A custom database class to demonstrate how WordPress' wpdb class can be instantiated and extended to allow you to connect to another / an external or secondary database. The global $wpdb object is only capable of communicating with the WordPress database. Refer to http://codex.wordpress.org/Class_Reference/wpdb for more information.

external_database.php

<?php
/*
    The MIT License (MIT)
    Copyright © 2014 Ian Lai

    Permission is hereby granted, free of charge, to any person obtaining a copy
    of this software and associated documentation files (the “Software”), to deal
    in the Software without restriction, including without limitation the rights
    to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
    copies of the Software, and to permit persons to whom the Software is
    furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included in
    all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
    AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
    OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
    THE SOFTWARE.
*/

define('DB_HOST', '127.0.0.1');
define('DB_USER', 'root');
define('DB_PASS', 'password');
define('DB_NAME', 'school');

class CustomDatabase
{
	private $db;

	public function __construct() {
		// Connect To Database
		try {
			$this->db = new wpdb(DB_USER, DB_PASS, DB_NAME, DB_HOST);
			$this->db->show_errors(); // Debug
		} catch (Exception $e) {	// Database Error
			echo $e->getMessage();
		}
	}

	// Example Query -- Count Students
	public function count_users() {
		return $this->db->get_var("SELECT COUNT(*) FROM `students`;--");
	}

	// Example Query #2 -- Update Student Name
	public function update_student_id($student_id, $student_name) {
		return $this->db->update(
			'students',
			array('student_name' => $student_name), 
			array('student_id' => $student_id),
			array('%s'), array('%d')
		);
	}
}
$Custom_DB = new CustomDatabase;
?>

I love this concept and it solve one of three issues for me - the unsolved details are:

1. Where do you put this new class to prevent it from being overwritten when WP is updated and

2. where to Instantiate it -

@bhende19 apologies for the tardy response, but in case anyone is curious... this was originally designed for use in something like a plugin. So to answer 1. and 2., it is exactly that. Place it in plugin folder to avoid being overwritten, and instantiate it there. You can check if the class is defined beforehand to avoid collision. I don't know how relevant this file still is since it's been over 2 years...

which location, i am add this file.

I tried it but it doesn't seems to be catching errors when connection fails. Know any reason?

try {
	$mydb = new wpdb( $this->username, $this->password, $this->database, $this->hostname );
	$mydb->show_errors();
} catch( Exception $e ) {
	echo $e->getMessage();
}