AN INTERVAL FINITE DIFFERENCE METHOD FOR THE BIOHEAT TRANSFER PROBLEM DESCRIBED BY THE PENNES EQUATION WITH UNCERTAIN PARAMETERS

A three-dimensional (3D) simulation of bioheat transfer is crucial to analyze the physiological processes and evaluate many therapeutic/diagnostic practices spanning from high to low temperature medicine. In this paper we develop an efficient numerical scheme for solving 3D transient bioheat transfer equations based on the alternating direction implicit finite-difference method (ADI-FDM). An algorithm is proposed to deal with the boundary condition for irregular domain which could capture accurately the complex boundary and reduce considerably the staircase effects. Furthermore, the local adaptive mesh technology is introduced to improve the computational accuracy for irregular boundary and the domains with large temperature gradient. The detailed modification to ADI-FDM is given to accommodate such special grid structure, in particular. Combination of adaptive-mesh technology and ADI-FDM could significantly improve the computational accuracy and decrease the computational cost. Extensive results of numerical experiments demonstrate that the algorithm developed in the current work is very effective to predict the temperature distribution during hyperthermia and cryosurgery. This work may play an important role in developing a computational planning tool for hyperthermia and cryosurgery in the near future.

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Numerical Simulation by FDM of Unsteady Heat Transfer in Cylindrical Coordinates

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.851.322 ◽

2016 ◽

Vol 851 ◽

pp. 322-325

Author(s):

Cláudia Narumi Takayama Mori ◽

Estaner Claro Romão

Keyword(s):

Heat Transfer ◽

Numerical Simulation ◽

Finite Difference ◽

Finite Difference Method ◽

Exact Solutions ◽

Difference Method ◽

Transfer Problem ◽

Cylindrical Coordinates ◽

Unsteady Heat Transfer ◽

The Finite Difference Method

In this paper the heat transfer problem in transient and cylindrical coordinates will be solved by the Crank-Nicolson method in conjunction the Finite Difference Method. To validate the formulation will study the numerical efficiency by comparisons of numerical results compared with two exact solutions.

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Comparative Study of 1-Dimensional Heat Transfer Problem by Finite Difference Method and Finite Element Method

International Journal for Research in Applied Science and Engineering Technology ◽

10.22214/ijraset.2019.4546 ◽

2019 ◽

Vol 7 (4) ◽

pp. 3256-3263

Author(s):

Mr. Vasimakram Khatib

Keyword(s):

Heat Transfer ◽

Finite Element Method ◽

Finite Element ◽

Finite Difference ◽

Finite Difference Method ◽

Comparative Study ◽

Difference Method ◽

Transfer Problem ◽

Heat Transfer Problem ◽

Element Method

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Modelling of a desiccant rotor by using the collocation method

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-02-2012-0035 ◽

2013 ◽

Vol 24 (1) ◽

pp. 201-220 ◽

Cited By ~ 1

Author(s):

Marcello Aprile ◽

Mario Motta

Keyword(s):

Mass Transfer ◽

Finite Difference ◽

Finite Difference Method ◽

Heat And Mass Transfer ◽

Collocation Method ◽

Difference Method ◽

Transfer Problem ◽

Operating Conditions ◽

Content Type ◽

The Finite Difference Method

Purpose – This article aims to develop a fast numerical method for solving the one-dimensional heat and mass transfer problem within a desiccant rotor. Design/methodology/approach – The collocation method is used for discretizing the axial dimension and reducing the number of dependent variables. The resulting system of equation is then solved through backward differentiation formulas. Findings – The numerical results obtained here focus on verifying the accuracy and the computation time of the proposed method with respect to the finite difference method. The proposed numerical solution method resulted faster than, and as much accurate as, the finite difference method, over a large range of operating conditions that are of interest in desiccant cooling applications. Research limitations/implications – For heat and mass transfer analysis, constant average transfer coefficients are used. The results are calculated for NTU between 2 and 15 and for Le number between 0.5 and 2. Practical implications – The results can be used in designing desiccant heat exchangers and desiccant cooling systems including complex rotor arrangements. Originality/value – Different from other simplified solution techniques, the proposed method relies on few parameters that retain physical meaning and applies also to complex rotor configurations.

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