In present study, an analytical solution is proposed for the problem of transient anisotropic conductive heat transfer in composite cylindrical shells. The composite shells considered to have directional heat transfer properties which is due to the existence of fibers which can be winded in any direction. The composite shells usually show high conductivity in the direction parallel to fiber direction and low conductivity in other two orthogonal directions. To solve the heat transfer partial differential equation, finite Fourier transform and separation of variables method were used. The present solution is used to find the temperature distribution in a composite cylindrical vessel for which the composite material is graphite/epoxy and the vessel is prone to an external heat flux and also ambient flow. The analytical solution was verified perfectly by the data obtained from a second order finite difference solution. The solution is used to investigate the effects of values of fiber angle and material conductivity coefficients on the temperature distribution of the composite cylindrical vessel. The results show the major role of fiber angle values on the temperature distribution of vessel.

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