Dr. Shankar B M
Professor
 Teaching
About
Dr. B M Shankar is affiliated with the Department of Science and Humanities, PES University, where he works as a Professor of Mathematics. He has authored and coauthored several international publications and also worked as a reviewer for reputed professional journals. He has an active association with different societies and academies around the world. B M S's major research interests involve applied mathematics, hydrodynamic stability, fluid mechanics, and convection in porous media.
Associate Professor, PES University, 2018  2024
Assistant Professor, PES University, 2014  2018
Assistant Professor, PES Institute of Technology, 2011  2014
Professor, PES University, 2024  Till date
Junior Research Fellow in ISRO Respond Project. September 8, 2008  September 7,2010
Senior Research Fellow in ISRO Respond Project. September 8, 2010  August 11, 2011
One of my research articles entitled "Stability of doublediffusive natural convection in a vertical fluid layer" was chosen as the Editor's pick for the journal Physics of Fluids (2021).
Selected as an Editorial Advisory Board for Heat TransferWiley (2022)
Received "Award for Outstanding Research Publication" from Vision Group of Science and Technology (VGST), Government of Karnataka (20222023).
Selected as an Editorial Board Member for Discover Molecules, Springer Nature (2024)
Teaching Master of Technology and Bachelor of Technology Courses since 2011.
Faculty Adviser
Doctoral Committee Member
Student Welfare Coordinator
Test Coordinator
Atmatrisha Chief Coordinator
Anchor Teacher
Sports Coordinator
Hydrodynamic stability
Applied and Computational Mathematics
PES Internal Funding Project "Instability mechanism of magnetic nanofluids in a nonisothermal convective flow"

1. S.B. Naveen, B.M. Shankar, I.S. Shivakumara, Stability of natural convection in a vertical anisotropic porous channel with oblique principal axes under thermal nonequilibrium conditions, Proceedings of ICAFD 2018, Kumar et al (Eds.): Advances in Fluid Dynamics, Lecture Notes in Mechanical Engineering, pp. 641652, 2021.

2. S. Prema, B.M. Shankar, K.N. Seetharamu, Convection heat transfer in a porous medium saturated with an Oldroyd B fluid  A Review, International Conference on Thermofluids and Energy Systems (ICTES2019), Journal of Physics Conference Series 1473, pp. 012029, 2020.

3. B.M. Shankar, Jai Kumar, I.S. Shivakumara, Numerical investigation of EHD instability of natural convection in a vertical dielectric fluid saturated anisotropic porous layer, Proceedings of 4th Thermal and Fluids Engineering Conference, ASTFE Digital Library, USA, pp. 10611070, 2019.

B.M. Shankar, N. Rudraiah, Effect of Coriolis force and electric field on electrohydrodynamic stability of poorly conducting couple stress parallel fluid flow through a porous channel, Proceedings of 13 th Asian Congress Fluid Mechanics, Dhaka, Bangladesh, Section 7.0, pp. 493496, 2010.

B.M. Shankar, N. Rudraiah, Effects of electric field and Coriolis force on electrohydrodynamic stability of poorly conducting couple stress parallel fluid flow in a channel, Proceedings of 5 th INTERNATIONAL CONFERENCE ON THE FRONTIERS OF PLASMA PHYSICS AND TECHNOLOGY, Singapore, pp. 119, 2011. Journals
B.M. Shankar, I.S. Shivakumara, Benchmark solution for the stability of plane Couette flow with net throughflow. Scientific Reports 11, pp. 10901111, 2021.
B.M. Shankar, I.S. Shivakumara, Instability of natural convection in a vertical fluid layer with net horizontal throughflow. Zeitschrift fur angewandte Mathematik und Physik 72, pp. 89117, 2021.
B.M. Shankar, Jai Kumar, I.S. Shivakumara, Numerical investigation of the stability of mixed convection in a differentially heated vertical porous slab. Applied Mathematics and Computation 389, pp. 125486111, 2021.
B.M. Shankar, I.S. Shivakumara, Stability of Poiseuille flow in an anisotropic porous layer with oblique principal axes: More accurate solution. Zeitschrift fur angewandte Mathematik und Mechanik 101, pp. e201900264115, 2021.
B.M. Shankar, I.S. Shivakumara, Jai Kumar, Benchmark solution for the hydrodynamic stability of plane porousCouette flow. Physics of Fluids 32, pp. 104104111, 2020.
B.M. Shankar, I.S. Shivakumara, S.B. Naveen, Impact of thermal nonequilibrium on the stability of natural convection in an OldroydB fluidsaturated vertical porous layer with internal heat sources. Transport in Porous Media 133, pp. 437458, 2020.
