Spatial Derivatives Of Temperature Research Articles

Rapid and nondestructive testing for simultaneous measurement of thermal conductivity and thermal diffusivity of flat materials based on thermography

This study presents a novel experimental method that simultaneously supplies the thermal conductivity and thermal diffusivity of flat materials, which solves the limitations of traditional methods that have strict demands for thermal excitation, boundary, and size of samples. In this method, IR thermal imaging is used to collect data from the material surface temperature field caused by a laser excitation, and the differential terms in the basic heat-conduction differential equation are estimated by curve fitting. The differential equation is so transformed in an algebraic equation, which allows to simultaneously determine the thermal conductivity and thermal diffusivity. The measurement experiment does not require a strict control of the boundary or initial conditions, or thermal excitation modalities. The hypothesis this method is based on is that the spatial derivative of temperature in the Z-direction is linear with the temperature difference between the material surface and environment. Using this constraint the optimal operation conditions can be identified. The influence of operation conditions, including the heat transfer distance, excitation duration, material thickness, and number of sampling points on the measured surface, together with the results, were analysed by numerical simulation. The optimal operation conditions when testing two 304 stainless steel samples were found from this simulation analysis. Results of 304 stainless steel samples 1 and 2 mm thick show a deviation between the reference and measured values of the two thermal properties within 4.2 %, and repeatability within 5.5 %. Therefore, this method can realise rapid, nondestructive, and simultaneous measurements of thermal conductivity and thermal diffusivity.

Thermal characterisation of homogeneous materials using a weak formulation technique

A new method for the thermal characterisation of homogeneous materials is proposed. This method, specifically designed to measure the thermal diffusivity in the plane of thin specimens, is based on a low-order weak formulation (LOWF) method of the heat equation using a virtual test function. In this formulation, the spatial derivatives of temperature are coupled with an analytical expression less dependent on measurement noise. In this way, it is shown that the LOWF method leads to a robust method for the estimation of thermal diffusivity. The LOWF method is numerically tested on a two-dimensional model and validated on a homogeneous material using infrared thermography.

Effect of the separation between cold wires on the spatial derivatives of temperature in a turbulent flow

An analysis is made of the effect of spatial separation of a pair of parallel temperature sensors on the variance and spectrum of spatial temperature derivatives in a turbulent flow. The results of the analysis are compared with experimental results obtained when the separation between the sensors is in a direction either perpendicular or parallel to that of the main stream.

The spatial derivative of temperature in a turbulent flow and Taylor’s hypothesis

Statistics of the streamwise derivative of temperature fluctuations on the centerline and at one streamwise station in the self-preserving region of a turbulent plane jet have been obtained by two techniques. In one, the derivative is approximated by the difference between the signals from two cold wires separated in the streamwise direction. In the other, the streamwise derivative is inferred from the temporal derivative and different convection velocities. Instantaneous values, root-mean-square values, skewness, and flatness factors are in reasonable agreement for a sufficiently large range of separations regardless of whether the mean velocity (Taylor’s hypothesis) or the instantaneous velocity are used as the convection velocity. Corrections for turbulence intensity, that are often applied to Taylor’s hypothesis, do not seem warranted. The difference between spectra of the temperature difference and temporal derivative spectra cannot be resolved by identifying the convection velocity with a frequency-dependent phase velocity of the temperature fluctuation.

Correlations of squared velocity and temperature derivatives in a turbulent plane jet

Correlations, in a turbulent plane jet, of squared time derivatives of three components of velocity and of squared time and spatial derivatives of temperature indicate a value for the exponent μ of about 0.2 for velocity and 0.25 for temperature.

Skewness of spatial derivatives of temperature in a turbulent boundary layer

A simple model based on a geometrical property of the organized large scale motion is used to predict the relative magnitudes and signs of odd moments of the components of the temperature gradient in turbulent boundary layers.