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Session 1520

Developing Excel Macros for Solving Heat Diffusion Problems

N. N. Sarker and M. A. Ketkar Department of Engineering Technology Prairie View A&M University Prairie View, TX 77446

Abstract

This paper describes the use of Microsoft Excel Spreadsheet and Macro in solving diffusion problems. A one dimensional heat diffusion equation was transformed into a finite difference solution for a vertical grain storage bin. Crank-Nicholson method was added in the time dimension for a stable solution. The Excel spreadsheet has numerous tools that can solve differential equation transformed into finite difference form for both steady and unsteady boundary conditions. Its iterative scheme is easy in solving a problem with steady boundary condition. This paper describes a method to solve heat diffusion problem with unsteady boundary conditions using Excel based macros. Results obtained from the solution agreed well with the measured product temperature distribution for a period of two and half years.

Introduction

Commercial software or custom programs are usually used in studying complex problems. A commercial program may have limitations to certain conditions of a problem. A custom program requires adequate programming skills of the researchers. Microsoft Excel spreadsheet together with its macro capabilities, on the other hand, is a handy tool that can easily be programmed to suit the needs of solving diversified problems. Ketkar and Reddy 1 used Microsoft Excel for numerical solution of an unsteady state heat equation. In this study a heat diffusion problem was solved using the Excel spreadsheet. The time varying boundary condition of the problem did not follow any pattern. This dynamically changing behavior of the boundary condition was taken care of by interfacing some Excel macros with values in the spreadsheet.

Bala et al 2 wrote an elaborate computer program in BASIC language to simulate temperatures of wheat stored for two and a half years in a concrete bin of 778.7-m3 capacity with a diameter of 5.5m and a height of 33.5m located in Cheney, Kansas. This paper used their data but solved the same problem using Microsoft Excel macros interfaced with Excel spreadsheet.

Finite Difference Model for Heat Flow

The following partial differential equation describes transient heat transfer in the radial direction.

2 2 T T 1 T (1) t r2 r r where

Proceedings of the 2004 American Society for Engineering Education Annual Conferences & Exposition Copyright © 2004, American Society for Engineering Education

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Sarker, N., & Ketkar, M. (2004, June), Developing Excel Macros For Solving Heat Diffusion Problems Paper presented at 2004 Annual Conference, Salt Lake City, Utah. 10.18260/1-2--12895