The exercises explored through the text are specifically aimed at improving the ability to analyze and interpret the data and the final computed results. The book is divided into nine chapters that follow the entire paraphernalia surrounding the processes and the features of heat transfer and fluid flow with a mathematical focus in mind. The first chapter is the Introduction and from then on the book moves on to a Mathematical Description of Physical Phenomena.
In the next chapter, the author develops discretization methods and then explores Heat Conduction. The fifth chapter then looks at the processes of Convection and Diffusion. He then moves on to Calculating Flow Field and all of this converges to the seventh chapter titled Finishing Touches. Hereafter, Patankar explores the special topics that involve Numerical Heat Transfer And Fluid Flow and then finally closes the discussion of content intimate to the matter by allowing for a complete chapter on Illustrative Applications.
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Merlis Baby. Show More. Views Total views. Actions Shares. No notes for slide. Numerical methods for 2 d heat transfer 1. Types of Numerical Methods 1. The Finite Difference Method FDM — subdomains are rectangular and nodes form a regular grid network — nodal values of temperature constitute the numerical solution; no interpolation functions are included — discretization equations can be derived from Taylor series expansions or from a control volume approach 6.
The Finite Element Method FEM — subdomain may be any polygon shape, even with curved sides; nodes can be placed anywhere in subdomain — numerical solution is written as a finite series sum of interpolation functions, which may be linear, quadratic, cubic, etc. The Nodal Networks The basic idea is to subdivide the area of interest into sub-volumes with the distance between adjacent nodes by Dx and Dy as shown. If the distance between points is small enough, the differential equation can be approximated locally by a set of finite difference equations.
Each node now represents a small region where the nodal temperature is a measure of the average temperature of the region. Finite Difference Approximation cont. For each node, there is one such equation. Jump to Page. Search inside document. Brent Cullen. Ahmed Fgt Kaasehg. Hafidzul A'lim. Anonymous pSozzNFc. Nick Papavizas. Satyajit Samal. Sebastian Torres Montoya. Omar Najm. Dejan Kolarec. Mohammed Al-samarrae.
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Download Download PDF. Translate PDF. The geometry must be such that its entire surface can be described mathematically in a coordinate system by setting the variables equal to constants.
Also, heat transfer problems can not be solved analytically if the thermal conditions are not sufficiently simple. For example, the consideration of the variation of thermal conductivity with temperature, the variation of the heat transfer coefficient over the surface, or the radiation heat transfer on the surfaces can make it impossible to obtain an analytical solution.
Therefore, analytical solutions are limited to problems that are simple or can be simplified with reasonable approximations. The numerical solution methods are based on replacing the differential equations by algebraic equations.
In the case of the popular finite difference method, this is done by replacing the derivatives by differences. The analytical methods are simple and they provide solution functions applicable to the entire medium, but they are limited to simple problems in simple geometries. The numerical methods are usually more involved and the solutions are obtained at a number of points, but they are applicable to any geometry subjected to any kind of thermal conditions.
The formal finite difference method is based on replacing derivatives by their finite difference approximations. For a specified nodal network, these two methods will result in the same set of equations. Besides, once a person is used to solving problems numerically, it is very difficult to go back to solving differential equations by hand.
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