Boundary-value Heat Conduction Research Articles

Influence of convective cooling on the temperature in a frictionally heated strip and foundation

The analytical solution of a boundary-value heat conduction problem of friction for the tribosystem consisting of a semi-infinite foundation and a plane-parallel strip sliding over its surface is obtained. The evolution of temperature and its distribution in depth from a contact surface for materials of frictional couple, such as aluminum-steel, is studied.

Laser pulse transient method for measuring the normal spectral emissivity of samples with arbitrary surface quality

A laser pulse transient method for measuring normal spectral emissivity is described. In this method, a laser pulse (λ=1064 nm) irradiates the top surface of a flat specimen. A two-dimensional temperature response of the bottom surface is measured with a calibrated thermographic camera. By solving an axisymmetric boundary value heat conduction problem, the normal spectral emissivity at 1064 nm is determined by using an iterative nonlinear least-squares estimation procedure. The method can be applied to arbitrary sample surface quality. The method is tested on a nickel specimen and used to determine the normal spectral emissivity of AISI 304 stainless steel. The expanded combined uncertainty of the method has been estimated to be 18%.

One analytic approach to the solution of one-dimensional heat conduction problem with free boundaries

In recent years the boundary-value heat conduction problems in domains with free boundaries become important both in theoretical and applied branches of physics and mathematics. Over the last years the number of papers dedicated to the solution of similar problems essentially increased [1–9]. The analytic approach to the solution of boundary-value heat transfer problems in systems with free boundaries is one of the most difficult problems in the modern mathematical physics. Since the position of the characteristic part of the domain depends on time, the classical methods for partial differential equations are inapplicable to this class of problems. The reason is that these methods do not allow one to correlate the solution of the heat conduction equation with the motion of the phase transfer boundary.

Mathematical modeling of nonlinear processes of heating (counterflow and direct-flow heat exchange) in metallurgy and machine construction

Solutions of the problems of counterflow and direct-flow heating of metal constructed on the solutions (obtained by the authors) of the corresponding nonlinear boundary-value heat-conduction problems are presented. An example illustrating the acceptable accuracy of the procedure proposed is given.

Experimental Investigations of Heat Transfer in a Subcooled Twisted Flow

Methods for conducting experimental investigations of heat transfer to a subcooled twisted flow of water under the conditions of one-sided heating of the working section by a scanning electron beam. The methods allow using measured typical temperatures of the working section to determine temperature and density of the heat flux at the top point of the inner perimeter of the working section, without applying numerical solution of the boundary-value heat-conduction problem.

Modeling of Thermal Processes in Thermal Resistors with a Positive Temperature Coefficient of Resistance

The space-time temperature distribution in materials with a positive temperature coefficient of resistance under the action of electric current on them has been analyzed by numerical methods. The nonstationary boundary-value heat-conduction problem with a nonlinearity of the third kind has been solved. The results obtained theoretically have been compared to experimental data.

The effect of the reinforcement structure on the heat conductivity of shells of revolution with a system of tubes filled with a liquid heat-transfer agent

The initial boundary-value heat-conduction problem for shells reinforced by tubes filled with a flowing liquid heat-transfer agent is considered. The dependence of the coefficients in the heat-conduction equations on the thermophysical characteristics of the composition phases, reinforcement parameters, and shell geometry is studied. A comparative analysis of the stationary temperature fields in thin shells of revolution of different Gaussian curvature is performed for various reinforcement structures and heat-exchange regimes. It is shown that the temperature distribution in the shells depends strongly on the reinforcement structure and the shell geometry, which opens up new possibilities of designing optimal structures.

Calculation error of numerical solution for a boundary-value inverse heat conduction problem

A one-dimensional linear inverse heat conduction problem is studied in this paper. This ill-posed problem is replaced by the perturbed problem with a non-localized boundary condition. After the derivation of its closed-form analytical solution, the calculation error can be determined by the comparison between the numerical and exact solutions.

Temperature field in a heat-sensitive multilayer half-space

A method is proposed for solving a nonlinear axisymmetrical boundary-value heat-conduction problem for a multilayered half-space with heat transfer, heated by internal heat sources.

Maximum depth of keyhole melting of metals by a laser beam

A calculation is reported of the maximum depth and diameter of a narrow crater formed in a stationary metal target exposed to high-power cw CO2 laser radiation. The energy needed for erosion of a unit volume is assumed to be constant and the energy losses experienced by the beam in the vapor–gas channel are ignored. The heat losses in the metal are allowed for by an analytic solution of the three-dimensional boundary-value heat-conduction problem of the temperature field in the vicinity of a thin but long crater with a constant temperature on its surface. An approximate solution of this problem by a method proposed earlier by one of the present authors was tested on a computer. The dimensions of the thin crater were found to be very different from those obtained earlier subject to a less rigorous allowance for the heat losses.

Prediction of the stability of pool boiling heat transfer to finite disturbances

A theoretical study has been made of the pool boiling heat-transfer stability on a non-isothermal surface of the rod. The mathematical formulation of the problem is based on the thermal approach, which has allowed the stability study to be performed on the solution of the boundary-value heat-conduction problem for a rod with the boundary conditions of the first and the second kind. The stability to the finite temperature deviations has been analyzed. With the help of a variational principle a measure of stability is found which is a specially built functional. The suggested method is illustrated by calculation of the safe temperature distrubance.