Numerical solution for heat transfer in a staggered enclosure with wavy insulated baffles

Rashid Mahmood; Nusrat Rehman; Afraz Hussain Majeed; Khalil Ur Rehman; Wasfi Shatanawi; Rashid Mahmood; Nusrat Rehman; Afraz Hussain Majeed; Khalil Ur Rehman; Wasfi Shatanawi

doi:10.3934/math.2023420

AIMS Mathematics

2023, Volume 8, Issue 4: 8332-8348. doi: 10.3934/math.2023420

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Numerical solution for heat transfer in a staggered enclosure with wavy insulated baffles

1.
Faculty of Basic Applied Sciences, Department of Mathematics, Air University, PAF Complex E-9, Islamabad 44000, Pakistan
2.
Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
3.
Department of Mathematics, Air University, PAF Complex E-9, Islamabad 44000, Pakistan
4.
Department of Mathematics, Faculty of Science, The Hashemite University, P.O Box 330127, Zarqa 13133, Jordan

Received: 12 September 2022 Revised: 31 December 2022 Accepted: 09 January 2023 Published: 02 February 2023
MSC : 35A25, 65MO6, 76D05, 76M10

The present study contains examination on partial differential equations narrating heat transfer aspects in magnetized staggered cavity manifested with wavy insulated baffles. The nanoparticles namely Aluminium oxide are suspended in the flow regime within staggered enclosure having purely viscous fluid. The flow is modelled mathematically in terms of partial differential equations and the finite element is used to discretized the flow differential equations. The effects of several parameters such as Hartmann number $ \left(0\le Ha\le 100\right) $, Volume fraction $ \left(0.00\le \phi \le 0.08\right), $ Rayleigh number $ \left({10}^{3}\le Ra\le {10}^{5}\right), $ and angle of inclinaton $ \left({0}^{o}\le \gamma \le {60}^{o}\right) $ on the thermal flow and distribution of nanomaterials for natural convection are inspected. It is calculated how much Ha will affect velocities and isotherms wit h $ Ra = {10}^{4} $ and $ \phi = 0.02 $. With Ha = 20 and $ \phi $ = 0.02, the effect of Ra on velocity and isotherms is also estimated. The average Bejan number and average Nusselt number against Hartmann number are investigated. When the walls move in an opposite direction, line graphs of velocity distribution are created for both the u and v components. The presence of Hartmann number leads to increase in Bejan number while, opposite behavior can be observed in case of average Nusselt number. When the volume fraction is large, the velocity increases significantly. The flow strength is greater when the Rayleigh number is smaller. On the other hand, as Ra drops, or when $ Ra = {10}^{4} $, flow strength drops.
- heat transfer,
- staggered cavity,
- nanomaterials,
- insulated baffles,
- inclined MHD,
- finite element method
Citation: Rashid Mahmood, Nusrat Rehman, Afraz Hussain Majeed, Khalil Ur Rehman, Wasfi Shatanawi. Numerical solution for heat transfer in a staggered enclosure with wavy insulated baffles[J]. AIMS Mathematics, 2023, 8(4): 8332-8348. doi: 10.3934/math.2023420

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Abstract

The present study contains examination on partial differential equations narrating heat transfer aspects in magnetized staggered cavity manifested with wavy insulated baffles. The nanoparticles namely Aluminium oxide are suspended in the flow regime within staggered enclosure having purely viscous fluid. The flow is modelled mathematically in terms of partial differential equations and the finite element is used to discretized the flow differential equations. The effects of several parameters such as Hartmann number $ \left(0\le Ha\le 100\right) $, Volume fraction $ \left(0.00\le \phi \le 0.08\right), $ Rayleigh number $ \left({10}^{3}\le Ra\le {10}^{5}\right), $ and angle of inclinaton $ \left({0}^{o}\le \gamma \le {60}^{o}\right) $ on the thermal flow and distribution of nanomaterials for natural convection are inspected. It is calculated how much Ha will affect velocities and isotherms wit h $ Ra = {10}^{4} $ and $ \phi = 0.02 $. With Ha = 20 and $ \phi $ = 0.02, the effect of Ra on velocity and isotherms is also estimated. The average Bejan number and average Nusselt number against Hartmann number are investigated. When the walls move in an opposite direction, line graphs of velocity distribution are created for both the u and v components. The presence of Hartmann number leads to increase in Bejan number while, opposite behavior can be observed in case of average Nusselt number. When the volume fraction is large, the velocity increases significantly. The flow strength is greater when the Rayleigh number is smaller. On the other hand, as Ra drops, or when $ Ra = {10}^{4} $, flow strength drops.

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