The Combined Effect of Gravity Modulation and Throughflow on Thermal Instability in the Hele-Shaw Cell Filled with Oldroyd-B Nanofluid

Author:

Bhadauria B. S.1,Kumar Anish1,Kumar Awanish1,Rai S. N.1

Affiliation:

1. Department of Mathematics, School of Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, (A Central University) Lucknow, 226025, India

Abstract

This paper shows the combined effect of throughflow and gravity modulation on the stability of Oldroyd-B nanofluid filled in Hele-Shaw cell. Nanofluid compared to the base fluid has higher thermal conduction. The thermal conductivity of nanofluid increased and thus increases the amount of energy transferred. The Oldroyd-B fluid model is important because of its numerous applications such as production of plastic sheet and extrusion of polymers through a slit die in polymer industry, biological solution pant tars glues, etc. In linear stability analysis, we found the expression of the critical Hele-Shaw Rayleigh number by using the normal mode method. Two-term Fourier series method is used for non-linear stability analysis and is also considered the Brinkman model for flow of nanofluid in Hele-Shaw cell. In linear stability analysis, we observed that there is no effect of Oldroyd-B nanofluid, which means that Deborah number (λ1) and retardation parameter (λ2) do not affect the stability analysis. Oldroyd-B nanofluid is similar to ordinary nanofluid in linear analysis. In non-linear analysis, Deborah number, retardation parameter, throughflow, gravity modulation, and Hele-Shaw number play a major role in heat/mass transfer. Enhancement in both heat/mass transfer in the system while increasing throughflow and Deborah number. An increment in Hele-Shaw number (Hs), decreases heat/mass transfer in the system.

Publisher

American Scientific Publishers

Subject

Fluid Flow and Transfer Processes,Mechanical Engineering

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