By applying the Fourier law of heat conduction, the heat flux received by the sensing element can be evaluated at steady state by measuring the temperature difference between the two specific points in the sensing element. Since the sensing element is connected thermally to the heat pipe, the whole system will reach steady state in relatively short time duration.

Generalized Solution for Two-Dimensional Transient Heat Conduction Problems With Partial Heating Near a Corner

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Robert L. McMasters ◽  
Filippo de Monte ◽  
James V. Beck
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Heat Conduction ◽  
Steady State ◽  
Separation Of Variables ◽  
Transient Heat Conduction ◽  
Generalized Solution ◽  
Convective Heating ◽  
Two Dimensional ◽  
Partial Heating

A generalized solution for a two-dimensional (2D) transient heat conduction problem with a partial-heating boundary condition in rectangular coordinates is developed. The solution accommodates three kinds of boundary conditions: prescribed temperature, prescribed heat flux and convective. Also, the possibility of combining prescribed heat flux and convective heating/cooling on the same boundary is addressed. The means of dealing with these conditions involves adjusting the convection coefficient. Large convective coefficients such as 1010 effectively produce a prescribed-temperature boundary condition and small ones such as 10−10 produce an insulated boundary condition. This paper also presents three different methods to develop the computationally difficult steady-state component of the solution, as separation of variables (SOV) can be less efficient at the heated surface and another method (non-SOV) is more efficient there. Then, the use of the complementary transient part of the solution at early times is presented as a unique way to compute the steady-state solution. The solution method builds upon previous work done in generating analytical solutions in 2D problems with partial heating. But the generalized solution proposed here contains the possibility of hundreds or even thousands of individual solutions. An indexed numbering system is used in order to highlight these individual solutions. Heating along a variable length on the nonhomogeneous boundary is featured as part of the geometry and examples of the solution output are included in the results.

scholarly journals Non-steady-state heat conduction in composite walls

2014 ◽  
Vol 470 (2165) ◽  
pp. 20130605 ◽  
Author(s):  
Bernard Deconinck ◽  
Beatrice Pelloni ◽  
Natalie E. Sheils
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Steady State ◽  
Composite Materials ◽  
Solution Method ◽  
One Dimensional ◽  
Infinite Domains ◽  
Steady State Heat ◽  
The One ◽  
Composite Walls

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux is prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. We indicate also how to extend the solution method to the setting of one finite-sized domain surrounded on both sides by semi-infinite domains, and on that of three finite-sized domains.

Numerical Simulation of Heat Conduction for Error Analysis on Heat Flux Sensor Embedded in Flat Steel Plate

2014 ◽  
Vol 563 ◽  
pp. 133-136
Author(s):  
Chun Lai Tian ◽  
Shan Zhou ◽  
Li Yong Han
Keyword(s):  
Numerical Simulation ◽  
Heat Flux ◽  
Heat Conduction ◽  
Temperature Difference ◽  
Heat Conduction Problem ◽  
Maximum Temperature ◽  
Heat Flux Sensor ◽  
Maximum Temperature Difference ◽  
Maximum Heat ◽  
Errors Analysis

A numerical simulation model of heat flux sensors embedded in a flat plate is established. Each sensor has four thermal couples and is inserted into the specified hole. The problem is defined as a steady heat conduction problem with specified boundary conditions and solved by the finite element method. The results of the simulation case demonstrate that the maximum heat flux appears near the sensor shell. The average heat flux of the plate is much smaller than the maximum. Due to exiting of the contact heat resistance, the temperature of the sensor is much lower than that of the plate at horizontal surface. The maximum temperature difference appears on the bottom shell of the sensor. The maximum temperature difference between the simulation results and the experimental data at test points is 1.5 K. The model is verified and could be accepted for the further errors analysis.

Correlations Spanning the Entire Biot Number Range to Predict Near Steady State Condition in Transient 1-D Heat Conduction Problems

Volume 1 ◽  
2004 ◽  
Author(s):  
M. Kazmierczak ◽  
N. Sharma
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Biot Number ◽  
Common Knowledge ◽  
Plane Layer ◽  
Conduction Time ◽  
Time Duration ◽  
Transient Time ◽  
Number Range ◽  
Steady State Condition

Steady state criteria for vanishing small values of Biot number (lumped case) is well known and is reported in every undergraduate text on heat transfer. The heat conduction time scale for pure thermal diffusion problems (extremely large values of Biot number) is also a very well established fact and common knowledge to all well-schooled thermal engineers. However, to the best of the authors’ knowledge no attempt has been made so far to develop a generalized criterion encompassing the entire Biot number range. Hence, the objective of this paper is to construct a simple, but accurate, correlation to predict the onset of steady state for the three basic configurations (plane layer, cylinder, and sphere) for the complete range of Biot number from the high (Bi → ∞) to the low (Bi →0) Bi value limits, while spanning all values in between. Correlations are developed and reported in this paper such that they predict the transient time duration very close to those obtained from the theoretical solution to the problem. Moreover these proposed correlations are extremely simple in form and, as such, are ideal to be used by practicing thermal engineers in need of a quick estimate for the required time period to achieve steady state for problems that can be modeled from these basic geometries. A more accurate correlation, for the case of slab has also been proposed (containing two additional terms) which can be used if higher accuracy in the intermediate Biot number range were to be desired.

