An Engineer's Guide to Mathematica

11 Heat Transfer and Fluid Mechanics

11.1 Introduction

Several topics in heat transfer and fluid mechanics are examined numerically and interactive environments are developed to explore the characteristics of the different systems. In particular, the following applications are considered:

Conduction heat transfer –

• transient heat transfer in slabs, cylinders, and spheres subject to various initial conditions, boundary conditions, and a constant source;
• ablation of a tumor, which is modeled as two concentric spheres;
• efficiency of longitudinal and radial fins.

Convection heat transfer –

• natural convection from a heated vertical plate.

Radiation heat transfer –

• view factor between two parallel rectangular surfaces.

Internal viscous flow –

• laminar flow in horizontal pipes;
• flow in three reservoirs.

External flow –

• pressure distribution around a Joukowski airfoil;
• surface profile of nonuniform flow in open channels.

In addition, an interactive graphic for heat conduction in a slab has been demonstrated in Example 5.13 and for fluid mechanics, the air entrapment of liquid jets has been given in Example 5.14, the flow around a cylinder with circulation appears in Example 6.6, and the streamlines of flow around an ellipse have been demonstrated in Example 7.6.

11.2 Conduction Heat Transfer

11.2.1 One-Dimensional Transient Heat Diffusion in Solids

The flow of heat in three geometric shapes will be examined: a slab of uniform thickness 2L_o; a very long solid circular cylinder ...