The phrase "heavy demand" refers to a situation where a product or service is in great need or desire. However, there are several other terms that can be used to describe the same situation. These include high demand, strong demand, intense demand, soaring demand, and overwhelming demand. Each of these words carries a slightly different connotation, emphasizing the degree and urgency of the demand. Using synonyms for phrases like "heavy demand" in your writing can help to add variety and interest to your prose, while also giving you a more nuanced way of conveying information.