Transient Conduction Equation Research Articles

Soil Temperature in a Row Crop with Incomplete Surface Cover

AbstractA method is presented to predict soil temperature distribution between rows of crops that partially shade the soil surface. The method combines a model for predicting time and location of soil surface shading with a model for two‐dimensional soil heat transfer. The track of shadow model is general, and requires only plant shape parameters, field location coordinates, row spacing, and row direction to predict soil surface shading as a function of time. The soil heat transfer model is an explicit finite difference approximation of the transient conduction equation, allowing for time and space dependence of soil thermal properties. The surface boundary temperatures are computed by partitioning the surface net radiation into the sensible air, latent, and ground heat flux components. Standard meteorological inputs required to compute the energy partitioning are global radiation, air temperature and humidity, and windspeed. Observed and computed temperature distributions show agreement for a 1‐d simulation. To predict surface energy partitioning and soil temperature accurately for longer periods of time, the method must be expanded to account for water transport.

Transient boiling heat transfer from two different heat sources: Small diameter wire and thin film flat surface on a quartz substrate

Transient boiling heat transfer data are reported for two different heater surface geometries submerged in liquid nitrogen. During the early part of the transient heat pulse, the heat transfer coefficient for both geometries generally agrees with values predicted from classical transient pure conduction equations. The agreement persists until the time for onset of convection which varies approximately as 1 q 2 where q is the heat flux to the fluid.

Transient Conduction With Pyrolysis (Approximate Solutions for Charring of Wood Slabs)

The rate of charring of a heated one-dimensional, wood-like solid slab is predicted by solving the transient conduction equation with a phase-change energy sink term. This solution procedure uses an integral method with spatially-linear-temperature profiles. Two types of front-face boundary conditions are considered—prescribed temperature and prescribed heat flux. The backface is insulated. The prescribed temperature condition leads to the conclusion that for all reasonable exposure temperatures, the slab would only partially char. The maximum char depth is most sensitive to the char conductivity and exposure temperature and less sensitive to the char specific heat and charring endothermicity. Results of the constant flux are in reasonable agreement with the available experimental data both qualitatively and quantitatively.

The Thermal Response of a Human in the Near-Zone of a Resonant Thin-Wire Antenna

The thermal response of a human in the near-zone of an antenna was determined by numerical procedures. The approach taken was to modify the heat transfer equations for man in air to account for thermal loading due to the energy absorbed from the radiating antenna. The absorbed power density distribution in the human body was determined by considering the body and antenna to be a coupled system in which the resulting system of equations were solved by moment method procedures. This information was then analyzed by a thermal response model consisting of a series of transient conduction equations with internal heat generation due to metabolism, internal convective heat transfer due to blood flow, external interaction by convection and radiation, and cooling of the skin by sweating and evaporation. Internal heating patterns were calculated for two cases: a human in the near-zone of a quarter-wave monopole and a half-wave dipole operating at 45 and 200 MHz, respectively. It was found that negligible heating occurred for antennas with input power levels of less than 50 W.

A thermal model of the human body exposed to an electromagnetic field.

The human body was modeled by numerical procedures to determine the thermal response under varied electromagnetic (EM) exposures. The basic approach taken was to modify the heat transfer equations for man in air to account for thermal loading due to the energy absorbed from the EM field. The human body was represented in an EM model by a large number of small cubical cells of tissue, and the energy density was determined for each cell. This information was then analyzed by a thermal response model consisting of a series of two-dimensional transient conduction equations with internal heat generation due to metabolism, internal convective heat transfer due to blood flow, external interaction by convection and radiation, and cooling of the skin by sweating and evaporation. This model simulated the human body by a series of cylindrical segments. The local temperature of 61 discrete locations as well as the thermoregulatory responses of vasodilatation and sweating were computed for a number of EM field intensities and two frequencies, one near whole-body resonance.

A Digital Transfer Matrix for Fuel Pin Heat Transfer

A method for rapid numerical simulation of transient radial heat transfer in nuclear fuel pins is presented. The method is based on a z-transfer matrix formulation of the transient conduction equations and assumes constant physical properties. The elements of the z-transfer matrix are obtained from Laplace transfer functions that are polynomial approximations to the exact equations over a specifiable frequency band, weighted to a better fit in the least-squares sense for frequencies for which inputs are expected to have higher amplitudes than for frequencies for which amplitudes of inputs are expected to be lower. Examples that demonstrate the method suitable for a large number of the transients encountered in plant dynamic analysis are presented.

Solidification of a Sphere with Internal Heat Generation and Convective Cooling at the Surface

One-dimensional, nonhomogeneous transient conduction equations in both liquid and solid regions of a volumetrically heated sphere subjected to arbitrary time-independent convective cooling condition at the surface are numerically integrated. The results of numerical integration show that, depending on the relative magnitudes of the volumetric heat generation rate and the surface heat removal rate, the initially molten particle may completely solidify, temporarily solidify and then completely remelt, or have a solid outer crust with an inner molten core. The times needed to attain these quasi-stable states and the solidification and remelting rates prior to attaining these physical states are also computed.

Transient Response of Solid Sensible Heat Thermal Storage Units—Single Fluid

The transient response of a solid sensible heat storage unit which receives or supplies heat to a single flowing fluid is presented. The storage unit is composed of a number of rectangular cross-sectional channels for the flowing fluid, connected in parallel and separated by the heat storage material. The energy equation for the fluid and the transient conduction equation for the storage material are solved using finite difference techniques. The parameters which characterize the transient behavior of these units are identified. Results suitable for the prediction of the rate of heat storage and the outlet temperature of the fluid leaving the storage unit are presented as functions of the identified nondimensional parameters.

Combined Natural Convection, Conduction And Radiation Heat Transfer In A Cavity With Solar Control Coating Deposited To A Vertical Semitransparent Wall

This study presents a transient two-dimensional computational model of a combined natural convection, conduction, and radiation in a cavity with an aspect ratio of one containing air as a non participant fluid. The cavity has two opaque adiabatic horizontal walls, one opaque isothermal vertical wall The opposite vertical wall is a semitransparent wall that consists of a 6 mm glass sheet with a solar control coating of SnS-Cu*S facing the inside of the cavity permitting solar radiation exchanges between the cavity and its surroundings' The momentum and energy equations in transient state were solved by finite differences using the ADI technique. Coupled to this equations are the transient conduction equation and the radiative energy flux boundary conditions The results in this paper are limited to the range of 10*<Gr<10' with an isothermal vertical cold wall of 21°C, outside air temperatures (T.) of 35°C and incident solar radiation of AM2 (750 W/m') normal to the semitransparent wall A Nusselt number correlation as a function of the Rayleigh number is presented.

Hyperbolic Heat-Conduction Equation—A Solution for the Semi-Infinite Body Problem

This theoretical paper determines the effect of the propagation velocity of heat on the temperature and heat-flux distribution in a semi-infinite body due to a step change in temperature at the surface. The solution yields a maximum but finite heat flux under the conditions of a step change. This is contrary to the infinite value predicted by the error function solution to the Fourier transient conduction equation. In addition, assuming convection is conduction limited, an upper limit for convective heat transfer coefficients is postulated.

A model rate equation for transient thermal conduction

A model rate equation for transient thermal conduction