What is the equation for error function in heat transfer?

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    Error Function
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Discussion Overview

The discussion centers around the error function as it relates to heat transfer, exploring its definition, mathematical formulation, and applications in solving differential equations.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant inquires about the definition and derivation of the error function in the context of heat transfer.
  • Another participant suggests that the error function is related to the expression e-x², but this is later clarified.
  • A different participant provides the formal definition of the error function: erf(x) = (2 / sqrt(π)) ∫0..x e-x² dx, noting its relevance to Gaussian distributions.
  • It is mentioned that the error function can express many nonelementary functions in terms of elementary functions, enhancing the expressive power of closed forms.
  • Another participant states that the error function appears when solving certain differential equations, indicating its practical importance.
  • There is a reference to the Gaussian, Error, and Complementary Error functions, suggesting a broader context for the discussion.

Areas of Agreement / Disagreement

Participants present various definitions and applications of the error function, but there is no consensus on a singular definition or its derivation in the context of heat transfer.

Contextual Notes

Some participants express uncertainty about the relationship between the error function and other mathematical concepts, and there may be missing assumptions regarding its application in heat transfer scenarios.

Saint
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In heat transfer, some formulae are expressed in error function. what is it ?

How do we get the equation for error function ?[?]
 
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Isn't the error function e -x 2 ? Thats all I know...
 
Last edited:
Originally posted by On Radioactive Waves
Isn't the error function e -x 2 ? Thats all I know...
I've heard it's called imaginary error function in full.
 
Almost... erf(x) is:

erf(x) = (2 / sqrt(π)) ∫0..x e-x2 dx

It's immediate use is that it's the integral of a gaussian distribution, so it's directly applicable to statistical problems.

More generally, I understand that a lot of nonelementary functions can be expressed in terms of combinations of elementary functions and error functions, so erf expands the expressive power of closed forms.
 
It comes up when solving some differential equations, and it is thus good to have tabulated.
 

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