Qualification: 
Ph.D, MSc
k_shailendhra@cb.amrita.edu

Dr. Shailendhra K. currently serves as Associate Professor in the Department of Mathematics, Amrita School of Engineering, Coimbatore campus. He also heads the Dept. of Students’ Welfare which guides and coordinates the students, campus activities and helps them solve their academic and non academic problems. It is a bridge between the parents and the teachers, and offers counseling to students with low motivation levels and poor academic records. It ensures and sustains an academically friendly, quiet and career-driven atmosphere in the campus where achievers thrive.

Dr. Shailendhra K. is a recipient of Young Scientist Award from Indian Science Congress Association in 1994. He has published eleven papers and presented nine papers in conferences. He is a reviewer of many journals such as Journal of Physics D : Applied Physics (IOP UK), Physics Scripta (IOP UK), International Journal of Computational Science and Engineering (Inder Science UK) and Journal of Applied Fluid Mechanics (Iran). He is also guiding Ph. D. research scholars.

Publications

Publication Type: Journal Article

Year of Publication Title

2019

Gayathri K. and Dr. Shailendhra K., “MRI and Blood Flow in Human Arteries: Are There Any Adverse Effects?”, Cardiovasc Eng Technol, vol. 10, no. 2, pp. 242-256, 2019.[Abstract]


PURPOSE: To explore if there are any adverse effects on blood flow in human beings when they are exposed to high or ultra high intensity magnetic fields in MRI, by investigating both qualitatively and quantitatively the effects of such fields on the velocity of blood and medically significant hemodynamic wall parameters such as wall shear stress (WSS), oscillatory shear index (OSI) and relative residence time (RRT) in four human large arteries.

METHODS: Blood flow in an artery is approximated as a flow through a uniform circular tube with rigid porous walls and the well-known McDonalds model is employed by using pressure gradient waveforms reported in the medical literature.

RESULTS: No significant change in the above parameters is observed up to 3T in all these arteries except a discernible change in the velocity and RRT in the pulmonary artery. Very significant changes are noticed in the above parameters beyond 8T in the pulmonary artery. The common hypothesis that low WSS and high OSI co-locate is not acceptable.

CONCLUSIONS: Our results suggest that the clinical consequences are to be carefully considered before exposing human beings to ultra high field MRI. It may not be appropriate to conclude anything about the effect of magnetic field on blood flow in human beings based on experimental studies on animals, which is one of the reasons for the contradicting reports found in the literature. A slip condition at the wall which is appropriate to hemodynamics is yet to be developed.

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2018

Puvaneswari P. and Dr. Shailendhra K., “A dramatic enhancement of heat transfer in Dream Pipe with viscoelastic fluids”, Journal of Applied Fluid Mechanics, vol. 11, no. 3, pp. 621-635, 2018.[Abstract]


A mathematical investigation on the combined effect of oscillation and conjugation on the enhancement of heat transfer in a heat pipe called Dream Pipe is carried out, when viscoelastic fluids (CPyCl/NaSal) are employed as the heat carriers. Closed-form solutions for the momentum and heat equations are presented. The physical and thermal properties of the polymer solution used are obtained by experiments. The effects of thermal conductivity and thickness of the wall, fluid thickness, Womersley number (α), Deborah number and Prandtl number on the enhancement of heat transfer are examined. Results obtained in the present analysis are in excellent agreement with those of the existing literature. The effective thermal diffusivity (κe) is maximized at optimum α where the fluid flow exhibits a resonant behavior. Several maxima occur in κe for several resonant frequencies and the dramatic increase in κe due to oscillation for the viscoelastic fluid is 5.63 x 109 times higher than that obtained by the molecular motion. This increase is much higher than that (1.84 x 104 times) obtained for the Newtonian fluid. κe is increased with increasing wall thermal conductivity and thickness in the viscous regime whereas in the elastic regime the effect of conjugation is saturated. In the viscous regime, a maximum increase of 50.63% in κe is obtained by optimizing the wall thickness. Also κe increases with increasing molar ratio of concentrations of counterion to surfactant. A maximum heat flux of 4.54 x 1010 W/m2 is achieved using a viscoelastic fluid with thermally conducting wall and this highest heat flux is 207 times higher than that (2.19 x 108 W/m2) obtained with the Newtonian fluid (liquid metal). Hence, viscoelastic fluids are preferable to liquid metals as working fluids in the Dream Pipe. The new insights gained by the present investigation are useful while designing viscoelastic Dream Pipes and micro channel heat exchangers.

