Abstract Title

The Curious Case of Heat Transfer through Water, Solid and Atmosphere & Analytical Solution of Fin/Slab Heat Transfer and Property Distribution

Abstract

ABSTRACT: Our present research falls into two parts regarding Heat Equations.

Part one (Time Dependency, Unsteady Case): In lieu of experimentally determining the heat transfer in a two body system on a cold and snowy Ohio night, we shall direct our attention to the more scientifically expedient investigation of determining the heat transfer of heated water in a cup as it cools to the ambient temperature in order to show that cups of different materials affect the rate of heat transfer. The experiment will consist of three cups of the same size and shape but made of different materials. Then we will perform a non-linear regression of the experimental data.

Part Two (Spatial Dependency, Steady Case): The Adomian decomposition method has been applied to evaluate the conduction-convection heat transfer through a straight fin, property distribution due to convection-diffusion, and conduction heat transfer through a slab with temperature dependent thermal conductivity. The Adomian decomposition method (ADM) provides the closed form solution for non-linear problems without applying any non-realistic simplifications and/or approximations. The obtained analytical solutions are compared with exact and numerical solutions, using the finite difference/R-K method. It is shown that the numerical simulation has some limitations and may not always produce correct results. However, the Adomian decomposition method follows the correct trend of the exact solution by applying only a few terms.

Research Category

Computer Science/Mathematics

Primary Author's Major

Mathematics

Mentor #1 Information

Dr. Mahmoud Najafi

Mentor #2 Information

Mr. Greg Putman

Presentation Format

Poster

Start Date

11-3-2015 1:00 PM

End Date

11-3-2015 5:00 PM

Research Area

Numerical Analysis and Computation

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Mar 11th, 1:00 PM Mar 11th, 5:00 PM

The Curious Case of Heat Transfer through Water, Solid and Atmosphere & Analytical Solution of Fin/Slab Heat Transfer and Property Distribution

ABSTRACT: Our present research falls into two parts regarding Heat Equations.

Part one (Time Dependency, Unsteady Case): In lieu of experimentally determining the heat transfer in a two body system on a cold and snowy Ohio night, we shall direct our attention to the more scientifically expedient investigation of determining the heat transfer of heated water in a cup as it cools to the ambient temperature in order to show that cups of different materials affect the rate of heat transfer. The experiment will consist of three cups of the same size and shape but made of different materials. Then we will perform a non-linear regression of the experimental data.

Part Two (Spatial Dependency, Steady Case): The Adomian decomposition method has been applied to evaluate the conduction-convection heat transfer through a straight fin, property distribution due to convection-diffusion, and conduction heat transfer through a slab with temperature dependent thermal conductivity. The Adomian decomposition method (ADM) provides the closed form solution for non-linear problems without applying any non-realistic simplifications and/or approximations. The obtained analytical solutions are compared with exact and numerical solutions, using the finite difference/R-K method. It is shown that the numerical simulation has some limitations and may not always produce correct results. However, the Adomian decomposition method follows the correct trend of the exact solution by applying only a few terms.