Rao V. Arimilli

Inferring convective and radiative heating loads from transient surface temperature measurements in the half-space

The classical, one-dimensional, transient half-space heat conduction problem in an opaque material is revisited in order to highlight several important observations that can impact a variety of ill-posed problems. First, the differential statement is recast into an equivalent Abel integral equation that describes the penetrating (conductive) heat flux in terms of the surface temperature. In many aerospace studies, the surface temperature is measured and the surface heat flux is calculated. Though intuitively simple, using unfiltered, noisy temperature data leads to unstable heat flux predictions as the sample density increases. This article presents a clear mathematical proof using the Discrete Fourier Transform Method verifying that the root-mean square error of the surface heat flux grows as the square root of the sample size (i.e., it is ill-posed when based on surface temperature measurements containing white noise). Second, a digital filtering method is proposed to reduce the instability problem while permitting an accurate depiction of the surface heat flux. Third, the study indicates that it is possible to predict the radiative and convective heat loads based on surface temperature measurements without a priori specification of the heat transfer coefficient or emissivity. That is, the Abel formulation effectively uncouples the interior (conductive region) from the surface (convective and radiative regions). Finally, it is demonstrated that the average convective heat transfer coefficient and average emissivity can be determined through the decoupled formulation using a simple least-squares approach. Further, the effect of data filtering is illustrated on the predictions of both the convective and radiative heat loads. The proposed Gauss filter is well suited to this problem owing to (i) its inherent behavior as a low-pass filter in the frequency domain and (ii) maintaining smooth, analytic support in the time domain.

New In Situ Method for Estimating Thermal Diffusivity Using Rate-Based Temperature Sensors

This paper proposes an experimental methodology for estimating the thermal diffusivity, a in a one-dimensional, half-space geometry based on two in-situ positioned probes that can acquire temperature; and, the first- and second-time deriva tives of temperature. The thermal diffusivity is estimated at each sampled time by solving an n th -degree polynomial for the thermal diffusivity. The degree of the a-polynomial and required order of the time derivati ve sensors depend on the chosen spatial truncation of the Tayl or series. This approach does not require the specification of the imposed surface boundary condi tion. Additionally, a novel inter-sensitivity analysis is proposed for guiding sensor placement t hat ensures a maximum, absolute sensitivity between the two probes; and, develops a single, tim e-point estimation of thermal diffusivity at the maximum inter-sensitivity. As a preliminary ind icator of the newly proposed methodology, numerical simulation provides sufficient merit for further concept development and experimental verification.

Experimental and numerical study of solidification and melting of pure materials

Solidification experiments in an enclosure are performed with caprillic acid as the phase-change fluid, and the experimental results for the temperature and solidification front advancement are presented. Caprillic acid, with its less than ambient melting point and low volume reduction on solidification, emerges as a good candidate for solidification experiments. An enthalpy formulation for convection/diffusion phase change in conjunction with an algorithm similar to SIMPLER is used in a formulation developed by Voller for solid-liquid phase change, to generate a numerical solution for lowand high-Prandtl-number fluids. The numerical solution is compared with solidification experimental data. In addition, the numerical solution is also compared with experimental melting data of Wolf and Viskanta for pure tin. The results indicate a good agreement between the experimental data and numerical solutions. This adds confidence to the formulation used in this numerical model.

Design and analysis of a 55-kW air-cooled automotive traction drive inverter

The purpose of this study is to determine the thermal feasibility of an air-cooled 55-kW power inverter with SiC devices. Air flow rate, ambient air temperature, voltage, and device switching frequency were studied parametrically by performing transient and steady-state simulations. The transient simulations were based on inverter current that represents the US06 supplemental federal test procedure from the US EPA. The results demonstrate the thermal feasibility of using air to cool a cylindrical-shaped 55-kW SiC traction drive inverter with axial-flow of air. When the inverter model is subject to one or multiple current cycles, the maximum device temperature does not exceed 164°C (327°F) for an inlet flow rate of 270 cfm, ambient temperature of 120°C, voltage of 650 V, and switching frequency of 20 kHz. The results show that the ideal blower power input for the entire inverter with a total inlet air flow rate of 540 cfm is 312 W.

Feasibility study of a 55-kW air-cooled automotive inverter

The purpose of this study is to determine the thermal feasibility of an air-cooled 55-kW power inverter with SiC devices. Air flow rate, ambient air temperature, voltage, and device switching frequency were studied parametrically by performing transient and steady-state simulations. The transient simulations were based on inverter current that represents the US06 supplemental federal test procedure from the US EPA. The results demonstrate the thermal feasibility of using air to cool a rectangular-shaped 55-kW SiC traction drive inverter. When the inverter model is subject to one or multiple current cycles, the maximum device temperature does not exceed 146°C for an inlet flow rate of 270 cfm, ambient temperature of 120°C, voltage of 650 V, and switching frequency of 20 kHz. The results show that the ideal blower power input for the entire inverter with a total inlet air flow rate of 540 cfm is 105 W.

