Nonlinear analysis of irregular temperature distribution in a heat exchanger using fractional derivative

A nonlinear system of fractional differential equations with variable specific heat was solved to investigate the heat transfer in a shell and tube heat exchanger. The fractional differential transform method (FDTM) is implemented to transform the governing nonlinear energy balance equations into recursive relations and algebraic expressions. Using inverse differential transform method, these recurrence equations are solved and the closed-form series solutions are obtained to predict the temperature distributions and the effect of variable-specific heat for different values of nonlinearity. The current results perfectly coincide with the solution obtained by the finite difference method. The irregular temperature distributions obtained for different values are statistically validated. The comparative study is carried out among the proposed FDTM, Fractional Generalized Homotopy Analysis Method and Homotopy Perturbation Method for the fractional system to strengthen the results. Using the reduced linear system of energy balance equations, the exit temperatures are predicted and the results are verified by the log mean temperature difference method. The obtained solutions reveal that with minimum computational effort FDTM can produce accurate results for nonlinear ordinary and partial differential equations, that often arise in the heat transfer analysis in a heat exchanger equipment.