Analytical solution of two-dimensional contact problems of unsteady heat conduction in the presence of mixed boundary conditions in the contact plane

A method for solution of systems of parabolic differential equations of heat conduction on the model of thermal contact between two bodies with different thermophysical characteristics in the presence of mixed boundary conditions in the plane of their contact has been suggested for the first time. The case of contact of two semibounded bodies has been considered. In this case, a heat source of low heat capacity acts in a circular region of finite radius on the contact surface, and beyond this region the initial temperature is maintained during the whole period of heat transfer

Solution of a heat equation of hyperbolic type with mixed boundary conditions on the surface of an isotropic half-space

Translated from Differentsial'nye Uravneniya. - 2002. - Vol. 38, № 7. - P. 989–991

Solution of a heat-conduction problem for a finite cylinder and semispace under mixed local boundary conditions in the plane of their contact

With the use of the method of summator–integral equations, an axisymmetric problem has been investigated that deals with the development of spatial temperature fields appearing in a finite cylinder with an arbitrary distribution of initial temperature when the cylinder comes in contact with a semiinfinite body that has a constant initial temperature. The essential feature of the considered thermophysical model of heat exchange is that mixed boundary conditions of the second and fourth kind are assigned in the plane of contact of the finite body with the semispace. The thermophysical properties of the bodies considered are different

Method of summation-integral equations for solving the mixed problem of nonstationary heat conduction

The solution of a mixed axisymmetric nonstationary problem of heat conduction is obtained in the region of Laplace transforms. In solution of this problem, there occur summation−integral equations with the parameter of the integral Laplace transform (L-parameter) and the additional parameter of the finite integral Hankel transform (H-parameter). The laws governing the development of spatial nonstationary temperature fields in a bounded cylinder and a half-space when one end surface of the cylinder is in contact with the surface of the half-space in a circular region are determined

Nonstationary temperature fields in an isotropic half-space under mixed boundary conditions characteristic of technologies of laser therapy in medicine

For the first time, the solution of the heat-conduction equation with mixed boundalw, conditions (BCs) is obtained as applied to the model of an isotropic nontransparent half-space, whose surface z = 0 is heated through the circular region of radius r = R with a heat-flux densi~, characteristic of a laser heat source, while outside of the circle of r > R and z = 0 there occurs intense cooling at the value of the heat-transfer coefficient o~ = oo

Solution of mixed contact problems in the theory nonstationary heat conduction by the metod of summation-integral equations

The laws governing the development of spatial nonstationary temperature fields in a bounded cylinder and a half-space where one of the end surfaces of the cylinder touches the surface of the half-space in a circular region are determined. A solution of a mixed axisymmetric nonstationary problem of heat conduction is obtained in the region of Laplace transforms. In solution of this problem, there appear summation-integral equations with the parameter of the integral Laplace transform (L-parameter) and the parameter of the finite integral Hankel transform (H-parameter)

Solution of nonlinear two-dimensional differential equations of transfer with discontinuity boundary conditions on the surface of an isotropic semiinfinite body in its heating through a circle of known radius

An analytical solution of the heat-conduction problem is obtained by the method of linearization of a nonlinear equation of transfer and combined application of integral transforms to the linearized problem for an isotropic half-space heated through a circular region 0 < r < R on its surface z = 0