The correct answer is B) increase the rate of heat transfer to the waterside. The purpose of designing waste heat boilers with sinuous (winding or serpentine) fire tubes is to increase the surface area of the heat transfer surfaces, which in turn enhances the rate of heat transfer from the hot exhaust gases to the water or steam in the boiler. The sinuous shape creates more surface area compared to a straight tube, allowing more efficient heat absorption and a higher overall heat transfer rate. The other options are incorrect because they do not directly address the primary purpose of the sinuous fire tube design. Option A is focused on reducing carbon deposits, option C is about increasing exhaust gas velocity, and option D is about eliminating exhaust gas pulsations and noise, which are not the main reasons for the sinuous fire tube design.