Thermal efficiency is a measure of how effectively an engine converts heat energy into useful work. The higher the thermal efficiency, the more efficient the engine is in converting heat into work. In this question, we are comparing the thermal efficiencies of three different cycles: Otto, Diesel, and dual.

1. Otto Cycle:
- The Otto cycle is the idealized cycle for spark-ignition gasoline engines.
- It consists of four processes: isentropic compression, constant volume heat addition, isentropic expansion, and constant volume heat rejection.
- The compression ratio of the Otto cycle is typically lower than that of the Diesel cycle.
- The thermal efficiency of the Otto cycle is given by the formula:
η = 1 - (1 / r^(γ-1)), where r is the compression ratio and γ is the specific heat ratio of the working fluid.
- For the same compression ratio and the same heat input, the thermal efficiency of the Otto cycle will be higher than that of the Diesel cycle.

2. Diesel Cycle:
- The Diesel cycle is the idealized cycle for compression-ignition diesel engines.
- It consists of four processes: isentropic compression, constant pressure heat addition, isentropic expansion, and constant volume heat rejection.
- The compression ratio of the Diesel cycle is typically higher than that of the Otto cycle.
- The thermal efficiency of the Diesel cycle is given by the formula:
η = 1 - (1 / r^(γ-1)), where r is the compression ratio and γ is the specific heat ratio of the working fluid.
- For the same compression ratio and the same heat input, the thermal efficiency of the Diesel cycle will be lower than that of the Otto cycle.

3. Dual Cycle:
- The dual cycle combines the features of both the Otto and Diesel cycles.
- It consists of five processes: isentropic compression, constant volume heat addition, constant pressure heat addition, isentropic expansion, and constant volume heat rejection.
- The dual cycle is a more idealized representation of the actual combustion process in engines.
- The thermal efficiency of the dual cycle is higher than that of both the Otto and Diesel cycles.
- For the same compression ratio and the same heat input, the thermal efficiency of the dual cycle will be higher than that of both the Otto and Diesel cycles.

Based on the above explanations, we can conclude that the correct sequence of the increasing order of the thermal efficiencies of the given cycles is Diesel, Otto, dual. The Diesel cycle has the lowest thermal efficiency, followed by the Otto cycle, and the dual cycle has the highest thermal efficiency. Therefore, option 'B' is the correct answer.