Onset of internally heated convection in a porous layer with variable gravity: a brinkmann model
Keywords:
linear stability, porous layer, variable gravityAbstract
The influence of heat source, and variable gravity field on the stability of convective
phenomena in a porous layer is investigated numerically by considering brinkmann’s
model. Three types of gravity variations, such as, linear, parabolic, and cubic functions
are considered. For linear theory, the method of normal modes has been employed to
solve governing dimensionless equations which led an eigenvalue problem. The onset
of convection is delayed by increasing Darcy number and gravity variation parameter.
An enhancement of internal heat source makes the system unstable.
Downloads
References
C.W. Horton, and F.T. Rogers, Convection Currents in a Porous Medium, J. Appl.
Phys., 16, (1945) 367370.
E.R. Lapwood, Convection of a Fluid in a Porous Medium, Proc. Cambridge
Philos. Soc., 44 , (1948) 508521.
B. S. Bhadauria, P. G. Siddheshwar, Jogendra Kumar and Om P. Suthar,
Weakly Nonlinear Stability Analysis of Temperature/Gravity-Modulated Stationary
RayleighBnard Convection in a Rotating Porous Medium, Transp Porous Med
, (2012) 633-647.
G. M. Homsy and A. E. Sherwood, Convective Instabilities in Porous Media with
Through Flow, AlChE Journal 22(1), (1976) 168-174.
D. A. Nield, and A. Bejan , Convection in porous media, (Springer, New York,
110-113.
J.W. Elder, , Steady free convection in a porous medium heated from below, Journal
of Fluid Mechanics, 27(1), (1967) 29-48.
D.A. Nield and A.V. Kuznetsov, Thermal instability in a porous medium layer
saturated by a nanofluid: A revised model, International Journal of Heat and Mass
Transfer, 68, (2014) 211-214.
D. A. Nield, Convection in a porous medium with inclined temperature gradient
and vertical throughflow, Int. J. Heat Mass Transfer, 41(1), (1998) 241-243.
S. P Suma and Y. H Gangadharaiah , R. Indira , Effect of throughflow and variable
gravity field on thermal convection in a porous layer, International Journal of
Engineering Science and Technology, 3(10), (2011) 7657-7668.
Seema Kumari and P. V. S. N. Murthy, Convective Stability of Vertical Throughflow
of a Non-Newtonian Fluid in a Porous Channel with Soret Effect, Transp
Porous Med, 122, (2018) 125-143.
A. Benerji Babu, Ragoju Ravi and S.G. Tagare Nonlinear rotating convection in
a sparsely packed porous medium, Commun Nonlinear Sci Numer Simulat 17,
(2012) 5042-5063.
Dhananjay Yadav, Numerical investigation of the combined impact of variable
gravity field and throughflow on the onset of convective motion in a porous
medium layer, International Communications in Heat and Mass Transfer 108,
(2019) 104274.
Dhananjay Yadav, Effects of rotation and varying gravity on the onset of convection
in a porous medium layer: a numerical study, World Journal of Engineering,
(6), (2020) 785-793.
Ragoju. Ravi, C. Kanchana and P. G. Ssddheshwar, Effects of second diffusing
component and cross diffusion on primary and secondary thermoconvective instabilities
in couple stress liquids, Appl. Math. Mech. Engl. Ed., 38(11), (2017)
-1600
Ragoju Ravi, C. Kanchana and G. Janardhana Reddy, and Hussain Basha, Study
of Soret and Dufour effects and secondary instabilities on Rayleigh-Benard convection
in a couple stress fluid, Eur. Phys. J. Plus 133:513, (2018) 1-14.
A.V.Kuznetsov and D.A. Nield, The onset of double-diffusive nanofluid convection
in a layer of saturated porous medium, Transport in Porous Media, 85, (2010)
-951.
A.V.Kuznetsov and D.A. Nield, Thermal instability in a porous medium layer
saturated by a nanofluid: Brinkman Model, Transport in Porous Media, 81, (2010)
-422.
A.V.Kuznetsov and D.A. Nield, Effect of local thermal non-equilibrium on the
onset of convection in a porous medium layer saturated by a nanofluid, Transport
in Porous Media, 83, (2010) 425-436.
