0 votes
in Maths & Statistics by (user.guest)

For laminar flow in a tube with a constant wall heat flux, it can be shown that the
microscopic energy equation can be reduced to the following form where 
qis the
heat flux in the y direction

In the above equation, v0 is the fluid velocity, which is assumed to be linear and
R is the tube radius and α is the thermal diffusivity.
(a) Transform the above equation to an equivalent form by introducing the
following dimensionless variables


(b) Next, introduce a new independent variable called a similarity variable into the
equation derived in the previous step defined as

Show that the following transformed ordinary differential equation emerges from this

(c) Suppose that the boundary conditions are 

Using these boundary conditions, show that the solution to the transformed ODE

shown in step (b) is: 

here x is a dummy variable for integration and Γ is the gamma function. Refer to
Chapter 4 in the text for the definition of the gamma function.
(d) Starting with the definition for the heat flux

Show that the temperature profile can be obtained by integrating the heat flux 

Then, show that the following dimensionless form can be derived from the above


Your answer

Help us make this a great place for discussion by always working to provide accurate answers.
Privacy: Your email address will only be used for sending these notifications.

Related questions

Welcome to CPEN Talk
Solution-oriented students of computer engineering on one platform to get you that


Everybody thinks the Galaxy Note 7 is explosive. In fact it is only Chuck Norris who tries to send a WhatsApp message with a selfie to his fans.