Comparative Assessment of the Finite Difference, Finite Element, and Finite Volume Methods for a Benchmark One-Dimensional Steady-State Heat Conduction Problem

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Sandip Mazumder
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Heat Conduction ◽  
Steady State ◽  
Energy Conservation ◽  
Heat Conduction Problem ◽  
Mesh Size ◽  
The Other ◽  
One Dimensional ◽  
Steady State Heat

The finite difference (FD), finite element (FE), and finite volume (FV) methods are critically assessed by comparing the solutions produced by the three methods for a simple one-dimensional steady-state heat conduction problem with heat generation. Three issues are assessed: (1) accuracy of temperature, (2) accuracy of heat flux, and (3) satisfaction of global energy conservation. It is found that if the order of accuracy of the numerical discretization schemes is the same (central difference for FD and FV, linear basis functions for FE), the accuracy of the temperature produced by the three methods is similar, except close to the boundaries where the FV method outshines the other two methods. Consequently, the FV method is found to predict more accurate heat fluxes at the boundaries compared to the other two methods and is found to be the only method that guarantees both local and global conservation of energy irrespective of mesh size. The FD and FE methods both violate energy conservation, and the degree to which energy conservation is violated is found to be mesh size dependent. Furthermore, it is shown that in the case of prescribed heat flux (Neumann) and Newton cooling (Robin) boundary conditions, the accuracy of the FD method depends in large part on how the boundary condition is implemented. If the boundary condition and the governing equation are both satisfied at the boundary, the predicted temperatures are more accurate than in the case where only the boundary condition is satisfied.

scholarly journals Low-Temperature Heat Conduction in Pure, Monocrystalline Ice

1975 ◽  
Vol 14 (72) ◽  
pp. 517-528 ◽  
Author(s):  
J. Klinger
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Steady State ◽  
Low Temperature ◽  
Cooling Rate ◽  
Single Crystals ◽  
Liquid Nitrogen Temperature ◽  
Flux Method ◽  
Temperature Heat ◽  
Steady State Heat

The heat conduction of ice single crystals is measured by a steady-state heat-flux method between 1.7 K and 100 K. For temperatures higher than 16 K all experimental points are found to be on the same curve. For temperatures lower than 16 K the heat conduction curves depend on the material of the crystallization vessel, the ageing of the sample and the cooling rate between the temperature of the mount (≈ 260 K) and liquid-nitrogen temperature. No anisotropy can be found for temperatures higher than 9 K. Computer fits are made, based on Callaway’s model of heat conduction in dielectric crystals. An attempt is made to explain the observed extrinsic heat conduction by the presence of microstructures in ice. It is shown that heat-conduction measurements can be used to establish a “quality-list” of samples studied in laboratories.

scholarly journals Development of a Thermal Equilibrium Prediction Algorithm

2002 ◽  
Author(s):  
Cuauhtemoc Aviles-Ramos
Keyword(s):  
Heat Flux ◽  
Exact Solution ◽  
Heat Conduction ◽  
Thermal Diffusivity ◽  
Thermal Equilibrium ◽  
Measurement Time ◽  
Prediction Algorithm ◽  
Heat Flux Sensor ◽  
Data Sets ◽  
Flux Sensor

A thermal equilibrium prediction algorithm is developed and tested using a heat conduction model and data sets from calorimetric measurements. The physical model used in this study is the exact solution of a system of two partial differential equations that govern the heat conduction in the calorimeter. A multi-parameter estimation technique is developed and implemented to estimate the effective volumetric heat generation and thermal diffusivity in the calorimeter measurement chamber, and the effective thermal diffusivity of the heat flux sensor. These effective properties and the exact solution are used to predict the heat flux sensor voltage readings at thermal equilibrium. Thermal equilibrium predictions are carried out considering only 20% of the total measurement time required for thermal equilibrium. A comparison of the predicted and experimental thermal equilibrium voltages shows that the average percentage error from 330 data sets is only 0.1%. The data sets used in this study come from calorimeters of different sizes that use different kinds of heat flux sensors. Furthermore, different nuclear material matrices were assayed in the process of generating these data sets. This study shows that the integration of this algorithm into the calorimeter data acquisition software will result in an 80% reduction of measurement time. This reduction results in a significant cutback in operational costs for the calorimetric assay of nuclear materials.

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