The basic idea in this paper is to transform the coefficient and source inverse problems into non-classical forward problems. Then a loaded equation method is employed for the estimation of unknown time-dependent convection coefficient and source in 1-D magnetohydrodynamics flow system. In this inverse problem two integral observations are posed when the both two unknown functions are unknown. We also consider two simpler cases, when the convection coefficient or source are unknown at the corresponding integral observation. We use implicit finite difference schemes to the solution of the differential problems. We proposed effective decomposition algorithms for solution of the non-local difference problems. Numerical test examples are discussed.