Effect of Viscous Dissipation on Heat Transfer in Laminar Flow

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

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

This Demonstration shows the effect of axial conduction and viscous dissipation on heat transfer between a fluid in laminar flow and a tube at constant temperature.


Consider the fully developed laminar flow of a fluid in a tube with a wall temperature ; the fluid enters at a uniform temperature . Assuming constant physical properties and axial symmetry, the dimensionless energy equation is:


with boundary conditions:

, ,

, , in which the dimensionless variables are given by:









and are the radial and axial coordinates, respectively,

is the tube radius,

is the tube length,

is the fluid specific gravity,

is the fluid heat capacity,

is the average laminar velocity, and

is the fluid thermal conductivity.

The dimensionless equation is solved using the built-in Mathematica function NDSolve; the effect of the Péclet number and the Brinkman number on the temperature distribution is shown.


Contributed by: Clay Gruesbeck (January 2020)
Open content licensed under CC BY-NC-SA



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.