Simultaneous transient conduction and radiation heat transfer with heat generation is investigated. Analysis is carried out for both steady and unsteady situations. two-dimensional gray cylindrical enclosure with an absorbing, emitting, and isotropically scattering medium is considered. Enclosure boundaries are assumed at specified temperatures. The heat generation rate is considered uniform an...

The lattice Boltzmann method (LBM) was used to analyze two-dimensional (2D) non-Fourier heat conduction with temperature-dependent thermal conductivity. To this end, the evolution of wave-like temperature distributions in a 2D plate was obtained. The temperature distributions along certain parts of the plate, which was subjected to heat generation and constant thermal conductivity condit...

In this paper the description of the simplest variant of conservative averaging method for partial differential (or integro-differential) equations in cylinder type domain is given. Different types of boundary conditions (both linear and non-linear) are considered. As application of the method the process of intensive steel quenching as the time inverse ill-posed problem for the hyperbolic heat...

The numerical methods of the structural design optimization with transient response constraints have been studied in the paper. The new methods of the response analysis and sensitivity analysis for the transient dynamics and the heat conduction constraints with the precise time integration have been proposed. Particularly, an efficient method of sensitivity analysis for nonlinear transient heat...

Rapid transient heat conduction in multilayer materials under pulsed heating is solved numerically based on a hyperbolic heat conduction equation and taking into consideration the non-Fourier heat conduction effects. An implicit difference scheme is presented and a stability analysis conducted, which shows that the implicit scheme for the hyperbolic equation is stable. The code is validated by ...

we develop and apply the product integration method to a large class of linear weakly singular volterra systems. we show that under certain sufficient conditions this method converges. numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

The transient hot-wire method has been widely used to measure the thermal conductivity of fluids. The ideal working equation is based on the solution of the transient heat conduction equation for an infinite linear heat source assuming no natural convection or thermal end effects. In practice, the assumptions inherent in the model are only valid for a portion of the measurement time. In this st...

The one-dimensional, cylindrical coordinate, non-linear partial differential equation of transient heat conduction through a hollow thermal insulation material conductivity temperature dependent property proposed by an available empirical function is solved analytically using Kirchhoff’s transformation. It assumed that this insulating initially at uniform temperature. Then, it suddenly subjecte...