#### Keywords

Carburizing, Diffusion, Material Science, PDE Solutions, MATLAB Programming

#### Abstract

**Diffusion PDE Application to Carburizing Treatment of Steel Base Gear**

An introductory materials-science course is required in the mechanical engineering curriculum of many universities. This article describes an example effort to incorporate programming, diffusion transfer, heat treatment process and mechanical-property determination as an integral part of the materials-science course instruction. This effort was undertaken in order to give students additional experience in Fick’s 1^{st} and 2^{nd} laws and in-depth understanding of physics and mathematics involved in diffusion analysis. We chose to focus on Fick’s second law because its applications are not restricted to the materials-science field [1]. As a matter of fact, the same form of parabolic partial differential equation also finds applications in financial derivatives pressure, heat transfer, and soil mechanics consolidation [2,3]. For instance, the diffusion coefficients all share the units of m^{2}/s [2].

From the perspective of materials science, diffusion refers to an observable net flux of atoms or other species [1,4,5]. It depends upon the concentration gradient and temperature. It is vital for the carburization process (Carbon diffusion into steel), determining the proper hardness values not only for surface hardness of gear teeth but also for carbon penetration into specified depths. Students will be required to write a MATLAB program with input parameters of diffusion couple to calculate the atomic flux on the basis of diffusivity and concentration gradient. They are able to predict heat furnace design temperature and time required to heat the metal using error function values and one-dimensional diffusion equation with the specified boundary conditions. This paper focuses on the application of diffusion to material science engineering and provides an example of how diffusion may be adopted in an integrated instruction of materials science instructions.

**Keywords: **Materials Science**, **Diffusion, Carburizing**, **PDE Solutions, MATLAB Programming

#### Included in

Curriculum and Instruction Commons, Mechanical Engineering Commons, Structural Materials Commons

Design of a Carburizing Treatment of Steel Base Gear in the Materials Science Course

**Diffusion PDE Application to Carburizing Treatment of Steel Base Gear**

An introductory materials-science course is required in the mechanical engineering curriculum of many universities. This article describes an example effort to incorporate programming, diffusion transfer, heat treatment process and mechanical-property determination as an integral part of the materials-science course instruction. This effort was undertaken in order to give students additional experience in Fick’s 1^{st} and 2^{nd} laws and in-depth understanding of physics and mathematics involved in diffusion analysis. We chose to focus on Fick’s second law because its applications are not restricted to the materials-science field [1]. As a matter of fact, the same form of parabolic partial differential equation also finds applications in financial derivatives pressure, heat transfer, and soil mechanics consolidation [2,3]. For instance, the diffusion coefficients all share the units of m^{2}/s [2].

From the perspective of materials science, diffusion refers to an observable net flux of atoms or other species [1,4,5]. It depends upon the concentration gradient and temperature. It is vital for the carburization process (Carbon diffusion into steel), determining the proper hardness values not only for surface hardness of gear teeth but also for carbon penetration into specified depths. Students will be required to write a MATLAB program with input parameters of diffusion couple to calculate the atomic flux on the basis of diffusivity and concentration gradient. They are able to predict heat furnace design temperature and time required to heat the metal using error function values and one-dimensional diffusion equation with the specified boundary conditions. This paper focuses on the application of diffusion to material science engineering and provides an example of how diffusion may be adopted in an integrated instruction of materials science instructions.

**Keywords: **Materials Science**, **Diffusion, Carburizing**, **PDE Solutions, MATLAB Programming