Energy conservation of nanofluids from a biomagnetic needle in the presence of Stefan blowing: Lie symmetry and numerical simulation

Abstract

Thermal energy management associated with the transmission of heat is one of the main \nproblems in many industrial setups (e.g. pharmaceutical, chemical and food) and bioengineering \ndevices (e.g. hospital ventilation, heating, cooling devices, heat exchanger and \ndrying food, etc). The current study aims to examine thermo-bioconvection of oxytactic \nmicroorganisms taking place in a nanofluid-saturated needle with the magnetic field. Stefanblowing \nis applied. The leading equations of continuity, momentum and energy, species \ntransport equations for oxygen concentration and population density of microorganisms are \nreduced dimensionless and Lie symmetry group transformations are used to generate \nappropriate invariant transformations. The resulting similarity boundary value problem (in \nwhich the blowing parameter is coupled with concentration) have been simulated using \nMATLAB (2015a) bvp5c built in function. The impact of the emerging factors on the \nnondimensional velocity, temperature, nanoparticle concentration and motile microorganism \ndensity functions and their slopes at the wall, are pictured and tabulated. Justification with \npublished results are included. It is found that all physical quantities decrease with Stefan \nblowing and increase with power law index parameter. With elevation in magnetic field \nparameter i.e., Lorentzian drag force, the friction factor \nreduces while the local Nusselt number, \nlocal Sherwood number, and the local motile microorganism density wall gradient increase. \nPresent study could be used in food and pharmaceutical industries, chemical processing \nequipment, fuel cell technology, enhanced oil recovery, etc.