Effect of Nature Convection on Heat Transfer in the Liquid LiPb Blanket

2008 ◽  
Author(s):  
Hongyan Wang ◽  
Xidong Zhang
Keyword(s):  
Heat Transfer ◽  
Cross Flow ◽  
Internal Heat ◽  
Mhd Flow ◽  
Outlet Temperature ◽  
Heat Sources ◽  
Material Technology ◽  
Volumetric Heating ◽  
Flow And Heat Transfer ◽  
Internal Heat Sources

In some liquid blankets (or liquid blanket module) of fusion reactor, the liquid metal, i.e. LiPb flow, as only tritium breeder is characterized by lower outlet temperature and slower flow velocity that allows the utilization of relatively mature material technology [1–2]. The magnetohydrodynamic (MHD) flow and heat transfer become very complex resulting from the differential heating of walls of the channels, especially adjacent to the First Wall (FW), and internal heat sources inside of the liquid LiPb. The nature convection of the liquid LiPb, due to thermal diffusion, in the poloidal channel adjacent to the FW in the presence of the strong magnetic field of the blanket has been considered and studied. The temperature distribution is changed and there is a strong thermal coupling, modifying importantly the magnitude of the flow. The effect of the buoyancy on pressure driven duct flows has been investigated. The buoyant convection was found to be sufficiently strong to impose its flow pattern on the cross flow in the region of intense volumetric heating.

scholarly journals CONCEPTION QUASIDERIVATIVES IN THE PROBLEMS OF MATHEMATICAL MODELING OF HEAT TRANSFER

2020 ◽  
Vol 21 ◽  
pp. 79-85
Author(s):  
R. Tatsii ◽  
M. Stasiyk ◽  
O. Pazen ◽  
L. Shypot
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Closed Form ◽  
Critical Radius ◽  
Internal Heat ◽  
Heat Sources ◽  
Internal Heat Sources

In this paper, in closed form, the problems of determining stationary temperature fields in multilayer (flat, cylindrical and spherical) structures in the presence of discrete-continuous internal and point heat sources are solved. The one-dimensional differential equation of thermal conductivity in different coordinate systems is given through one parametric family of quasi-differential equations. It is assumed that the coefficients of the differential equation of thermal conductivity are piecewise constant functions. A system of two linearly independent boundary conditions is added to the equation, which in the general case are nonlocal. The solutions of such problems are constructive and are expressed exclusively through their initial data. The basic provisions of the concept of quasi-derivatives, the provisions of the theory of heat transfer, the theory of generalized systems of linear differential equations, elements of the theory of generalized functions are used. For the mathematical model of stationary thermal conductivity, the practical use of the concept of quasi-derivatives is illustrated, for the efficient construction, in a closed form, of solutions of boundary value problems with the most general boundary conditions. As an example, the problem of finding the critical radii of thermal insulation of multilayer hollow cylinders and spheres, taking into account the internal heat sources in the layers. Boundary conditions of the first and third kind. It is established that the value of the critical radius does not depend on the number of layers and the intensity of internal heat sources, but only on the thermal conductivity of the outer layer of the structure and the heat transfer coefficient between the structure and the environment. The formula for determining the critical radius of thermal insulation for a multilayer cylindrical and spherical structure is derived. The methods developed in this work have the prospect of further development and can be used in engineering calculations.

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