Mathematical Model of Copper Nanofluid Flow Past a Spherical Enclosure
Alalibo T. Ngiangia
Department of Physics, University of Port Harcourt, Choba, Nigeria.
Tombotamunoa W. J. Lawson *
Department of Mathematics/Statistics, Ignatius Ajuru University of Education, Port Harcourt, Nigeria.
Peter O. Nwabuzor
Department of Physics/Electronics Technology, University of Port Harcourt, Choba, Nigeria.
Chijioke A. Egbo
Department of Science Laboratory, Federal Polytechnic of Oil and Gas, Bonny Island, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The study examined mathematical models for describing the behavior of copper nanoparticles in water base fluid. Coupled hydrodynamic governing equations of momentum, energy and concentration were non dimensionalized and solved using installed Laplace transform technique in Mathematica 12.3. The solution obtained were used to analyze the effect of the material parameters on the concentration, temperature and velocity profiles of the copper nanofluid. Results of the study using graphs reveal that an enhancement of the nanoparticle size results in a depreciation of the concentration of the copper nanofluid and escalate the temperature and velocity profiles of the copper nanofluid. Also, the twin effect of an increase in Thermophoresis and Brownian motion bring about a decrease in the concentration of the nanofluid and an increase in the temperature and velocity of the nanofluid. An increase in the radiation parameter, enhanced the temperature of the nanofluid and depreciate the concentration and velocity of the nanofluid while an increase in the magnetic Hartmann number inhibits the velocity of the nanofluid, while an enhancement of the Lewis and Prandtl numbers led to a depreciation of the concentration, an increase in the temperature is observed, for the velocity, it is enhanced by sharp increase in the lewis number and accordingly depreciates by an increase in the Prandtl number. The Reynolds number increase also escalates the velocity profile of the copper nanofluid. Generally, it was observed that the copper nanofluid in some cases react abnormally in the presence of some material parameters under investigation which is a reflection of its characteristics.
Keywords: Copper nanoparticles, water, laplace transform, spherical coordinate, hydrodynamic equations