S.B. Naveen, B.M. Shankar, I.S. Shivakumara, Finite DarcyPrandtl number and maximum density effects on Gill's stability problem. ASMEJournal of Heat Transfer 142, pp. 10260118, 2020.
B.M. Shankar, I.S. Shivakumara, Stability of porousPoiseuille flow with uniform vertical throughflow: High accurate solution. Physics of Fluids 32, pp. 04410119, 2020.
S.B. Naveen Kumar, I.S. Shivakumara, B.M. Shankar, Linear and weakly nonlinear doublediffusive magnetoconvection in a nonNewtonian fluid layer. Microgravity Science and Technology 32, pp. 629646, 2020.
Kh.S. Mekheimer, B.M. Shankar, R.E. AboElkhair, Effects of hall current and permeability on the stability of peristaltic flow. SN Applied Sciences 1, pp. 161019, 2019.
B.M. Shankar, Jai Kumar, I.S. Shivakumara, S.B. Naveen Kumar, MHD instability of pressuredriven flow of a nonNewtonian fluid. SN Applied Sciences 1, pp. 1523111, 2019.
B.M. Shankar, Jai Kumar, I.S. Shivakumara, Stability of mixed convection in a differentially heated vertical fluid layer with internal heat sources. Fluid Dynamics Research 51, pp. 055501130, 2019.
S.B. Naveen Kumar, I.S. Shivakumara, B.M. Shankar, Exploration of Coriolis force on the linear stability of couple stress fluid flow induced by double diffusive convection. ASMEJournal of Heat Transfer 141, pp. 122502111, 2019.
N. Rudraiah, B.M. Shankar, C.O. Ng, Electrohydrodynamic stability of couple stress fluid flow in a channel occupied by a porous medium. Special Topics and Reviews in Porous Media 2, pp. 1122, 2011.
B.M. Shankar, Jai Kumar, I.S. Shivakumara, C.O. Ng, Stability of fluid flow in a Brinkman porous medium  A numerical study*. Journal of Hydrodynamics 26, pp. 681688, 2014.
B.M. Shankar, Jai Kumar, I.S. Shivakumara, Stability of natural convection in a vertical couple stress fluid layer. International Journal of Heat and Mass Transfer 78, pp. 447459, 2014
B.M. Shankar, Jai Kumar, I.S. Shivakumara, S.B. Naveen Kumar, Effect of horizontal AC electric field on the stability of natural convection in a vertical dielectric fluid layer. Journal of Applied Fluid Mechanics 9, pp. 30733086, 2016
B.M. Shankar, Jai Kumar, I.S. Shivakumara, S.B. Naveen Kumar, Effect of horizontal AC electric field on the stability of natural convection in a vertical dielectric fluid layer. Journal of Applied Fluid Mechanics 9, pp. 30733086, 2016
B.M. Shankar, Jai Kumar, I.S. Shivakumara, S.B. Naveen Kumar, Effect of horizontal AC electric field on the stability of natural convection in a vertical dielectric fluid layer. Journal of Applied Fluid Mechanics 9, pp. 30733086, 2016
B.M. Shankar, I.S. Shivakumara, C.O. Ng, Stability of couple stress fluid flow through a horizontal porous layer. Journal of Porous Media 19, pp. 391404, 2016
B.M. Shankar, Jai Kumar, I.S. Shivakumara, Stability of natural convection in a vertical layer of Brinkman porous medium. Acta Mechanica 228, pp. 119, 2017.
B.M. Shankar, I.S. Shivakumara, Effect of local thermal nonequilibrium on the stability of natural convection in an OldroydB fluid saturated vertical porous layer. ASMEJournal of Heat Transfer 139, pp. 041001110, 2017.
B.M. Shankar, I.S. Shivakumara, On the stability of natural convection in a porous vertical slab saturated with an OldroydB fluid. Theoretical and Computational Fluid Dynamics 31, pp. 221231, 2017.
B.M. Shankar, Jai Kumar, I.S. Shivakumara, Magnetohydrodynamic stability of natural convection in a vertical porous slab. Journal of Magnetism and Magnetic Materials 421, pp. 152164, 2017.
B.M. Shankar, Jai Kumar, I.S. Shivakumara, Boundary and inertia effects on the stability of natural convection in a vertical layer of an anisotropic LapwoodBrinkman porous medium. Acta Mechanica 228, pp. 22692282, 2017.
B.M. Shankar, Jai Kumar, I.S. Shivakumara, Numerical investigation of electrohydrodynamic instability in a vertical porous layer. Applied Mathematics and Computation 310, pp. 1539, 2017
B.M. Shankar, Jai Kumar, I.S. Shivakumara, Stability of natural convection in a vertical dielectric couple stress fluid layer in the presence of a horizontal ac electric field. Applied Mathematical Modelling 40, pp. 54625481, 2016.
