Purpose -The purpose of this paper is to solve an unsteady nonlinear convective-radiative equation and a nonlinear convective-radiative-conduction equation containing two small parameters of 1 1 and 1 2 by variational homotopy perturbation method. Design/methodology/approach -The heat transfer equations are described. The variational homotopy perturbation method as a powerful method for solving linear and nonlinear equations is applied to find the solutions of our model equations.Findings -The solutions of heat transfer equations are calculated in the form of convergent series with easily computable components. Two examples are solved as illustrations, using symbolic computation. Originality/value -The results show that the suggested method is easy to implement and has high level of accuracy. The method introduces a reliable tool for solving many linear and nonlinear differential equations. Nomenclature

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Unit-1 of the Bushehr nuclear power plant (BNPP-1) is a VVER-type reactor with 1,000-MWe power constructed near Bushehr city at the coast of the Persian Gulf, Iran. The reactor has been recently operational to near its full power. The radiological impact of nuclear power plant (NPP) accidents is of public concern, and the assessment of radiological consequences of any hypothetical nuclear accident on public exposure is vital. The hypothetical accident scenario considered in this paper is a design-basis accident, that is, a primary coolant leakage to the secondary circuit. This scenario was selected in order to compare and verify the results obtained in the present paper with those reported in the Final Safety Analysis Report (FSAR 2007) of the BNPP-1 and to develop a well-proven methodology that can be used to study other and more severe hypothetical accident scenarios for this reactor. In the present study, the version 2.01 of the PC COSYMA code was applied. In the early phase of the accidental releases, effective doses (from external and internal exposures) as well as individual and collective doses (due to the late phase of accidental releases) were evaluated. The surrounding area of the BNPP-1 within a radius of 80 km was subdivided into seven concentric rings and 16 sectors, and distribution of population and agricultural products was calculated for this grid. The results show that during the first year following the modeled hypothetical accident, the effective doses do not exceed the limit of 5 mSv, for the considered distances from the BNPP-1. The results obtained in this study are in good agreement with those in the FSAR-2007 report. The agreement obtained is in light of many inherent uncertainties and variables existing in the two modeling procedures applied and proves that the methodology applied here can also be used to model other severe hypothetical accident scenarios of the BNPP-1 such as a small and large break in the reactor coolant system as well as beyond design-basis accidents. Such scenarios are planned to be studied in the near future, for this reactor.

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