How to convert the following node evaluation procedure to a non recursive solution?

I have the following recursive method.

It evaluates a node (that represent a logical expression), using deep first search traversal :

EvaluateNode(Node node)
{
    bool result;
    switch(node.Type)
    {
        case AND_OPERATOR:
            result = true;
            foreach(Node nodeChild in node.Childrens)
            {
                childresult = EvaluateNode(nodeChild);
                result = result && childresult;
            }
        case OR_OPERATOR:
            result = false;                
            foreach(Node nodeChild in node.Childrens)
            {
                childresult = EvaluateNode(nodeChild);
                result = result || childresult;
            }
        case VALUE:
            result = node.Value;
    }

    return result;
}

I'd like to convert this to a stack/queue based, non recursive solution. Here is what I tried so far (incomplete) :

bool result;
stack.Push(node);
while(!stack.Empty())
{
    Node node = stack.Pop();
    switch(node.Type)
    {
        case AND_OPERATOR:
            foreach(Node nodeChild in node.Childrens)
            {
                stack.Push(nodeChild);
            }   
        case OR_OPERATOR:
            foreach(Node nodeChild in node.Childrens)
            {
                stack.Push(nodeChild);
            }           
        case VALUE:
            result = node.Value;
    }
}

My guess is that I would need another stack for storing results but I have not been able to figure this out.