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2018

Gayathri K. and Dr. Shailendhra K., “A mathematical modelling on the effect of high intensity magnetic fields on pulsatile blood flow in human arteries”, International Journal of Bioinformatics Research and Applications (IJBRA), , vol. 14, no. 1/2, 2018.[Abstract]


An attempt is made to investigate whether the static magnetic field (SMF) employed in magnetic resonance imaging (MRI) have any adverse effect on the hemodynamic wall parameters in large arteries or not. With the intention of addressing the controversy in the safety issues during MRI exposure, haemodynamics and pathology of large arteries, such as brachial, femoral and pulmonary artery, are compared by varying the intensity of SMF from high to ultrahigh. To be more medically accurate physiological pressure gradient waveforms taken from cardiology literature were digitised and adequate number of harmonics were extracted in order to represent them as Fourier series. All the medically relevant parameters related to endothelial functioning are significantly affected during the time of exposure to ultrahigh intensity SMF, irrespective of the fact whether the artery is closer or away from the heart. In such fields, the fluctuation of Wall Shear Stress (WSS) vector in pulmonary artery is too severe as inferred from oscillatory shear index (OSI) values. The common hypothesis that low WSS and high OSI colocate is not acceptable both in the absence and the presence of magnetic field. It is also inferred that relative residence time can be considered as a single robust metric to predict the pathogenesis of vascular diseases when OSI is moderate. It is felt that more research is necessary, especially to clarify many existing contradictory results in this regard. The controversial reports in the literature of SMF motivated us to mathematically investigate the possible adverse effects of ultrahigh SMFs on pulsatile blood flow in large human arteries and find the maximum intensity of SMF up to which the blood flow and other medically relevant parameters are not significantly affected.

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2018

Gayathri K. and Dr. Shailendhra K., “Mathematical investigation of aetiology and pathogenesis of atherosclerosis in human arteries”, International Journal of Bioinformatics Research and Applications (IJBRA), vol. 14, no. 1/2, 2018.[Abstract]


To understand the role of medically significant hemodynamic wall parameters in the pathogenesis of vascular diseases, pulsatile blood flow in large human arteries of systemic, pulmonary and coronary circulation is investigated by mathematical modelling. To be medically realistic, the pressure gradient waveforms reported in the cardiology literature for the arteries considered are digitised and developed in Fourier series (McDonald's model). Three objectives of the article are to (i) compare qualitatively and quantitatively the pulsatile blood flow between the parallel plate and circular geometry, (ii) compare the hemodynamic wall parameters in the three major circulations mentioned above to gain new medical or physiological insights and (iii) understand if slip at the wall has significant influence on the hemodynamic wall parameters. Our model is reliable since the results obtained here through exact solutions are in great agreement with those reported in the medical literature. New insights gained from our study, documented here for the first time in the hemodynamic literature, are as follows: parallel plate geometry approximation is not reliable quantitatively; larger the radius (Womersley number), larger is the value of relative residence time and hence, higher the probability for vascular diseases; none of the commonly employed interface conditions are suitable for the hemodynamic studies. Comparing our results with earlier studies, we recommend that future research should focus on developing an interface condition exclusively for haemodynamics. We support the recent understanding that low wall shear stress and high oscillatory shear index need not co-locate. We have rendered new physiological insight for this result.

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2017

Puvaneswari P. and Dr. Shailendhra K., “Study of Conjugate Heat Transfer in Electromagnetic Liquid Metal Dream Pipe”, Archive of Mechanical Engineering, vol. 64, no. 3, pp. 375 - 399, 2017.[Abstract]


The combined effect of conjugation, external magnetic field and oscillation on the enhancement of heat transfer in the laminar flow of liquid metals between parallel plate channels is analyzed. In order to make our results useful to the design engineers, we have considered here only the wall materials that are widely employed in liquid metal heat exchangers. Indeed, all the results obtained through this mathematical investigation are in excellent agreement with the available experimental results. The effective thermal diffusivity κe is increased by 3 · 106 times due to oscillation and that the heat flux as high as 1.5 · 1010 (W/m2 ) can be achieved. Based on our investigation, we have recommended the best choice of liquid metal heat carrier, wall material and its optimum thickness along with the optimum value of the frequency to maximize the heat transfer rate. At the optimum frequency, by choosing a wall of high thermal conductivity and optimum thickness, an increase of 19.98% in κe can be achieved. Our results are directly relevant to the design of a heat transfer device known as electromagnetic dream pipe which is a very recent development.

