Casson nanofluid, unsteady flow over an isothermal vertical plate with Newtonian heating (NH) is investigated. Sodium alginate (base fluid)is taken as counter example of Casson fluid. MHD and porosity effects are considered. Effects of thermal radiation along with heat generation are examined. Sodium alginate with Silver, Titanium oxide, Copper and Aluminum oxide are added as nano particles. Initial value problem with physical boundary condition is solved by using Laplace transform method. Exact results are obtained for temperature and velocity fields. Skin-friction and Nusselt number are calculated. The obtained results are analyzed graphically for emerging flow parameters and discussed. It is bring into being that temperature and velocity profile are decreasing with increasing nano particles volume fraction.

The aim of this article is to study the combined effects of heat generation and chemical reaction on magnetohydrodynamic (MHD) natural convection flow over a moving plate embedded in a porous medium. Natural convection is caused due to buoyancy forced which has been induced because of temperature and concentration gradients. The general condition of velocity has been considered on the plate surface with Newtonian heating and constant wall concentration. The effect of thermal radiation is also considered in the energy equation. The main objective here is to study the relative behavior of the magnetic field. That is the magnetic field shows two types of relative behavior. More exactly, when the magnetic field is fixed relative to the fluid (MFFRF) and the magnetic field is fixed relative to the plate (MFFRP). The general exact solution of the problem is determined by the Laplace transform method. Particular solutions for two special cases namely the plate with variable vibration and the plate with sine and cosine oscillations are also determined. Moreover, the solutions when ζ → ∞ for both cases i.e. MFFRF and MFFRP are also obtained as special cases. The velocity profile is presented in the form of mechanical, thermal and concentration components. Velocity obtained for oscillating plate condition is written in terms of steady-state and transient parts. Exact solutions obtained in this paper are interpreted graphically using computational software Mathcad-15 to examine the effects of various pertinent parameters such as Casson fluid parameter, the permeability of porous medium, chemical reaction parameter, heat generation parameter, buoyancy force parameter, magnetic parameter, and radiation parameter. Results for Sherwood number, skin-friction, and Nusselt number are numerically computed and discussed.

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