Abstract
The unsteady free flow of a Casson fluid past an oscillating vertical plate with constant wall temperature has been studied. The Casson fluid model is used to distinguish the non-Newtonian fluid behaviour. The governing partial differential equations corresponding to the momentum and energy equations are transformed into linear ordinary differential equations by using nondimensional variables. Laplace transform method is used to find the exact solutions of these equations. Expressions for shear stress in terms of skin friction and the rate of heat transfer in terms of Nusselt number are also obtained. Numerical results of velocity and temperature profiles with various values of embedded flow parameters are shown graphically and their effects are discussed in detail.
Highlights
Newtonian fluids described by Navier-Stokes equations are extensively studied in the literature for the past few decades
Motivated by the above investigations, the present analysis is focused on the study of unsteady boundary layer flow of a Casson fluid past an oscillating vertical plate with constant wall temperature
Let us consider the effect of heat transfer on unsteady boundary layer flow of an incompressible Casson fluid past an infinite vertical flat plate situated at the flow being confined to y > 0, where y is the coordinate measured in the normal direction to the surface
Summary
Newtonian fluids described by Navier-Stokes equations are extensively studied in the literature for the past few decades. The understanding of flow characteristics of non-Newtonian fluids is very important because they play a significant role in industry and engineering Such interest is motivated because of extensive applications in diverse areas of biorheology, geophysics, and chemical and petroleum industries [11, 12]. The flow of Casson fluids (such as drilling muds, clay coatings and other suspensions, certain oils and greases, polymer melts, blood, and many emulsions), in the presence of heat transfer, is an important research area due to its relevance to the optimized processing of chocolate, toffee, and other foodstuffs [26]. Motivated by the above investigations, the present analysis is focused on the study of unsteady boundary layer flow of a Casson fluid past an oscillating vertical plate with constant wall temperature. Exact solutions obtained in this paper are important; do they correspond to some fundamental flow situations, and they are useful for explaining the flow physics in detail as well as for being used as a benchmark for validation of other solutions obtained via approximate or numerical schemes
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