There is a header.php file and it contains some php codes that return HTML. I know I can use require, include to echo the results, but what I want to do is to store its proc
Don't use eval() - it's evil!
Use the relative local path an automatically map it to a absolute URL.
If URL wrappers are enabled and you want the output of header.php (and you don't want to keep session state) you could use $headerHTML=file_get_contents('http://yourdomain.tld/path/to/header.php');, though why you would want to do such a thing eludes me. Are you sure you're not trying to do something that could easily be solved by using templates and caching?
You can check http://in2.php.net/manual/en/function.eval.php#56641, hope it helps.
I'd rather use require() wrapped inside ob_start() and ob_get_clean(). I am sure there is nothing wrong with this approach.