Your HTML form is missing the start form tag.
make sure your html form start with form tag and method is post with action is the php mail script file name.
Ex:
and in mail.php enter the mail script as follow
$fullname = $_POST['fullname'];
$age = $_POST['age'];
$gender = $_POST['gender'];
$department = $_POST['department'];
$consult = $_POST['consult'];
$date = $_POST['date'];
$request = $_POST['request'];
$time = $_POST['time'];
$email = $_POST['email'];
$tel = $_POST['tel'];
$to = "example@email.com";
$subject = "message goes here";
$message="Name: ".$fullname."
Age: ".$age,"
Gender",$gender."
Phone".$phone."
Dept:".$department;
if(mail ($to, $subject,$message, "From: " .$fullname)){
echo "Success";
} else {
echo "not sent";
}
Also make sure that php mail server is configured properly.
If you are testing it on localhost on windows/Linux machine then you should first configure your SMTP setting and enable to send mail from localhost.
If you are testing it on live server then contact your service provider to enable sending mails
