Symmetry of heat and mass transfer equations in case of dependence of thermal diffusivity coefficient either on temperature or concentration

The point of this short paper is to provide a useful set of equations governing stratified convection, expressed solely in terms of two thermodynamic variables, i.e. the pressure and the entropy, and the velocity field of the flow, free from any additional assumptions about the properties of turbulence. The pressure fluctuation is entirely eliminated from the energy equation and it appears only in the momentum balance, easily removable by taking its curl. This goal is achieved through the well-known anelastic approximation and an assumption of constant thermal diffusivity coefficient. The rigorously derived system of anelastic liquid equations constitutes a useful tool for modelling the dynamics of stellar interiors.

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An Efficient Acceleration of Solving Heat and Mass Transfer Equations with the Second Kind Boundary Conditions in Capillary Porous Radially Composite Cylinder Using Programmable Graphics Hardware

Computer and Information Science ◽

10.5539/cis.v13n2p75 ◽

2020 ◽

Vol 13 (2) ◽

pp. 75

Author(s):

Hira Narang ◽

Fan Wu ◽

Abdul Rafae Mohammed

Keyword(s):

Mass Transfer ◽

Boundary Conditions ◽

Heat And Mass Transfer ◽

Numerical Solutions ◽

Programming Model ◽

Graphics Hardware ◽

Processing Unit ◽

Composite Cylinder ◽

Acceleration Techniques ◽

Transfer Equations

With the recent developments in computing technology, increased efforts have gone into the simulation of various scientific methods and phenomenon in engineering fields. One such case is the simulation of heat and mass transfer equations which is becoming more and more important in analyzing various scenarios in engineering applications. Analysing the heat and mass transfer phenomenon under various environmental conditions require us to simulate it. However, this process of numerical solution of heat and mass transfer equations is very time consuming. Therefore, this paper aims at utilizing one of the acceleration techniques developed in the graphics community that exploits a graphics processing unit (GPU) which is applied to the numerical solutions of heat and mass transfer equations. The nVidia Compute Unified Device Architecture (CUDA) programming model can be a good method of applying parallel computing to program the graphical processing unit. This paper shows a good improvement in the performance, while solving the heat and mass transfer equations for a capillary porous radially composite cylinder with the second kind of boundary conditions, numerically running on GPU. This heat and mass transfer simulation is implemented using CUDA platform on nVidia Quadro FX 4800 graphics card. Our experimental results depict the drastic performance improvement when GPU is used to perform heat and mass transfer simulation. GPU can significantly accelerate the performance with a maximum observed speedup of more than 8 fold times. Therefore, the GPU is a good approach to accelerate the heat and mass transfer simulation.

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