In one pass shell and tube heat exchanger with baffles one fluid flows inside of parallel tubes and other fluid flows outside of tubes in perpendicular to tube axis changing alternately its direction. Passing the window of the baffles the shell side fluid deviates its flow direction rapidly. This creates just behind the window of each baffle a so-called “dead volume” which renders a stagnation of flow. This dead volume assumed to be triangular in shape causing the flow behind the window to be conical.In this thermal model the “dead volume” taken into account and change of temperature of the shell side fluid during its flow from tube to tube is considered. The thermal analysis of the cross- counter flow arrangement for any number of tube in bundle with progressive changes in tube length has been carried out. The numerical computations with different tube and baffle numbers are performed. It is found that at the beginning the effectiveness of the heat exchanger increases distinctly with increasing tube number and baffle number. But after certain number of tube and baffles the increasing rate weakens and it becomes very small. Due to the presence of “dead volume” there is reduction in the thermally active heat transfer surface area which leads to a smaller value of Number of Transfer Units (NTU). Hence, the results of computation obtained in this paper with the consideration of the “dead volume” will provide lower value of the effectiveness than that of without the consideration of it.