A conceptual model is an explanation, usually highly simplified, of how something works. It doesn’t have to be complete. It can be an approximation. But it has to be usable.
How can you better convey the conceptual model of anything?
Conceptual models are a form of story, resulting from our pre-disposition to find explanations. They are essential in helping us understand our experiences, predict outcome of our actions, and handle unexpected occurrences.
We base our models on whatever knowledge we have, real or imaginary, naive or sophisticated - most often from fragmentary evidence.
Your model should be as close as to reality to avoid frustrations.