Diffusion of heat and mass in flow of viscous fluid over a moving porous and rotating disk

Abstract

In this paper, we have studied the transport of heat and mass in viscous fluid flow over a disk, rotating with variable angular velocity, whereas, both the nonuniform injection and suction velocities can take place through its porous surface. Moreover, the disk is stretched (shrunk) with variable velocity in its own plane. Besides that the temperature and concentration functions, defined at the surface of disk, are assumed nonuniform and nonlinear, whereas, their nonlinear nature can be expressed in the form of algebraic and non-algebraic functions, however, the uniform and linearly variable temperature and concentration functions at the surface of the disk are easily obtained by fixing the exponents of these functions either zero or one. Diffusion of these two quantities in flows over such disk are the fundamental objective of current investigations. Six PDE’s control the fluid motion along with the diffusion of heat and mass in flow over the rotating disk of such special characteristics. The system of PDE’s is transformed into a set of ODE’s, which is solved numerically with the help of bvp4c package of MATLAB. The present simulation and its solution are exactly matched with the solution of classical problems of rotating disk flows with the additional characteristic of diffusion of heat and mass in flows. Therefore, we have seen the individual and combined effects of all physical parameters on field variables under consideration. The higher order governing equations are nonlinear PDE’s, which are converted into the system of ODE’s in view of proper similarity transformations. Moreover, the tangential and radial shears, shaft torque, rates of the diffusion are evaluated at the surface of the disk, whereas, they are graphed against different parameters and interesting results have been presented. It is found that the nonlinear nature of surface temperature and concentration reduced the thermal and concentration boundary layers, however, the large negative values of power index parameters give rise to an overshoot in temperature and concentration profiles.