In this work, we analyze Couette flow problem for an unsteady mangneto-hydrodynamic (MHD) third-grade fluid in the presence of a pressure gradient and Hall currents. Existing literature on the topic shows that the effecs of Hall current on Couette flow of an unsteady MHD third-grade fluid with a pressure gradient has not yet been investigated. The arising non-linear problem is solved by the homotopy analysis method (HAM) and the convergence of the obtained complex series solution is carefully

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... alyzed. The effects of pressure number, Hartmann number and Hall parameter on unsteady velocity are discussed via analysis of plots. ABSTRAK: Kajian dijalan untuk menganalisa masalah aliran Couette bagi bendalir MHD gred ketiga dan arus Hall. Bagi topik ini kesan arus Hall terhadap aliran Couette dalam bendalir MHD gred ketiga tak mantap dengan kecerunan tekanan, belum pernah dikaji selidik. Masalah tak linear berbangkit diselesaikan dengan kaedah analisis homotopi (HAM) dan ketumpuan solusi rangkaian kompleks dianalisa dengan teliti. Kesan nilai tekanan, nombor Hartmann dan parameter Hall terhadap halaju tak mantap diperbincangkan melalui plot yang dianalisis.