Heat conduction in a series of inhomogeneous slabs

A general theory is worked out for boundary-value problems of steady-state, two-dimensional heat conduction in a series of inhomogeneous media. Specific examples are discussed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vo. 28, No. 6, pp. 1088–1093, June, 1975.     

Heat conduction of orthotropic half-space for mixed discontinuous boundary conditions

The nonstationary temperature field in a half-space heated across a circular region with a known radius r=R over a surface z=0 of a semibounded body is found Outside the circular region r>R the initial temperature ϕ(r, 0, τ)=T(r, 0, τ)−T₀=0 is maintained on the surface z=0. Particular regularities of development of nonstationary temperature fileds along the axisr=0, z≥0 and over the surface z=0, 0≤r<R are given. Belarusian State University, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 69, No. 5, pp. 826–833, September–October, 1996.     

Error in the numerical solution to the heat conduction problem with a nonlinear boundary condition

Concerning the heat conduction problem with a nonlinear boundary condition, as in the case of a boiling process, the effect of the time interval in the numerical solution scheme on the error of the solution is analyzed here.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.22, No. 5, pp. 894–898, May, 1972.     

Numerical solution of nonlinear inverse heat conduction problem with a radiation boundary condition

A finite difference solution for the transient nonlinear heat conduction equation in a finite slab with a radiation boundary condition is proposed. An implicit finite difference approximation is used which enables accurate estimation of the surface temperature as well as prevention of oscillation of computed values at the surfaces. A two-time level implicit method is used, while Taylor's forward projection method is employed for taking account of the nonlinearities. An iterative method is described which predicts unknown surface conditions. An example is illustrated which is typical of those that arise in practical applications. The results demonstrate that the method is remarkable in its stability to predict surface conditions without debilitation.     

Reflection of plane waves at the boundary of a pre-stressed elastic half-space subject to biaxial stretch and simple shear

This paper is concerned with the effect of finite pure homogeneous biaxial stretch together with simple shear deformation on the reflection from a plane boundary of elastic waves propagating in a half-space of incompressible isotropic elastic material. This generalizes the previous work in which, separately, pure homogeneous strain and simple shear were considered. For a special class of constitutive law, it is shown that an incident plane harmonic wave propagating in the considered plane gives rise to a surface wave in addition to a reflected wave for every angle of incidence. The amplitude of the surface wave may vanish at certain discrete angles depending on the state of stress, biaxial stretch and simple shear deformation and then specialized to recover results obtained previously. The amplitude of the reflected wave is independent of the pre-stress but does depend upon the magnitude of deformation under consideration. The dependence of the reflected and surface wave behavior on the angle of incidence, amount of shear strain, biaxial stretch and the state of stress is illustrated graphically.     

Some heat conduction problems in an inhomogeneous body

Solutions are obtained for the heat conduction equation in the case when the thermal conductivity is a homogeneous function of the coordinates.     

Thermal stresses in an intersecting-shell subject to nonlinear strain

Thermal stresses are considered in a system of intersecting cylindrical shells in which there is geometrical nonlinearity. The normal displacements are close to the thickness but are small by comparison with the other linear dimensions. The problem is solved by successive approximation by the use of finite differences. The effects of the geometrical nonlinearity are examined along with those of the average temperature and the temperature difference across the thickness in relation to the state of strain.Translated from Problemy Prochnosti, No. 4, pp. 73–83, April, 1996.     

A boundary integral equation method for the two-dimensional diffusion equation subject to a non-local condition

A boundary integral equation method is proposed for the numerical solution of the two-dimensional diffusion equation subject to a non-local condition. The non-local condition is in the form of a double integral giving the specification of mass in a region which is a subset of the solution domain. A specific test problem is solved using the method.     

Flow and conduction of inhomogeneous media. II. Variation of the basic model of an inhomogeneous medium

On the basis of a basic model of an inhomogeneous medium, different variations are proposed. Analytical dependences are obtained for the conduction of the in homogeneous medium and the results of calculation and experiment are compared.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 46, No. 2, pp. 247–252, February, 1982.     

An implicit-iterative solution of the heat conduction equation with a radiation boundary condition

In predicting temperatures with an implicit finite difference method there is a tendency for the surface temperature to oscillate if a non-linear radiation boundary condition is imposed. An iterative method is described which eliminates these oscillations in temperature prediction. Several examples are given that allow a comparison with other implicit methods. These examples are for cases which are typical of those that arise in practical applications. The results demonstrate that the method is remarkable in its ability to predict surface conditions without the debilitation of other methods in regard to step size control, along with the ease of incorporating it into the solution routine.     

