Description:
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It appears to me that stream_set_timout() does not do anything of value.  

You can set it prior to a while loop; but, it does nothing to help you exit the loop if the time expires. e.g.,
 
stream_set_timeout($fp, 20);	

$status = socket_get_status($fp);
while (!feof($fp) && !$status['timed_out']) {
    $chunk = fread($fp, 10000);
    $length = strlen($chunk);
    $html_str .= $chunk;
    sleep(2);
    $status = socket_get_status($fp);
} //end while, fetching data

If fread() hangs up, the script hangs.  

You can do exactly the same thing by simply keeping track of elapsed time in the loop. 

Set stream_set_blocking($fp, FALSE ) so fread() keeps going and the loop continues until the elapsed time expires.