A new three-dimensional heat flux–temperature integral relationship for half-space transient diffusion

Abstract This paper derives a new integral relationship between heat flux and temperature in a transient, three-dimensional heat conducting Cartesian half space ( x > 0 , y ∈ ( − ∞ , ∞ ) , z ∈ ( − ∞ , ∞ ) ). A unified mathematical treatment has been developed based on operational and transform methods; and singular integral equation regularization. Regularization is accomplished based on a series of observations involving the diffusive nature of the operator. This newly developed relationship provides the local heat flux perpendicular to the front surface at any location within the half space. This expression suggests that an embedded plane of temperature sensors parallel to the surface can be used to acquire the local, in-depth heat flux in the x -direction. The relationship does not require a priori knowledge of the surface boundary condition which has analytically been removed in the process. The ill-posed nature of diffusion is highlighted owing to the appearance of the heating/cooling rate (°C/s) in the integrand of the new relationship. Integral relationships of this type are highly useful for experimental investigations since the in-depth heat flux can be extracted from well-established temperature transducers.

Transient thermal analysis of three fast-charging latent heat storage configurations

A space-based thermal storage application must accept large quantities of heat in a short period of time at an elevated temperature. A model of a lithium hydride phase change energy storage system was used to estimate reasonable physical dimensions for this application, which included the use of a liquid metal heat transfer fluid. A finite difference computer code was developed and used to evaluate three methods of enhancing heat transfer in the phase change material energy storage system. None of the following methods, inserting thin fins, reticulated nickel, or liquid lithium, significantly improved the system performance. The use of a 95% void fraction reticulated nickel insert was found to increase the storage capacity (total energy stored) of the system slightly with only a small decrease in the system energy density (energy storage/system mass). The addition of 10% liquid lithium was found to cause minor increases in both storage density and storage capacity with the added benefit of reducing the hydrogen pressure of the lithium hydride.

Radiation heat transfer in enclosures with discrete heat sources

Abstract The potential for the enhancement of heat transfer by thermal radiation within enclosures containing modern electronic equipment is established on the basis of a diffuse-gray analysis of the thermal radiation heat transfer in a rectangular enclosure with discrete heat sources when the medium enclosed is radiatively nonparticipating. The geometry considered is representative of a unit cell of parallel-circuit board inside of modern electronic equipment. The results are presented for heat fluxes in the range of 0.01 to 25 W/cm 2 , emissivity values of 0.1 to 1.0, the ratios of the distance between center line of the heaters to the spacing between heaters of 1 to 3, and enclosure height-to-width (H/W) ratios of 1 to 4. For the problem considered, the results indicate the following: (1) Surface temperature reduction of at least 50°C can be achieved when emissivities of the surfaces of the enclosure are increased from 0.25 to 1.0. (2) The influence of H/W is, however less significant. (3) The surface temperature of the constant-flux heat sources is essentially uniform. Also a simple dimensionless correlation between the average temperature of the heat sources to the heat flux supplied to them is presented for use by designers for estimation purposes.

Performance Evaluation of a Prototype TurbX™ Engine

A revolutionary new concept internal-combustion engine called TurbX™ was invented and a prototype was built by an independent inventor, M. A. Wilson. Theoretically, the TurbX™ engine cycle can be represented by the Atkinson thermodynamic cycle with a continuous combustion process. Because of these attributes, this concept has the potential for higher fuel economy and power density relative to other internal combustion engine types. To evaluate the performance of this prototype, Oak Ridge National Laboratory and The University of Tennessee conducted an independent experimental study. Two series of tests were performed: cold-flow and fuel-fired tests. Cold-flow, compressed-air driven, tests were performed by pressurizing the combustion chamber with shop air to demonstrate the prototype performance of the turbine section. These results showed positive but unremarkable torque for combustion chamber air pressures above 300 kPa with a functional relationship illustrative of typical gas turbines with respect to shaft speed. The fuel-fired tests consisted of 26 constant-speed runs between 1800 and 9500 RPM. The experimental apparatus limited the maximum test speed to 9500 RPM. The TurbX™ engine produced no net output power for all fuel-fired tests conducted. The temperature measurements indicated that for most of the runs there was sustained combustion. However, even in runs where satisfactory combustion was observed, measured gage pressure inside the combustion chamber never exceeded 15.5 kPa. The lack of sufficient pressure rise inside the combustion chamber is indicative of excessive leakage of the combustion products through the preliminary prototype engine internals. Based on the results and the experience gained through this independent testing of this preliminary prototype, further development of this concept is recommended. Three major issues are specifically identified: 1) the internal components must be redesigned to reduce leakage, 2) combustion chamber design and 3) improve the overall aerodynamic performance of the engine internal components.Copyright

Analysis of conduction heat transfer problems in steady, 2D regions with circular holes using a special boundary integral method

Abstract A special boundary integral method developed for two-dimensional regions containing circular holes is used to calculate temperature and heat transfer on the boundaries of several selected regions. The geometrical configuration of the region is arbitrary and convective boundary conditions are assumed. An important feature of the method is analytic representation of temperature and its normal derivative on the interior circular holes in the form of a harmonic series. This makes the application of the boundary integral method convenient and free from conditioning problems associated with small interior boundaries. Heat transfer from circular isothermal interior holes are calculated for several illustrative examples using three terms of the harmonic series representation for heat transfer at each of the circular boundaries. The results are presented and discussed.