Thermal boundary layer on a plate in a non-Newtonian fluid with nonlinear heat conduction law

The flat-plate boundary layer equation for a rheological power law and a proposed nonlinear law of heat conduction is reduced to an ordinary differential equation, which is solved in quadratures using previously calculated [2] velocity profiles. Graphs of the temperature and heat transfer coefficient profiles are presented.     

Application of the boundary element method to transient heat conduction

An advanced boundary element method (BEM) is presented for the transient heat conduction analysis of engineering components. The numerical implementation necessarily includes higher-order conforming elements, self-adaptive integration and a multiregion capability. Planar, three-dimensional and axisymmetric analyses are all addressed with a consistent time-domain convolution approach, which completely eliminates the need for volume discretization for most practical analyses. The resulting general purpose algorithm establishes BEM as an attractive alternative to the more familiar finite difference and finite element methods for this class of problems. Several detailed numerical examples are included to emphasize the accuracy, stability and generality of the present BEM., Furthermore, a new efficient treatment is introduced for bodies with embedded holes. This development provides a powerful analytical tool for transient solutions of components, such as casting moulds and turbine blades, which are cumbersome to model when employing the conventional domain-based methods.     

Accurate H-shaped absorbing boundary condition in frequency domain for scalar wave propagation in layered half-space

An accurate absorbing boundary condition (ABC) is developed in frequency domain for finite element analysis of scalar wave propagation in unbounded layered half-space. The proposed ABC is H-shaped line that consists of two parts: a new ABC at horizontal bottom boundary of finite domain to replace semiinfinite strip below horizontal boundary and between two vertical boundaries, and a general consistent ABC at vertical lateral boundary to replace semiinfinite layered half-space outside vertical boundary. The key point for constructing the ABC is that a new continued fraction (CF) is presented to expand dynamic stiffness of underlying half-space, and the CF-based stress-displacement relationship is then transformed into an auxiliary variable system with square of horizontal wavenumber. The ABC has only one undetermined real parameter that is the CF-order independent of frequency and incidence angle of propagating outgoing waves. The parameter can be chosen relatively small value to achieve an accurate ABC. Moreover, the ABC can couple seamlessly with finite element method of finite domain. The finite domain can be chosen very small size due to high accuracy of the ABC. Numerical examples are finally given to demonstrate the effectiveness of the ABC.     

Disturbance of SH-type waves due to moving stress discontinuity in an anisotropic soil layer overlying an inhomogeneous elastic half-space

The disturbance and propagation of SH-type waves in an anisotropic soil layer overlying an inhomogeneous elastic half-space by a moving stress discontinuity is considered. Stress discontinuity moves with non-uniform velocity and is impulsive in nature. The displacements are obtained in exact form by the method due to Cagniard modified by de Hoop. The numerical result is calculated for special cases and the natures are depicted graphically.     

Heat conduction and mass transfer in a MHD nanofluid flow subject to generalized Fourier and Fick’s law

Abstract

Heat and mass transmission in Casson nanofluid flow induced by a linearly placed stretching sheet due to Cattaneo-Christov double diffusion convection with the company of thermal radiation scrutinized here. Multiple slip boundary conditions have been accounted here. Leading equations of the course have been normalized via similarity approach and unraveled resulting equations numerically by using RK-4 shooting procedure. Here dual characteristic of velocity field has been perceived for the parameters, velocity slip and Casson fluid. After numerical designs, influence of emergent flow parameters on flow specific are made appropriately via graphs and charts and explained the consequences with proper reasoning.     

A boundary element method for the solution of a class of heat conduction problems for inhomogeneous media

A boundary element method is derived for solving the two-dimensional heat equation for an inhomogeneous body subject to suitably prescribed temperature and/or heat flux on the boundary of the solution domain. Numerical results for a specific test problem is given.     

Solution of a nonlinear heat conduction problem with boundary conditions of the fourth kind

We present a method for electrically modelling nonlinear contact heat-transfer problems both with and without taking into account the thermal conductivity of the contact layer.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 18, No. 2, pp. 328–332, February, 1970.     

A dual-reciprocity boundary element approach for axisymmetric nonlinear time-dependent heat conduction in a nonhomogeneous solid

A dual-reciprocity boundary element method is presented for the numerical solution of a nonsteady axisymmetric heat conduction problem involving a nonhomogeneous solid with temperature dependent properties. It is applied to solve some specific problems including one which involves the laser heating of a cylindrical solid.     

Dynamic-stiffness matrix for SH-waves in a layered depth dependent randomly inhomogeneous half-space

Summary This paper is concerned with the derivation of the dynamic-stiffness matrix for a multilayered viscoelastic half-space, with material parameters which are depth dependent random functions. The mean displacements and stresses are obtained for the out-of-plane motion resulting from inclined SH-waves. An explicit solution for the case of exponential correlation function is obtained.