Mathematical formulation and numerical solution

Aniruddha Bagchi; Francis A. Kulacki

doi:10.1007/978-1-4614-6576-8_3

Mathematical formulation and numerical solution

Aniruddha Bagchi, Francis A. Kulacki

Mechanical Engineering

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Abstract

In this chapter, the mathematical formulation of the convective heat transfer problem is presented. The governing equations for natural convection in two-dimensional fluid and saturated porous layers are described first. Thereafter the boundary conditions for the problem are elucidated. In particular, boundary conditions at the interface of the fluid and porous layers are discussed in detail. The one-domain formulation is then derived, and the governing equations are presented in dimensionless form using the vorticity-stream function formulation.

Original language	English (US)
Title of host publication	SpringerBriefs in Applied Sciences and Technology
Publisher	Springer Verlag
Pages	15-26
Number of pages	12
Edition	9781461465751
DOIs	https://doi.org/10.1007/978-1-4614-6576-8_3
State	Published - 2014

Publication series

Name	SpringerBriefs in Applied Sciences and Technology
Number	9781461465751
ISSN (Print)	2191-530X
ISSN (Electronic)	2191-5318

Bibliographical note

Publisher Copyright:
© The Author(s) 2014.

Keywords

Finite-volume method
Interfacial conditions
Numerical solution
One-domain formulation
Two-domain formulation
Volume averaging

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10.1007/978-1-4614-6576-8_3

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AB - In this chapter, the mathematical formulation of the convective heat transfer problem is presented. The governing equations for natural convection in two-dimensional fluid and saturated porous layers are described first. Thereafter the boundary conditions for the problem are elucidated. In particular, boundary conditions at the interface of the fluid and porous layers are discussed in detail. The one-domain formulation is then derived, and the governing equations are presented in dimensionless form using the vorticity-stream function formulation.

KW - Finite-volume method

KW - Interfacial conditions

KW - Numerical solution

KW - One-domain formulation

KW - Two-domain formulation

KW - Volume averaging

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Mathematical formulation and numerical solution

Abstract

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Keywords

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