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2017

Puvaneswari P. and Dr. Shailendhra K., “Enhancement of Heat Transfer in a Laminar Hydromagnetic Flow of a Liquid Metal Past a Thermally Conducting and Oscillating Infinite Flat Plate”, Heat Transfer Asian Research, vol. 46, no. 6, pp. 598-622, 2017.[Abstract]


The combined effects of conjugation and magnetic field on the heat transfer enhancement in a laminar liquid metal flow past a thermally conducting and sinusoidally oscillating infinite flat plate are investigated. The wall materials used are compatible with the liquid metals and are assumed to be of finite thickness. Analytical solutions are obtained for the velocity and the temperature distributions. The combined effects of thermal conductivity, the thickness of the plate, and the transverse magnetic field on the net heat flux transported are analyzed in detail and it is found that such effects are same as those on the transverse temperature gradient at any frequency. Due to oscillation, the heat flux is enhanced by O(103). The optimum value of wall thickness and the corresponding boundary layer thickness for which the maximum heat flux is obtained are reported. The heat flux transported can be increased by choosing a wall of low thermal conductivity. A maximum increase of 52.03% in heat flux can be achieved by optimizing the wall thickness. These information may be useful while designing magnetohydrodynamic liquid metal heat transfer systems. All the results obtained are in good agreement with the results reported earlier.

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2016

P. Puvaneswari and Dr. Shailendhra K., “Enhancement of heat transfer in a liquid metal flow past a thermally conducting and oscillating infinite flat plate”, Journal of Applied Fluid Mechanics, vol. 9, pp. 1395-1407, 2016.[Abstract]


The effect of conjugation on the enhancement of heat transfer in a liquid metal flow past a thermally conducting and sinusoidally oscillating infinite flat plate, when a constant temperature gradient is superimposed on the fluid, is investigated. The plate is made up of the materials compatible with the liquid metals used and is considered to be of finite thickness. Analytical solutions for the velocity and the temperature of the fluid and the solid are obtained. The effects of thermal conductivity and the thickness of the plate on the total time averaged heat flux transported and the thermal boundary layer thickness are investigated in detail. It is found that the effects of wall thickness and wall thermal conductivity on the heat flux transported depend on their effects on the transverse temperature gradient at any frequency. The optimum value of wall thickness at which the net heat flux transported attains the maximum value, for each fluid and for each wall material under consideration, is reported. A maximum increase of 46.14%in the heat flux transported can be achieved by optimizing the wall thickness. A maximum convective heat flux of 1:87×108W/m2 is achieved using Na with AISI 316 wall. All the results obtained have been compared with the experimental and analytical results reported in the literature and are found to be in good agreement. It is believed that the new insights gained will be of significant use while designing liquid metal heat transfer systems.

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2014

K. Gayathri and Dr. Shailendhra K., “Pulsatile blood flow in large arteries: Comparative study of Burton's and McDonald's models”, Applied Mathematics and Mechanics (English Edition), vol. 35, pp. 575-590, 2014.[Abstract]


To get a clear picture of the pulsatile nature of blood flow and its role in the pathogenesis of atherosclerosis, a comparative study of blood flow in large arteries is carried out using the two widely used models, McDonald's and Burton's models, for the pressure gradient. For both models, the blood velocity in the lumen is obtained analytically. Elaborate investigations on the wall shear stress (WSS) and oscillatory shear index (OSI) are carried out. The results are in good agreement with the available data in the literature. The superiority of McDonald's model in capturing the pulsatile nature of blood flow, especially the OSI, is highlighted. The present investigation supports the hypothesis that not only WSS but also OSI are the essential features determining the pathogenesis of atherosclerosis. Finally, by reviewing the limitations of the present investigation, the possibility of improvement is explored. © 2014 Shanghai University and Springer-Verlag Berlin Heidelberg.

