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This paper presents the method of effectiveness NTU for bayonet tube heat exchangers thermal analysis, with uniform conditions along the outer tube wall surface. Using bayonet tube control volume's energy balance, linear fluid temperatures differential equations and boundary conditions are derived at steady state conditions. The governing equations and boundary conditions are expressed in non-dimensional form. The temperature is found to be dependent on four parameters Hurd number (Hu), ratio of outer tube convective heat transfer coefficient(ξ,), number of transfer unit (NTU), and flow path. The method of fourth order Runge- Kutta was used for numerical integration of the coupled linear temperature differential equations and the results are presented graphically for selected values of Hu,ξ, NTU and flow path. The effectiveness is obtained to be dependent on NTU and fluid temperature at the shell side. It was observed from the tubes temperature distribution at a low Hu value, that little heat is exchanged within the tubes. Heat transfer to shell side fluid increases with an increase in ξ value. Maximum heat transfer is achieved by reverse flow path B. [ABSTRACT FROM AUTHOR]