Unsteady magnetohydrodynamic flow of Casson fluid over an infinite vertical plate is examined under ramped temperature and velocity conditions at the wall. Thermal radiation flux and heat injection/suction terms are also incorporated in the energy equation. The electrically conducting fluid is flowing through a porous material and these phenomena are governed by partial differential equations. After employing some adequate dimensionless variables, the solutions are evaluated by dint of Laplace transform. In addition, the physical contribution of substantial parameters such as Grashof number, radiation parameter, heat injection/suction parameter, porosity parameter, Prandtl number, and magnetic parameter is appropriately elucidated with the aid of graphical and tabular illustrations. The expressions for skin friction and Nusselt number are also derived to observe wall shear stress and rate of heat transfer. A graphical comparison between solutions corresponding to ramped and constant conditions at the wall is also provided. It is observed that graphs of the solutions computed under constant conditions are always superior with respect to graphs of ramped conditions. The magnetic field decelerates the flow, whereas the radiative flux leads to an upsurge in the flow. Furthermore, the shear stress is a decreasing function of the magnetic parameter.

This article investigates the influence of ramped wall velocity and ramped wall temperature on time dependent, magnetohydrodynamic (MHD) natural convection flow of some nanofluids close to an infinitely long vertical plate nested in porous medium. Combination of water as base fluid and three types of nanoparticles named as copper, titanium dioxide and aluminum oxide is taken into account. Impacts of non linear thermal radiation flux and heat injection/consumption are also evaluated. The solutions of principal equations of mass and heat transfer are computed in close form by applying Laplace transform. The physical features of connected parameters are discussed and elucidated with the assistance of graphs. The expressions for Nusselt number and skin friction are also calculated and control of pertinent parameters on both phenomenons is presented in tables. A comparative study is performed for ramped wall and isothermal wall to evaluate the application extent of both boundary conditions.

The influence of simultaneously applied ramped boundary conditions on unsteady magnetohydrodynamic natural convective motion of a secondgrade fluid is investigated and analyzed in this study.

This study explains the transient free convection phenomenon in a vertical porous channel subject to nonlinear thermal radiation. The infinite vertical channel encloses magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid. The left channel wall possesses time-dependent velocity u 0 g ( t ˜ ) , while the right wall exhibits no motion. The momentum and temperature field equations are developed on the bases of momentum conservation law and Fourier’s principle of heat transfer. Laplace transformation technique and Durbin’s numerical inversion method are jointly incorporated to compute the solutions of the formulated problem. The influences of flow and material parameters on heat transfer and fluid velocity are graphically scrutinized with physical aspects. The numerical computations for skin friction and temperature gradient are tabularized to comprehensively examine the wall shear stress and heat transfer rate. Finally, velocity fields for Maxwell fluid, second grade fluid, and viscous fluid are traced out as limiting cases and their comparison is drawn with the velocity field of an Oldroyd-B fluid. Besides this, some newly published results are also deduced from the acquired solutions. It is observed that increasing the magnitude of radiation parameter Rd rapidly enhances the rate of heat transfer at the right channel wall while an inverse behavior of Nusselt number is witnessed at the left channel wall. The Maxwell fluid and second grade fluid indicate the swiftest and slowest channel flow rates respectively. The shear stress specifies dual nature for relaxation and retardation parameters subject to static and moving wall. Additionally, it is found that the flow of an Oldroyd-B fluid is retarded by a magnetic field.

A non-equilibrium non-isothermal lumped kinetic model (LKM) is analytically and numerically investigated to evaluate the effects of inherent temperature fluctuations in an adiabatic chromatographic column. The model comprises of convectiondiffusion partial differential equations quantifying mass and energy balances in the mobile phase coupled with differential and algebraic equations for mass and energy in the stationary phase. Besides two mass transfer coefficients, two heat transfer coefficients are involved in the model equations. The properties of the considered model are investigated for linear concentration and temperature dependencies of the equilibrium loadings. The Laplace transformation and eigen-decomposition techniques are utilized to solve the set of equations. These solutions are helpful for understanding,