 Extended Graetz Problem

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration illustrates the effect of axial conduction in the Graetz problem of heat transfer between a fluid in laminar flow and a tube at constant temperature.

[more]

Consider the fully developed laminar flow of a fluid in a tube with a wall temperature ; the fluid has an entering uniform temperature . The dimensionless energy equation, assuming constant physical properties and axis symmetry, is: ,

with boundary conditions: , , , ,

in which dimensionless variables are defined by: , , , ,

where and are the radial and axial coordinates, respectively, is the tube radius, is the fluid specific gravity, is the fluid heat capacity, is the maximum laminar velocity, and is the fluid heat transfer coefficient.

The dimensionless equation is solved using the built-in Mathematica function NDSolve, and the effect of the Péclet number on temperature is shown for various radial and axial positions. The Péclet number is the ratio of convective to conductive heat transfer; thus the effect of axial diffusion becomes important at small Péclet numbers, for example, heat transfer in liquid metals.

[less]

Contributed by: Clay Gruesbeck (May 2017)
Open content licensed under CC BY-NC-SA

Snapshots   Permanent Citation

Clay Gruesbeck

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send