Stability analysis for the Walters-B model saturated with permeable nanofluid is taken under study including cross diffusion effects. The porous medium is defined using modified Darcy model, and the nanofluid is considered to have the impact of thermophoresis and Brownian motion. The thermal energy equation includes the effects of diffusion and also cross diffusion. For the study of linear theory, normal mode procedure is applied and to understand the nonlinear theory, the method of minimal representation of double Fourier series is utilized. The effects of nondimensional parameters such as concentration Rayleigh number, Lewis number, Soret and Dufour parameters, Solutal Rayleigh number, elastic parameter, Prandtl number, viscosity ratio, and conductivity ratio on the stationary and oscillatory convections are represented graphically. The effect of time on transient Nusselt numbers is also taken under investigation. It is concluded that when time is small, the three Nusselt numbers oscillate for all the governing parameters and approach to steady-state as time increases.
Skip Nav Destination
Article navigation
August 2019
Research-Article
Stability Analysis of Cross Diffusion for the Walters B Fluid Model Saturated With Permeable Nanofluid
J. C. Umavathi,
J. C. Umavathi
Department of Mathematics,
Gulbarga University,
Gulbarga, Karnataka 585 106, India
e-mail: drumavathi@rediffmail.com
Gulbarga University,
Gulbarga, Karnataka 585 106, India
e-mail: drumavathi@rediffmail.com
1Corresponding author.
Search for other works by this author on:
Ali J. Chamkha
Ali J. Chamkha
Mechanical Engineering Department,
Prince Sultan Endowment for
Energy and Environment,
Prince Mohammad Bin Fahd University,
Al-Khobar 31952, Saudi Arabia;
Prince Sultan Endowment for
Energy and Environment,
Prince Mohammad Bin Fahd University,
Al-Khobar 31952, Saudi Arabia;
RAK Research and Innovation Center,
American University of Ras Al Khaimah,
P.O. Box 10021,
Ras Al Khaimah 10021, United Arab Emirates
American University of Ras Al Khaimah,
P.O. Box 10021,
Ras Al Khaimah 10021, United Arab Emirates
Search for other works by this author on:
J. C. Umavathi
Department of Mathematics,
Gulbarga University,
Gulbarga, Karnataka 585 106, India
e-mail: drumavathi@rediffmail.com
Gulbarga University,
Gulbarga, Karnataka 585 106, India
e-mail: drumavathi@rediffmail.com
Ali J. Chamkha
Mechanical Engineering Department,
Prince Sultan Endowment for
Energy and Environment,
Prince Mohammad Bin Fahd University,
Al-Khobar 31952, Saudi Arabia;
Prince Sultan Endowment for
Energy and Environment,
Prince Mohammad Bin Fahd University,
Al-Khobar 31952, Saudi Arabia;
RAK Research and Innovation Center,
American University of Ras Al Khaimah,
P.O. Box 10021,
Ras Al Khaimah 10021, United Arab Emirates
American University of Ras Al Khaimah,
P.O. Box 10021,
Ras Al Khaimah 10021, United Arab Emirates
1Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received November 10, 2018; final manuscript received June 18, 2019; published online July 15, 2019. Assoc. Editor: Yit Fatt Yap.
J. Thermal Sci. Eng. Appl. Aug 2019, 11(4): 041014 (16 pages)
Published Online: July 15, 2019
Article history
Received:
November 10, 2018
Revised:
June 18, 2019
Citation
Umavathi, J. C., and Chamkha, A. J. (July 15, 2019). "Stability Analysis of Cross Diffusion for the Walters B Fluid Model Saturated With Permeable Nanofluid." ASME. J. Thermal Sci. Eng. Appl. August 2019; 11(4): 041014. https://doi.org/10.1115/1.4044078
Download citation file:
Get Email Alerts
Cited By
Design Optimization of a Shell-and-Tube Heat Exchanger based on Variable Baffle Cuts and Sizing
J. Thermal Sci. Eng. Appl
Related Articles
Onset of Convection in a Porous Medium Layer Saturated With an Oldroyd-B Nanofluid
J. Heat Transfer (January,2017)
Stability Analysis of Binary Casson Nanofluid Convection With Viscosity and Conductivity Variations Using Darcy–Brinkman Model
J. Heat Transfer (December,2022)
Instability
of Nanofluids in Natural Convection
J. Heat Transfer (July,2008)
Free Convection Boundary Layer Flow Past a Horizontal Flat Plate Embedded in a Porous Medium Filled With a Nanofluid
J. Heat Transfer (September,2011)
Related Proceedings Papers
Related Chapters
An Approach for Optimizing Thermal Conductivity in Nanofluids
Inaugural US-EU-China Thermophysics Conference-Renewable Energy 2009 (UECTC 2009 Proceedings)
Study on the Dispersion Stability Influencing Factors of Nanofluids
Inaugural US-EU-China Thermophysics Conference-Renewable Energy 2009 (UECTC 2009 Proceedings)
Heat Transfer Characteristics of CNT-Heat Transfer Oil Nanofluid Flow Inside Helically Coiled Tubes under Uniform Wall Tempoerature Condition
International Conference on Computer and Electrical Engineering 4th (ICCEE 2011)