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Results for “heat equation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

A Fourier-Chebyshev pseudospectral method for solving steady 3-D Navier-Stokes and heat equations in cylindrical cavities

A Fourier-Chebyshev pseudospectral method for solving steady 3D Navier-Stokes equations in cylindrical cavities is presented and discussed. The general method is pseudo-unsteady and uses a semi-implicit finite difference scheme for the time discretization. The generalized ADI (Alternating Direction Implicit) procedure is then applied to reduce the problem to a successive solution of one-dimensional problems. The spatial approximation uses a Fourier-Galerkin approximation in the periodic direction and a Chebyshev-collocation approximation in the other directions. Difficulties related to the pressure are surmounted by using the artifical compressibility method. A suitable variable change was chosen to avoid the problem of singularity at the axis generated by cylindrical coordinates. The method is first tested on an advection-diffusion equation and then on the Navier-Stokes equations. Finally, the method is illustrated by a convection problem of a differentially heated fluid.

Pulicani, J. P.↗
DOE OSTI2024

Restoring the discontinuous heat equation source using sparse boundary data and dynamic sensors

Abstract This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been established that utilizing sparse boundary flux data can enable source recovery, the presence of a limited number of observation sensors poses a challenge for accurately tracing the inverse quantity of interest. To overcome this limitation, we introduce a sampling algorithm grounded in Langevin dynamics that incorporates dynamic sensors to capture the flux information. Furthermore, we propose and discuss two distinct dynamic sensor migration strategies. Remarkably, our findings demonstrate that even with only two observation sensors at our disposal, it remains feasible to successfully reconstruct the high-dimensional unknown parameters.

Mathematics↗
NASA NTRS1980

Solutions of the equation of heat flow

The geometry of sunspots has been used to suggest a problem in heat flow. The equation of heat transport is solved for the case of a cylinder with a given thermal conductivity imbedded in an otherwise uniform medium with different conductivity. The surface of this region radiates heat with flux proportional to temperature. At a lower surface, either in heat flux or temperature is held constant. The cylinder can have an anisotropic thermal conductivity. The variations in temperature along the radiating surface have been determined. A simple approximation is noted which has been found to give a general solution with acceptable accuracy. This method may be of some use in other situations requiring the solution of Laplace's equation with a free surface. The analysis is used to set limits on the ratio of diameter to depth for cases which preserve the sharp surface temperature transition across the cylinder.

Margolis, S. H.↗
NASA NTRS2012

Heat Stress Equation Development and Usage for Dryden Flight Research Center (DFRC)

Heat Stress Indices are equations that integrate some or all variables (e.g. temperature, relative humidity, wind speed), directly or indirectly, to produce a number for thermal stress on humans for a particular environment. There are a large number of equations that have been developed which range from simple equations that may ignore basic factors (e.g. wind effects on thermal loading, fixed contribution from solar heating) to complex equations that attempt to incorporate all variables. Each equation is evaluated for a particular use, as well as considering the ease of use and reliability of the results. The meteorology group at the Dryden Flight Research Center has utilized and enhanced the American College of Sports Medicine equation to represent the specific environment of the Mojave Desert. The Dryden WBGT Heat Stress equation has been vetted and implemented as an automated notification to the entire facility for the safety of all personnel and visitors.

Houtas, Franzeska↗
NASA NTRS1983

A new explicit method for the numerical solution of parabolic differential equations

A new method is derived for solving parabolic partial differential equations arising in transient heat conduction or in boundary-layer flows. The method is based on a combination of the modified differential quadrature (MDQ) method with the rational Runge-Kutta time-integration scheme. It is fully explicit, requires no matrix inversion, and is stable for any time-step for the heat equations. Burgers equation and the one- and two-dimensional heat equations are solved to demonstrate the accuracy and efficiency of the proposed algorithm. The present method is found to be very accurate and efficient when results are compared with analytic solutions.

Satofuka, N.↗
NASA NTRS2020

A Second-Order Closure Turbulence Model: New Heat Flux Equations and No Critical Richardson Number

We formulate a new second-order closure turbulence model by employing a recent closure for the pressure-temperature correlation at the equation level. As a result, we obtain new heat flux equations that avoid the long-standing issue of a finite critical Richardson number. The new, structurally simpler model improves on the Mellor-Yamada 1982 and Galperin et al. 1988 models; key feature includes enhanced mixing under stable conditions facilitating agreement with observational, experimental and high-resolution numerical data sets. The model predicts a planetary boundary layer height deeper than predicted by models with low critical Richardson numbers, as demonstrated in single column model runs of the GISS ModelE general circulation model.

second-order closure turbulence model↗
NASA NTRS1985

Generating Tables of Thermodynamic Properties

Thermodynamic Property Generation program produces tables for any fluid for which state equation, vapor pressure equation, specific heat equation, and critical constants are known. Program calculates thermodynamic properties at any state providing way of obtaining properties at extreme environmental conditions.

Nguyen, S. N.↗
NASA NTRS1974

The nature of the sunspot phenomenon. I - Solutions of the heat transport equation

It is pointed out that sunspots represent a disruption in the uniform flow of heat through the convective zone. The basic sunspot structure is, therefore, determined by the energy transport equation. The solutions of this equation for the case of stochastic heat transport are examined. It is concluded that a sunspot is basically a region of enhanced, rather than inhibited, energy transport and emissivity. The heat flow equations are discussed and attention is given to the shallow depth of the sunspot phenomenon. The sunspot is seen as a heat engine of high efficiency which converts most of the heat flux into hydromagnetic waves.

Parker, E. N.↗