Abstract
In this study, the impact of changeable internal heat source function on the onset of convective motion in an anisotropic porous matrix is explored, where the flow is controlled by the Brinkman extension of Darcy’s law. We considered three cases of variable internal heat source functions: (a) linear (b) parabolic and (c) cubic. The linear stability analyses and the perturbation procedure are carried out in order to test the system's stability characteristics. Results indicate that the impact of the increasing values of heat source parameter and mechanical anisotropic parameter will enhance the convection of a porous layer system while the increasing of thermal anisotropic parameter and amount of Darcy number will improve to stabilize the system. The system is also found to be more stable for cubic variation of the heat source function and less stable in the case of linear type variation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Mahad BA, Shariff MHBM, Isa M, Aziz ZA (2015) Constitutive model for anterior leaflet of heart with physical invariants. J Adv Res Appl Mech 5(1):15–29
Degan G, Vasseur P (2003) Influence of anisotropy on convection in porous media with nonuniform thermal gradient. Int J Heat Mass Transfer 46:781–789
Suma SP, Gangadharaiah YH, Indira R, Shivakumara IS (2012) Throughflow effects on penetrative convection in superposed fluid and porous layers. Transp. Porous Med. 95:91–110
Shivakumara IS, Suma SP, Indira R, Gangadharaiah YH (2012) Effect of internal heat generation on the onset of Marangoni convection in a fluid layer overlying a layer of an anisotropic porous medium. Transp Porous Media 92:727–743
Gangadharaiah YH (2016) Onset of Benard–Marangoni convection in a composite layers with anisotropic porous material. J Appl Fluid Mech 9:1551–1558
Bhadauria BS (2012) Double diffusive convection in a saturated anisotropic porous layer with internal heat source. Transp Porous Med 9:299–320
Nouri-Borujerdi A, Noghrehabadi AR, Rees DAS (2007) Onset of convection in a horizontal porous channel with uniform heat generation using a thermal nonequilibrium model. Transp Porous Med 69:343–357
Nouri-Borujerdi A, Noghrehabadi AR, Rees DAS (2008) Influence of Darcy number on the onset of convection in porous layer with a uniform heat source. Int J Th Sci 47:1020–1025
Rionero S, Straughan B (1990) Convection in a porous medium with internal heat source and variable gravity effects. Int J Eng Sci 28:497–503
Straughan B (1989) Convection in a variable gravity field. J Appl Math 140:467–475
Mahajan A, Nandal R (2019) Penetrative convection in a fluid saturated Darcy-Brinkman porous media with LTNE via internal heat source. Nonlinear Eng 8:546–58
Mahabaleshwar US, Basavaraja SW, Lorenzini G, Lorenzini E (2017) Convection in a porous medium with variable internal heat source and variable gravity. Int J Heat Mass Transfer 111:651–656
Ananda K, Gangadharaiah YH, Nagarathnamma H (2020) Combined impact of variable internal heat source and variable viscosity onset of convection motion in a porous layer. Malaya J Matematik 8:915–919
Degan G, Vasseur P, Bilgen E (1995) Convective heat transfer in a vertical anisotropic porous layer. Int J Heat Mass Transf 38(11):1975–1987
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Gangadharaiah, Y.H., Kiran, S., Nagarathnamma, H., Ananda, K. (2021). Effect of Variable Heat Source on the Onset of Darcy‐Brinkman Convection in an Anisotropic Porous Medium. In: Manik, G., Kalia, S., Sahoo, S.K., Sharma, T.K., Verma, O.P. (eds) Advances in Mechanical Engineering. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-16-0942-8_40
Download citation
DOI: https://doi.org/10.1007/978-981-16-0942-8_40
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-0941-1
Online ISBN: 978-981-16-0942-8
eBook Packages: EngineeringEngineering (R0)