This work investigates the unsteady natural convection flow of a viscous, incompressible and electrically conducting fluid near an infinite vertical plate with ramped temperature and ramped motion. A unified closed form solution is obtained for the velocity field and skin friction coefficient corresponding to the case when the magnetic field fixed relative to the fluid or the moving boundary. It is assumed that the boundary plate has a ramped temperature profile and ramped motion subject to a uniform transverse magnetic field under the supposition of negligible induced magnetic field. Exact solutions of energy and momentum equations are obtained using the Laplace transform techniques. Graphical representations are attained for different values of the Prandtl number, magnetic field and heat sink parameter. Results show that wall ramped temperature and ramped motion tend to decrease fluid temperature, velocity, Nusselt number and skin friction.
Statisticians have created and proposed new families of distribution by extending or generalizing existing distributions. These families of distributions are made more flexible in fitting different types of data by adding one or more parameters to the baseline distributions. In this article, we present a new family of distributions called Type II half-logistic exponentiated-G family of distributions. We discuss some of the statistical properties of the proposed family such as explicit expressions for the quantile function, probability weighted moments, moments, generating function, survival and order statistics. The new family’s sub-models were discussed. We discuss the estimation of the model parameters by maximum likelihood. Two real data sets were employed to show the usefulness and flexibility of the new family
An unsteady flow formation in Couette motion of an electrically conducting fluid subject to transverse magnetic field has been analyzed in the presence of suction/injection through the porous plates when one of the porous plates is in ramped motion. It is assumed that the porous plates are uniformly permeable and the fluid is entering the flow region through one of the porous plates at same rate as it is leaving through the other porous plate. The resulting boundary value problem has been solved exactly under the assumption of a negligible induced magnetic field, external electric field and pressure gradient. Unified closed form expressions for the velocity field and skin-friction corresponding to the case of a magnetic field fixed relative to the fluid or to the moving porous plate have been presented. In order to highlight the impact of the ramp motion of the porous plate on the fluid flow, it has also been compared with Couette flow between porous plates when one of the porous plates has been set into an impulsive motion.
The effects of relative motion of magnetic field on unsteady magnetohydrodynamic free convection flow with ramped motion and temperature-dependent heat source/sink have been analyzed. The motion of the inner cylinder is ramped while the motion of the outer cylinder is fixed. The momentum and energy equations are solved using the well-known Laplace transform. The time-domain solution is obtained using the Riemann-sum approximation method. The influence of the governing parameters on fluid velocity, fluid temperature, volume flow rate, and rate of heat transfer are discussed with the help of line graphs. It is found that Hartmann number has a retarding effect on fluid velocity, skin friction at the outer surface of the inner cylinder, and mass flow rate when the magnetic field is fixed with the fluid and when the velocity of the magnetic field is less than the velocity of the moving cylinder. Whereas, the reverse effect is noticed when the magnetic field is fixed with the moving cylinder.
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