Combined effects of thermal radiation and variable viscosity on a time-dependent boundary-layer flow of magnetic nanofluids over a rotating disk in the presence of the porous medium have been numerically investigated. To carry out the study, hydrocarbon based magnetic nanofluid containing magnetite Fe 3 O 4 particles of 10 nm with magnetic phase concentration of 10% has been taken. For numerical solutions of the modelled system containing the governing equation of the flow, a MATLAB tool ODE45 is employed with shooting technique for the initial guess of the unknown boundary conditions. The flow phenomenon and heat transfer on the plate surface are characterised by various flow parameters such as viscosity variations, unsteady rotation parameter, Prandtl number, and radiation parameter. Also, a comparative thermal analysis has been carried out for magnetic nanofluids having three different bases viz. hydrocarbon, fluorocarbon, and water. Results reveal that heat transfer rate of hydrocarbon base magnetic nanofluids is 73.4511% faster than water base magnetic nanofluids, and 239.7458% faster than fluorocarbon base magnetic nanofluids. This enhanced heat transfer capacity of hydrocarbon base magnetic nanofluids will help in improving the performance of oil and ore extraction drilling systems used in mining industry and other geothermal applications.

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An attempt has been made to describe the effects of geothermal viscosity with viscous dissipation on the three dimensional time dependent boundary layer flow of magnetic nanofluids due to a stretchable rotating plate in the presence of a porous medium. The modelled governing time dependent equations are transformed a from boundary value problem to an initial value problem, and thereafter solved by a fourth order Runge-Kutta method in MAT-LAB with a shooting technique for the initial guess. The influences of mixed temperature, depth dependent viscosity, and the rotation strength parameter on the flow field and temperature field generated on the plate surface are investigated. The derived results show direct impact in the problems of heat transfer in high speed computer disks (Herrero et al. [1]) and turbine rotor systems (Owen and Rogers [2]).

This work aims to investigate mass transport phenomena on time dependent Bödewadt flow of magnetic Nanoliquid embedded in the porous medium with vertical polarization force and geothermal viscosity variations. The resultant nonlinear coupled system of partial differential equations is solved numerically. For thorough understanding of flow and transport phenomenon, a wider range of Prandtl number is taken to analyze the effects of various physical entities including polarization force, geothermal viscosity, permeability and rotation. Eventually, some new marvels are found. The diffusion rate enhances significantly for higher values of Prandtl, Schmidt numbers and the boundary layer thickness decimates with all parameters except depth dependent viscosity. Besides, frictions on the surface of the plate have also been computed and found them very high for all above mentioned entities. In nutshell, to have the realistic view, this investigation reveals that the polarization force and viscosity variation due to the temperature and depth have imperative role on the unsteady transport phenomenon in ferrofluid flow.