WordPress helper functions to display child terms by parent slug

pd_display_child_terms.php

<?php
// helper function to get term children
function pd_get_term_children($slug, $term_type = 'category'){

    // set up category by slug
    $category = get_term_by('slug', "{$slug}", "{$term_type}");

    // get out if no category
    if(!$category){return;}

    $cat_id = $category->term_id;

    //get the children as an array
    $cat_children = get_term_children( $cat_id, "{$term_type}");

    // call a display function to show the children
    return pd_display_term_children($cat_children, $term_type);

}

// helper function to display term children
function pd_display_term_children($cat_children, $term_type){
    echo '<ul>';
    foreach ( $cat_children as $child ) {
        $term = get_term_by( 'id', $child, $term_type );
        echo '<li><a href="' . get_term_link( $child, $taxonomy_name ) . '">' . $term->name . '</a></li>';
    }
    echo '</ul>';
}

//use case example
pd_get_term_children('parentcat', 'category');