B.M. Shankar, Jai Kumar, I.S. Shivakumara, Stability of natural convection in a vertical dielectric couple stress fluid layer in the presence of a horizontal ac electric field. Applied Mathematical Modelling 40, pp. 54625481, 2016.
B.M. Shankar, I.S. Shivakumara, Magnetohydrodynamic stability of pressuredriven flow in an anisotropic porous channel: Accurate solution. Applied Mathematics and Computation 321, pp. 752767, 2018.
B.M. Shankar, I.S. Shivakumara, Stability of penetrative natural convection in a nonNewtonian fluidsaturated vertical porous layer. Transport in Porous Media 124, pp. 395411, 2018.
B.M. Shankar, Jai Kumar, I.S. Shivakumara, Magnetohydrodynamic instability of mixed convection in a differentially heated vertical channel. The European Physical Journal Plus, 134, pp. 5364, 2019.
K.S. Mekheimer, B.M. Shankar, S.F. Ramadan, H.E. Mallik, M.S. Mohamed, On the stability of convection in a nonNewtonian vertical fluid layer in the presence of gold nanoparticles: drug agent for thermotherapy. Mathematics 9, pp. 1302115, 2021.
C. Hemanthkumar, I.S. Shivakumara, B.M. Shankar, G. Pallavi, Exploration of anisotropy on nonlinear stability of thermohaline viscoelastic porous convection. International Communications in Heat and Mass Transfer 126, pp. 105427115, 2021.
B.M. Shankar, I.S. Shivakumara, Changes in the hydrodynamic stability of plane porousCouette flow due to vertical throughflow. Physics of Fluids 33, pp. 074103113, 2021.
C. Hemanthkumar, I.S. Shivakumara, B.M. Shankar, G. Pallavi, Horizontal pressure gradient and Soret effects on the onset of thermosolutal porous convection. Heat Transfer 50, pp. 82048223, 2021.
B.M. Shankar, Jai Kumar, I.S. Shivakumara, Stability of doublediffusive natural convection in a vertical fluid layer. Physics of Fluids 33, pp. 094113115, 2021.
B.M. Shankar, I.S. Shivakumara, S.B. Naveen, Density maximum and finite DarcyPrandtl number outlooks on Gill's stability problem subject to a lack of thermal equilibrium. Physics of Fluids 33, pp. 124108116, 2021.
B.M. Shankar, S.B. Naveen, I.S. Shivakumara, Stability of doublediffusive natural convection in a vertical porous layer. Transport in Porous Media 141, pp. 87105, 2022.
C. Hemanth Kumar, B.M. Shankar, I.S. Shivakumara, Thermosolutal LTNE porous mixed convection under the influence of the Soret effect. ASMEJournal of Heat Transfer 144, pp. 042602112, 2022.
I.S. Shivakumara, B.M. Shankar, S.B. Naveen Kumar, On the stability of thermosolutal rotating porous convection subject to a lack of thermal equilibrium. International Communications in Heat and Mass Transfer 133, pp. 105928118, 2022.
C. Hemanth Kumar, B.M. Shankar, I.S. Shivakumara, Weakly nonlinear stability of thermosolutal convection in an OldroydB fluidsaturated anisotropic porous layer using a local thermal nonequilibrium model. ASMEJournal of Heat Transfer 144, pp. 072701118, 2022.
B.M. Shankar, I.S. Shivakumara, Gill's stability problem may be unstable with horizontal heterogeneity in permeability. Journal of Fluid Mechanics 943, pp. A20121, 2022.
B.M. Shankar, K.V. Nagamani, I.S. Shivakumara, The role of a second diffusing component on the GillRees stability problem. Scientific Reports 12, pp. 19326118, 2022.
K.V. Nagamani, B.M. Shankar, I.S. Shivakumara, Maximum density perspectives on the stability of Brinkman porous convection in a vertical channel. Physics of Fluids 35, pp. 014110115, 2023.
B.M. Shankar, I.S. Shivakumara, Stability of natural convection in a vertical layer of NavierStokesVoigt fluid. International Communications in Heat and Mass Transfer 144, pp. 10678319, 2023.
K.V. Nagamani, B.M. Shankar, I.S. Shivakumara, The PrandtlDarcy convection in a vertical porous layer may be unstable with internal heating. Transport in Porous Media 148, pp. 417431, 2023.
B.M. Shankar, I.S. Shivakumara, Stability of plane Poiseuille and Couette flows of NavierStokesVoigt fluid. Acta Mechanica 234, pp. 45894609, 2023.
