Library Subscription: Guest
ICHMT DL Home Current Year Archives Executive Committee International Centre for Heat and Mass Transfer

COMPUTATIONAL HEAT TRANSFER WITH MATHEMATICA

DOI: 10.1615/ICHMT.1997.IntSymLiqTwoPhaseFlowTranspPhenCHT.80
15 pages

Mikhail D. Mikhailov
Applied Mathematics Center, PO Box 384, Sofia, Technical University, Sofia, Bulgaria; and Mechanical Engineering Department—EE/COPPE/UFRJ, Universidade Federal do Rio de Janeiro, Cidade Universitaria, CP 68.503, Rio de Janeiro, RJ, 21945-970, Brasil

Abstract

Some new perspectives for generalized integral transform method(GITT)and finite difference method(FDM), when using the Mathematica software system are demonstrated. First, the GITT is applied to find the transient temperature distribution in a slab with temperature dependent thermal conductivity. The corresponding system of ordinary differential equations (ODE) is derived in non-expanded form which permitted efficient generation of the truncated ODE system. The coupling integrals are solved exactly by using a new approach. It consists of obtaining an algebraic system for the unknown integrals by using an integral identity and some properties of the eigenfunctions. Next, the Laplace equation is solved by generating non uniform finite difference templates that include the boundary conditions. In order to obtain optimal finite difference formulae, exact polynomial solutions of the Laplace equation are used. An efficient rule for generation of such polynomials is given. The final Mathematica finite difference solution gives numerical value for any specified location in the solution domain. The technique developed is applicable to many other problems and makes FDM comparable to FEM in dealing with irregular geometry.

ICHMT Digital Library

Bow shocks on a jet-like solid body shape. Thermal Sciences 2004, 2004. Pulsed, supersonic fuel jets - their characteristics and potential for improved diesel engine injection. PULSED, SUPERSONIC FUEL JETS - THEIR CHARACTERISTICS AND POTENTIAL FOR IMPROVED DIESEL ENGINE INJECTION
View of engine compartment components (left). Plots of temperature distributions in centreplane, forward of engine (right). CHT-04 - Advances in Computational Heat Transfer III, 2004. Devel... DEVELOPMENT AND CURRENT STATUS OF INDUSTRIAL THERMOFLUIDS CFD ANALYSIS
Pratt & Whitney's F-135 Joint Strike Fighter Engine under test in Florida is a 3600F class jet engine. TURBINE-09, 2009. Turbine airfoil leading edge stagnation aerodynamics and heat transfe... TURBINE AIRFOIL LEADING EDGE STAGNATION AERODYNAMICS AND HEAT TRANSFER - A REVIEW
Refractive index reconstructed field. (a) Second iteration. (b) Fourth iteration. Radiative Transfer - VI, 2010. Theoretical development for refractive index reconstruction from a radiative ... THEORETICAL DEVELOPMENT FOR REFRACTIVE INDEX RECONSTRUCTION FROM A RADIATIVE TRANSFER EQUATION-BASED ALGORITHM
Two inclusion test, four collimated sources. Radiative Transfer - VI, 2010. New developments in frequency domain optical tomography. Part II. Application with a L-BFGS associated to an inexa... NEW DEVELOPMENTS IN FREQUENCY DOMAIN OPTICAL TOMOGRAPHY. PART II. APPLICATION WITH A L-BFGS ASSOCIATED TO AN INEXACT LINE SEARCH