Solving Differential Equations as functions - Combined Heat Transfer

[jroth]

Hello,

I am currently looking at combined heat transfer (radiation - convection - conduction). When radiation is considered, the differential equation becomes non-linear, and thus I figured using MathCad would be great for solving the DEQ as a function of parameters.

As a note, the text I am using/refering to is: Thermal Radiation Heat Transfer 5th Ed. by Howell & Siegel, Chapter 7.

This chapter is mainly dealing with numerical solutions and setting up the equations, but I would like to know how to solve them using MathCad.

Attached is a worksheet and a few pictures of the example problems I am trying to solve, in which there is a graph showing the solutions. I am hoping I can get Mathcad to solve the equations as a function of parameters.

[Werner_E · Accepted solution]

The attached shet should help!

[jroth]

Werner,

Thank you for the response. It was exactly what I was looking for. I assumed it would take a long time to calculate as we have to solve the ODE for each plot.

[pugged]

Hello,

I am trying to open the combined heat transfer file and cannot seem to do so, either in Mathcad 15, or Mathcad Prime 1.0.

Can you kindly advise?

Best regards.

[jroth]

Chuck,

You will need to have Prime 3.0 to open the file. None of the prime files are backwards compatible to earlier Prime versions or to earlier versions of MathCAD.'

I can see about doing it in 15 or something.

[Werner_E]

I am trying to open the combined heat transfer file and cannot seem to do so, either in Mathcad 15, or Mathcad Prime 1.0.

Can you kindly advise?

Unfortunately PTC provides no way to convert a Prime 3 file into Prime 1 or 2 or Mathcad 15 format.

The best I can do is to provide a pdf-print of the file so you can see what its all about and if you like it you will have to retype.

You could also download and install the Prime3 trial but I am not sure in which way this would change your P1 installation. I guess that at least you would lose the ability to convert MC15 files tp P1 format.

If your options are Mathcad 15 and Prime 1 I would strongly advise you forget about Prime and use Mathcad 15 (to be honest my advise would be the same if your choices would be MC15 and P3).

[pugged]

Thanks very much. I could not make my mathcad document solve properly. However, the prime document using solver was straightforward and accurate.

If I deleted off the radiation component, then the mathcad sheet solved properly.

[Werner_E]

In your Mathcad 15 sheet something is wrong with the definition of the variable Tb. I can't see whats wrong but if you retype this definition your solve block works OK.