The flow dynamics of a finite two layered fluid system driven by thermocapillary effects when heated from the side is studied in the absence of gravity. The configuration is of low aspect ratio with a third dimension several orders of magnitude larger. The case of a low Prandtl number Newtonian fluid in the bottom layer encapsulated by a high Prandtl number viscoinelastic fluid with a shear rate and temperature dependent viscosity in the top layer is investigated numerically using the method of finite volumes together with the case of a high Prandtl number viscoinelastic fluid encapsulating another high Prandtl number viscoinelastic fluid in the lower layer both when the top surface is free and a no-slip solid cover. In either case, the top surface is considered to be insulated together with the bottom and viscous dissipation is taken into account. Free surface and interface deformations are neglected. The results are reported for both high and low Marangoni numbers. Appropriate values of the ratio of the interfacial Marangoni number to the free surface Marangoni number are determined to bring the convective motion in the lower layer to a virtual halt.

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