B.M. Shankar, K.V. Nagamani, I.S. Shivakumara, Stability of flow of a variableviscosity fluid saturating a differentially heated vertical porous layer. Transport in Porous Media 150, pp. 114, 2023.
B.M. Shankar, K.V. Nagamani, I.S. Shivakumara, Further thoughts on buoyancyinduced instability of a variable viscosity fluid saturating a porous slab. Physics of Fluids 35, pp. 074106112, 2023.
S.B. Naveen Kumar, B.M. Shankar, N. Latha, I.S. Shivakumara, Instability thresholds for penetrative porous convection with variable viscosity fluids. International Communications in Heat and Mass Transfer 149, pp. 107056112, 2023.
Vinit Kumar Tripathi, B.M. Shankar, Amit Mahajan, I.S. Shivakumara, Global nonlinear stability of bidispersive porous convection with throughflow and depthdependent viscosity. Physics of Fluids 36, pp. 014110119, 2024
B.M. Shankar, I.S. Shivakumara, Imperfectly conducting eigenflows in a vertical fluid layer. Physics of Fluids 36, pp. 034112113, 2024.
G.N. Kavitha, B.M. Shankar, I.S. Shivakumara, On the magnetohydrodynamic stability of channel flow of NavierStokesVoigt fluid. Physics of Fluids 36, pp. 043105113, 2024.
B.M. Shankar, I.S. Shivakumara, Stability of triplediffusive convection in a vertical porous layer. Journal of Fluid Mechanics 989, pp. A8125, 2024.
B.M. Shankar, I.S. Shivakumara, Imperfectly impermeable boundaries and variable viscosity perspectives on the stability of natural convection in a vertical porous layer. Transport in Porous Media 151, pp. 18871901, 2024.
Attended the workshop on Emerging Trends in Green Technologies conducted by Department of Science and Humanities, PES University, Bangalore, during July 57, 2018
Attended the Faculty Development Program on Applications of Differential Equations in Engineering Problems conducted by Department of Science and Humanities, PES University, Bangalore, during July 2022, 2017
Attended Science Academies Lecture workshop on Applications of Differential Equations in Engineering and Biology organized by Department of Mathematics, Sri Venkateswara University, Tirupathi, during March 911, 2017.
Attended the National conference on Recent Advances in Applied Sciences organized by AMC Engineering College and presented the paper entitled Effect of magnetic field on Gill's stability problem held during April 25, 2016.
Attended the National workshop on Advances in Lithium ion Battery Materials organized by Department of Sciences and Humanities, PES University during Dec 28, 2015.
Attended the 5th International conference on the Frontiers of Plasma Physics and technology, Singapore organized in cooperation with International Atomic Energy Agency and presented the paper entitled Effect of electric field and Coriolis force on electrohydrodynamic stability of poorly conducting couple stress parallel fluid flow in a channel held during April 1822, 2011.
Three days national workshop on Elliptical partial differential equations, held at TIFR, Bangalore, during January 47, 2011
Attended the National Workshop on Recent Trends and applications of Fluid Mechanics, organized by Department of Mathematics, Banaras Hindu University, Varanasi, during July 0612, 2010
Attended the National Workshop on Recent Trends and applications of Fluid Mechanics, organized by Department of Mathematics, Banaras Hindu University, Varanasi, during July 0612, 2010
Attended the National Workshop on Recent Trends and applications of Fluid Mechanics, organized by Department of Mathematics, Banaras Hindu University, Varanasi, during July 0612, 2010
National Seminar on Fluid Mechanics, sponsored by UGC, New Delhi under Special Assistance Programme DRS, Gulbarga University, Gulbarga held during March 2435, 2009
International Conference on Frontiers in Fluid Mechanics at UGCCAS in Fluid Mechanics, Department of Mathematics, Bangalore University, Bangalore, during August 31September 2, 2009, presented the paper.
Attended 74th Annual Conference of Indian Mathematical Society held during December 2730, 2008 at University of Allahabad, Allahabad. December 2730, 2008, presented the paper
Attended the National symposium on Mathematics and its Applications organized by Department of Mathematics, Bangalore University, Bangalore and presented the paper entitled Impact of thermal nonequilibrium and internal heating effects on the stability of natural convection in an OldroydB fluid saturated vertical porous layer held during April 27, 2019.
Attended the International Conference on Mathematics and its Applications organized by Department of Mathematics, Bangalore University, Bangalore and presented the paper entitled Stability of pressure driven flow of a nonNewtonian fluid in a horizontal porous channel held during Feb 2829, 2020.
Education
Ph.D, Bangalore University, 2014
Master's degree, Bangalore University, 2008