Unsteady flow of a nanofluid over a sphere with nonlinear Boussinesq approximation

Vasu, B; Gorla, RSR; Beg, OA; Murthy, PVSN; Prasad, VR; Kadir, A

Abstract

A theoretical study is presented of transient mixed convection boundary layer flow of a nanofluid in the forward stagnation region of a heated sphere which is rotating with time dependent angular velocity. The effect of the non-linear Boussinesq approximation is taken into account. The nanofluid is treated as a two-component mixture i.e. nano-particles distributed homogenously in a base fluid (water or gas). The effects of the Brownian motion and thermophoresis are included for the nanofluid and constant wall temperature is imposed at the sphere surface. The first and second laws of thermodynamics are employed in order to study thermophysics as well as heat and mass transfer phenomena. By introducing appropriate similarity variables the governing equations are transformed into a system of dimensionless, nonlinear, coupled, ordinary differential equations which are solved numerically by applying the second-order accurate implicit finite difference Keller box method. The reliability and efficiency of the obtained numerical results are validated via comparison with the previously published results for special cases. The effects of various parameters on primary and secondary velocities, temperature, nanofluid volume fraction (concentration), primary and secondary shear stress functions, Nusselt number function (wall heat transfer rate) and Sherwood number function (wall nanoparticle mass transfer rate) are visualized. Furthermore the influence of non-linear temperature parameter, Brinkman parameter (ratio of Brinkman number to dimensionless temperature ratio), local Reynolds number and unsteadiness parameter on entropy generation number is computed. A strong elevation in entropy generation number is computed with both increasing Brinkman parameter and unsteadiness parameter. Primary and secondary surface shear stresses, Nusselt number and Sherwood number also increase with unsteadiness and rotation parameters. Primary shear stress is boosted with increasing mixed convection parameter and Brownian motion effect whereas secondary shear stress is depressed. Temperatures are suppressed with increasing nonlinear temperature parameter whereas nano-particle concentrations are elevated. Increasing thermophoresis parameter enhances both temperatures and nano-particle concentration values. The simulations find applications in rotating chemical engineering mixing systems and nano-coating transport phenomena.

Citation

Vasu, B., Gorla, R., Beg, O., Murthy, P., Prasad, V., & Kadir, A. (2019). Unsteady flow of a nanofluid over a sphere with nonlinear Boussinesq approximation. Journal of Thermophysics and Heat Transfer, 33(2), 343-355. https://doi.org/10.2514/1.T5516

• Journal Article Type: Article
• Acceptance Date: Jul 15, 2018
• Online Publication Date: Oct 12, 2018
• Publication Date: Apr 1, 2019
• Deposit Date: Jul 20, 2018
• Publicly Available Date: Jul 20, 2018
• Journal: Journal of Thermophysics and Heat Transfer
• Print ISSN: 0887-8722
• Electronic ISSN: 1533-6808
• Publisher: American Institute of Aeronautics and Astronautics
• Volume: 33
• Issue: 2
• Pages: 343-355
• DOI: https://doi.org/10.2514/1.T5516
• Publisher URL: https://doi.org/10.2514/1.T5516
• Related Public URLs: https://arc.aiaa.org/loi/jtht
• Additional Information: Funders : University Grants Commission, India; Projects : Nanofluid Dynamics Simulation for Aerospace; Grant Number: F.30-1/2014-16OB-ANP-5981 (SA-II)