Energy Conservation Equations in Polar Cylindrical and Spherical Coordinates for Incompressible Fluids With Constant Thermal Conductivity

2012 ◽  
pp. 453-453
Author(s):  
Mostafa Ghiaasiaan
2021 ◽  
Vol 321 ◽  
pp. 04004
Author(s):  
Santosh Kumar Rai ◽  
Neha Ahlawat ◽  
Pardeep Kumar ◽  
Vinay Panwar

In present paper, a mathematical model based on the one dimensional nonlinear mass, momentum and energy conservation equations has been developed to study the density wave instability (DWI) in horizontal heater and horizontal cooler supercritical water natural circulation loop (HHHC-SCWNCL). The one dimensional nonlinear mass, momentum and energy conservation equations are discretized by using finite difference method (FDM). The numerical model is validated with the benchmark results (NOLSTA model). Numerical simulations are performed to find the threshold stability zone (TSZ) and draw the stability map for natural circulation loop. Further, effect of change in diameter and riser height on the density wave instability of SCWNCL has been investigated.


2019 ◽  
Vol 91 ◽  
pp. 02032 ◽  
Author(s):  
Aleksey Zhukov ◽  
Timofey Dovydenko ◽  
Sergey Kozlov ◽  
Karapet Ter-Zakaryan ◽  
Ekaterina Bobrova

The article presents the results of the implementation of promising areas of construction and construction of low-rise buildings. The problems of improving the environmental safety and financial stability of agricultural construction through the implementation of effective systems that provide energy conservation, the creation of comfortable conditions in the rooms are considered. It is noted that a factor that has been given special attention in recent years is the environmental safety of the materials used and the reduction of the negative load on the environment of systems using these materials. The article provides the rationale that the heat-efficient system should not only be based on the use of materials with low thermal conductivity, but should also suggest a reasonable minimization of the joints between the products included in the insulation sheath and between products and structures. In constructions with the use of polyethylene foam, seamless insulating sheath is formed, which has high thermal resistance. The low vapor and wind permeability and moisture conductivity of polyethylene foam makes it possible to dispense with the construction without additional vapor barrier and wind protection, which improves the performance of the casing and its durability due to the reduction in the complexity of manufacturing wall structures.


Author(s):  
Ruixian Cai ◽  
Na Zhang

The analytical solutions of unsteady heat conduction with variable thermal properties (thermal conductivity, density and specific heat are functions of temperature or coordinates) are meaningful in theory. In addition, they are very useful to the computational heat conduction to check the numerical solutions and to develop numerical schemes, grid generation methods and so forth. Such solutions in rectangular coordinates have been derived by the authors; some other solutions for unsteady point symmetrical heat conduction in spherical coordinates are given in this paper to promote the heat conduction theory and to develop the relative computational heat conduction.


2014 ◽  
Vol 13 (2) ◽  
pp. 48
Author(s):  
R. M. S. Gama

This work discuss the usual constant conductivity assumption and its consequences when a given material presents a strong dependence between the temperature and the thermal conductivity. The discussion is carried out considering a sphere of silicon with a given heat generation concentrated in a vicinity of its centre, giving rise to high temperature gradients. This particular case is enough to show that the constant thermal conductivity hypothesis may give rise to very large errors and must be avoided. In order to surpass the mathematical complexity, the Kirchhoff transformation is used for constructing the solution of the problem. In addition, an equation correlating thermal conductivity and the temperature is proposed.


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