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The heat and mass transfer characteristics of a liquid film which contain thermosolutal capillarity and a variable magnetic field over an unsteady stretching sheet have been investigated. The governing equations for momentum, energy, and concentration are established and transformed to a set of coupled ordinary equations with the aid of similarity transformation. The analytical solutions are obtained using the double-parameter transformation perturbation expansion method. The effects of various relevant parameters such as unsteady parameter, Prandtl number, Schmidt number, thermocapillary number, and solutal capillary number on the velocity, temperature, and concentration fields are discussed and presented graphically. Results show that increasing values of thermocapillary number and solutal capillary number both lead to a decrease in the temperature and concentration fields. Furthermore, the influences of thermocapillary number on various fields are more remarkable in comparison to the solutal capillary number

mathematical problems in engineering

Heat and Mass Transfer in a Thin Liquid Film over an Unsteady Stretching Surface in the Presence of Thermosolutal Capillarity and Variable Magnetic Field