Exact solutions for unsteady free convection flow over an oscillating plate due to non-coaxial rotation

Abstract

BackgroundNon-coaxial rotation has wide applications in engineering devices, e.g. in food processing such as mixer machines and stirrers with a two-axis kneader, in cooling turbine blades, jet engines, pumps and vacuum cleaners, in designing thermal syphon tubes, and in geophysical flows. Therefore, this study aims to investigate unsteady free convection flow of viscous fluid due to non-coaxial rotation and fluid at infinity over an oscillating vertical plate with constant wall temperature.MethodsThe governing equations are modelled by a sudden coincidence of the axes of a disk and the fluid at infinity rotating with uniform angular velocity, together with initial and boundary conditions. Some suitable non-dimensional variables are introduced. The Laplace transform method is used to obtain the exact solutions of the corresponding non-dimensional momentum and energy equations with conditions. Solutions of the velocity for cosine and sine oscillations as well as for temperature fields are obtained and displayed graphically for different values of time (t ), the Grashof number (Gr), the Prandtl number (), and the phase angle (). Skin friction and the Nusselt number are also evaluated.ResultsThe exact solutions are obtained and in limiting cases, the present solutions are found to be identical to the published results. Further, the obtained exact solutions also validated by comparing with results obtained by using Gaver–Stehfest algorithm.ConclusionThe interested physical property such as velocity, temperature, skin friction and Nusselt number are affected by the embedded parameters time (t), the Grashof number (Gr), the Prandtl number (), and the phase angle ().

Analysis of Heat Transfer in Non-Coaxial Rotation of Newtonian Carbon Nanofluid Flow with Magnetohydrodynamics and Porosity Effects

“…This effect also signifies for a better heat transfer process that can be used in several engineering and industrial system. 18) with the published work by Mohamad et al [40] in Eq. (53).…”

“…The accuracy of the obtained solution is verified by comparing solution in Eq. ( 18) with the solution obtained by Mohamad et al [40] in Eq. (53).…”

“…Comparison of g profiles from present results in Eq. ( 18) with the published work by Mohamad et al [40] in Eq. ( 53).…”

“…Mixer machines in food processing industry, cooling pad of electronic devices and rotating propellers for aircraft have become great application to exemplify the noncoaxial rotating phenomenon in various industries. Mohamad et al [40] presented the mathematical expression for heat transfer in non-coaxial rotation of viscous fluid flow. As the extension of the previous study, the heat and mass transfer effects (double diffusion) were considered by Mohamad et al [41] and followed by Mohamad et al [42] investigating porosity effect in double diffusion flow of MHD fluid.…”

Analytical study of heat and mass transfer effects on unsteady Casson fluid flow over an oscillating plate with thermal and solutal boundary conditions

“…The study of hydromagnetic flow due to an oscillating plate in the presence of thermal boundary conditions is investigated by Das et al 17 Influences of Newtonian heating and conjugate parameter on concentration on a non‐Newtonian fluid flow due to a stretching surface is investigated by Awais et al 18 Influence of mass transfer on fluid flow due to an impulsively started infinite vertical plate along with thermal convective boundary condition is studied by Rajesh 19 . More recently, heat and mass transfer effects on time‐dependent fluid flow over an oscillating plate are analyzed by Endalew et al, 20 Mohamad et al, 21 and and so on.…”