G. K. Pradhan and P. C. Samal, Thermal Stability of a Fluid Layer under Variable
Body Forces, Journal of mathematical analysis and applications, 122, (1987) 487-
A. J. Harfash and A. K. Alshara, Chemical reaction effect on double diffusive
convection in porous media with magnetic and variable gravity effects, Korean J.
Chem. Eng., 32(6), (2015), 1046-1059.
S. Rionero and B . Straughani, Convection in a porous medium with internal heat
source and variable gravity effects, int. J. Engng. Sci., 28(6), (1990) 497-503.
Brian Straughan, Convection in a Variable Gravity Field, Journal of mathematical
analysis and applications, 140, (1989) 467-475.
A. J. Harfash, Three-Dimensional Simulations for Convection in a Porous
Medium with Internal Heat Source and Variable Gravity Effects, Transp Porous
Med, 101, (2014) 281-297.
N. Deepika and P. A. L. Narayana, Effects of Vertical Throughflow and Variable
Gravity on HadleyPrats Flow in a Porous Medium, Transp Porous Med, 109,
(2015) 455-468.
U.S. Mahabaleshwar , D. Basavaraja , S. Wang , G. Lorenzini and E. Lorenzini,
Convection in a porous medium with variable internal heat source and variable
gravity, International Journal of Heat and Mass Transfer, 111, (2017) 651-656.
Ramesh Chand, G. C. Rana and S. K. Kango, Effect of Variable Gravity on Thermal
Instability of Rotating Nanofluid in Porous Medium, FME Transactions 43,
(2015) 62-69.
Amit Mahajan and Monika Arora, Convection in rotating magnetic nanofluids,
Applied Mathematics and Computation, 219, 62846296, (2013) 6284-6294.
Amit Mahajan and Mahesh Kumar Sharma, The onset of convection in a magnetic
nanofluid layer with variable gravity effects, Applied Mathematics and Computation,
, (2018) 622-635.
P.N. Kaloni and Zongchun Qiao, Non-linear convection in a porous medium with
inclined temperature gradient and variable gravity effects, International Journal
of Heat and Mass Transfer 44, (2001) 1585-1591.
S. M. Alex and P. R. Patil, Effect of variable gravity field on soret driven thermosolutal
convection in a porous medium, Int. Comm. Hear Mass Transfec,
(4), (2001) 509-518.
S, M. Alex, P. R.Patil and Vankatakrishan, K.S., Variable gravity effects on thermal
instability in a porous medium with internal heat source and inclined temperature
gradient, Fluid Dynamics Research, 29, (2001) 1-6.
Dhananjay Yadav, The onset of Darcy-Brinkman convection in a porous medium
layer with vertical throughflow and variable gravity field effects, Heat Transfer,
(5), (2020) 1-10.
S. M. Alex and P.R. Patil, Effect of a variable gravity field on convection in an
anisotropic porous medium with an internal heat source and inclined temperature
gradient, J. Heat Transf. 124(1), (2002) 144-150.
Ramesh Chand, G.C Rana and S. Kumar, Variable gravity effects on thermal instability
of nanofluid in anisotropic porous medium, Int. J. of Appl. Mech. and
Engg., 18(3), (2013) 631-642.
Dhananjay Yadav, The density-driven nanofluid convection in an anisotropic
porous medium layer with rotation and variable gravity field: a numerical investigation,
Journal of Applied and Computational Mechanics, 6, (2020) 699-710.
Dhananjay Yadav, Numerical solution of the onset of buoyancy-driven nanofluid
convective motion in an anisotropic porous medium layer with variable gravity
and internal heating, Heat Transfer, 49(3), (2020) 1170-1191.
Ramesh Chand, Thermal instability of rotating Maxwell visco-elastic fluid with
variable gravity in porous medium, Journal of the Indian Math. Soc., 80, (2013)
-31.
Ramesh Chand, Effect of suspended particles on thermal instability of Maxwell
visco-elastic fluid with variable gravity in porous medium, Antarctica J. Math,
(6), (2011) 487-497.
Reddy, G. S. K., and Ragoju, R. Thermal instability of a powerlaw fluidsaturated
porous layer with an internal heat source and vertical throughflow, (accepted for
publication), Heat Transfer.
Reddy, G. S. K., and Ravi, R. Thermal instability of a Maxwell fluid saturated
porous layer with chemical reaction, (accepted for publication), Special Topics
and Reviews in Porous Media.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.