A numerical study has been performed to analyze the effect of radial magneticfield on free convective flow of an electrically conducting and viscous incompressiblefluid over the Ramped moving vertical cylinder with Ramped type temperature and concentration considered at the surface of vertical cylinder. The governing partial differential equations which describe theflow formation have been solved numerically by using implicit finite difference method of Crank-Nicolson type. The simulation results of the considered model have been shown graphically. One of the interesting result of our analysis is that the local as well as average skin-friction, Nusselt number and Sherwood number have increasing tendency in time interval (0, 1), thereafter these quantities decrease. We have also compared the case of Ramped type boundary conditions with that of constant boundary conditions with help of table. The advantage of taking Ramped type boundary conditions is that initial heat transfer rate and mass transfer rate are minimum in this case.

This study explores the time-dependent flow of MHD Oldroyd-B fluid under the effect of Ramped wall velocity and temperature. The flow is confined to an infinite vertical plate embedded in a permeable surface with the impact of heat generation and thermal radiation. Solutions of velocity, temperature, and concentration are derived symmetrically by applying non-dimensional parameters along with Laplace transformation (LT) and numerical inversion algorithm. Graphical results for different physical constraints are produced for the velocity, temperature, and concentration profiles. velocity and temperature profile decrease by increasing the effective Prandtl number. The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity. velocity is decreasing for κ, , M, Prreff, and Sc while increasing for Gr and Gc. temperature is an increasing function of the fractional parameter. Additionally, Atangana-Baleanu (ABC) model is good to explain the dynamics of fluid with better memory effect as compared to other fractional operators.

The effect of radiation on natural convection incompressible viscous fluid near a vertical flat plate with Ramped wall temperature has been studied. An analytical solution of the governing equation has been obtained by employing Laplace transform technique. It is examined that two different solutions for the fluid velocities, one valid for fluids of Prandtl number(Pr) different from 1+Ra, Ra being the radiation parameter and the other for which the Prandtl number equal to 1+Ra. The variations of velocities and fluid temperature are presented graphically. Furthermore, the radiative heat transfer on natural convection flow near a Ramped plate temperature has been compared with the flow near a plate with the constant wall temperature. It is found that an increase in radiation parameter leads to rise the fluid velocity as well as temperature.

The unsteady flow and heat transfer of a viscous incompressible, electrically conducting dusty fluid past vertical plate under the influence of a transverse magnetic field is studied with a view to examine the combined effects of suction, heat absorption and Ramped wall temperature. The temperature of the wall is assumed to have a temporarily Ramped profile which goes on increasing up to a certain time limit and then becomes constant. To investigate the effect of Rampedness in wall temperature, the solution for the flow past an isothermal wall is also obtained. The governing partial differential equations are solved using Laplace transformation technique in which the inversion is obtained numerically using Matlab. To validate the results of numerical inversion a comparison between the numerical and analytical values of fluid and particle temperatures and Nusselt number is also presented. The effects of pertinent flow parameters affecting the flow and heat transfer are investigated with the help of graphs and tables. It is found that the increase in suction, heat absorption and particle concentration contribute in thinning the thermal and momentum boundary layers and the velocity and temperature for both the fluid and particle phases are higher in the case of a flow past an isothermal plate than that of a flow past a plate with Ramped temperature.

Investigation of unsteady hydromagnetic natural convection flow with heat and mass transfer of a viscous, incompressible, electrically conducting, chemically reactive and optically thin radiating fluid past an exponentially accelerated moving vertical plate with arbitrary Ramped temperature embedded in a fluid saturated porous medium is carried out. Exact solutions of momentum, energy and concentration equations are obtained in closed form by Laplace transform technique. The expressions for the shear stress, rate of heat transfer and rate of mass transfer at the plate for both Ramped temperature and isothermal plates are derived. The numerical values of fluid velocity, fluid temperature and species concentration are displayed graphically whereas those of shear stress, rate of heat transfer and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. It is found that, for isothermal plate, the fluid temperature approaches steady state when t >1.5. Consequently, the rate of heat transfer at isothermal plate approaches steady state when t >1.5.

The effects of radiation and rotation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving infinite vertical plate with Ramped temperature in a porous medium are investigated. Exact solution of momentum and energy equations, under Boussinesq approximation, is obtained in closed form by Laplace transform technique. To compare the results obtained in this case with that of isothermal plate, exact solution of the governing equations is also obtained for isothermal plate. The expressions for the primary and secondary skin frictions and Nusselt number are also derived. It is noticed that, for both Ramped temperature and isothermal plates, rotation retards fluid flow in the primary flow direction whereas it accelerates fluid flow in the secondary flow direction in the boundary layer region while radiation exerts accelerating influence on the fluid flow in both the primary and secondary flow directions. For Ramped temperature plate radiation reduces primary skin friction whereas it tends to increase secondary skin friction. For isothermal plate radiation has tendency to reduce secondary skin friction. Radiation tends to increase fluid temperature for both Ramped temperature and isothermal plates. With the increase in time the rate of heat transfer at the plate is reduced for isothermal plate while it is increased for Ramped temperature plate.