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2013

Dr. Shailendhra K. and Ramakrishnan, K., “Hydromagnetic Blood flow through a Uniform Channel With Permeable Walls Covered by Porous Media of Finite Thicknes”, Journal of Applied Fluid Mechanics (Iran), vol. 6, no. 1, pp. 39-47, 2013.[Abstract]


The effects of Hartmann number, porous parameter and Darcy velocity on the steady flow of a viscous incompressible slightly conducting fluid through a uniform channel bounded by porous media of finite thickness under a uniform ransverse magnetic field are considered. It is assumed that the thickness of the porous media is much smaller than the width of the flow channel as in the case of blood flow in arteries and accordingly the BJR slip boundary condition has been employed. The effects of all the above parameters on the axial velocity of the flow and the shear stress have been investigated. Finally, these results are compared with a earlier problem of MHD flow through a uniform channel covered by porous media of infinite thickness where the BJ slip boundary condition has been employed. More »»

2012

Dr. Shailendhra K., Ramesan, C. V., and Devi, S. P. Anjali, “Hall effect on unsteady MHD free convection flow past an impulsively started porous plate with viscous and Joule’s dissipation”, International Journal of Science and Engineering Investigations (India), vol. 1, no. 6, pp. 64-71, 2012.

2011

K. Ramakrishnan and Dr. Shailendhra K., “Hydromagnetic flow through uniform channel bounded by porous media”, Applied Mathematics and Mechanics, vol. 32, no. 7, pp. 837–846, 2011.[Abstract]


The combined effects of the magnetic field, permeable walls, Darcy velocity, and slip parameter on the steady flow of a fluid in a channel of uniform width are studied. The fluid flowing in the channel is assumed to be homogeneous, incompressible, and Newtonian. Analytical solutions are constructed for the governing equations using Beavers-Joseph slip boundary conditions. Effects of the magnetic field, permeability, Darcy velocity, and slip parameter on the axial velocity, slip velocity, and shear stress are discussed in detail. It is shown that the Hartmann number, Darcy velocity, porous parameter, and slip parameter play a vital role in altering the flow and in turn the shear stress. More »»

2011

A. Devi S. Parthasarathy, Dr. Shailendhra K., and T., H. P., “Pulsated convective MHD flow with Hall current, heat source and viscous dissipation along a vertical porous plate”, International Journal of Applied Mathematics and Computation, vol. 3, pp. 141-150, 2011.[Abstract]


The convective MHD flow past a uniformly moving infinite vertical porous plate with Hall current, viscous dissipation, heat source and variable suction has been analyzed. The free stream velocity oscillates about a mean value. A pulsated suction is taken into account. Analytical solutions are obtained using perturbation method. The effects of Hall current over primary velocity, secondary velocity, and heat transfer amplitude and phase are analyzed. Effects of heat source parameter, Eckert number, and Prandtl number on the velocity components and temperature are also examined. More »»

2011

Dr. Shailendhra K. and Devi, S. PbAnjali, “On the enhanced heat transfer in the oscillatory flow of liquid metals”, Journal of Applied Fluid Mechanics, vol. 4, no. 3, pp. 57-62, 2011.[Abstract]


The enhanced heat transfer in the oscillatory flow of liquid metals between two thermally insulated infinite parallel plates, when a constant axial temperature gradient superimposed, is investigated. The fluid is set to oscillation by oscillating both the plates axially along with an axial oscillatory body force, having the same frequency as that of the plates. The effective average thermal diffusivity is calculated and the effect of oscillation of the plates and the oscillatory body force on the enhancement of heat transfer are discussed and compared. More »»

2007

Dr. Shailendhra K., “On the definition of equivalence relations”, Mathematics Education, no. 2, pp. 107-109, 2007.

1997

S. P. Anjali Devi and Dr. Shailendhra K., “Heat transport along an oscillating flat plate in the presence of a transverse magnetic field”, International Journal of Heat and Mass Transfer, vol. 40, no. 2, pp. 498-501, 1997.[Abstract]


In recent years, several investigations were carried out to study the characteristics of a novel heat transport mode in which heat is transported from a hot to a cold reservoir by means of sinusoidal oscillations of a viscous fluid contained within open-ended tubes connecting the reservoirs. It has been experimentally[1] and analytically [2] confirmed that such periodic longitudinal oscillations result in a very significant enhancement in axial transport capability of the fluid. More »»

1994

S. P. Anjali Devi, Dr. Shailendhra K., and Kavunthi, S., “Hydromagnetic flow due to torsional and longitudinal oscillation of a cylinder”, Far East Journal of Mathematical Sciences , vol. 2, pp. 149-162, 1994.

Publication Type: Conference Proceedings

Year of Publication Title

2016

V. Thiagarajan, Purushothaman, R. K., ,, Dr. Shailendhra K., and Gayathri K., “Pulsatile blood flow through large arteries with BJR slip condition”, 2016 International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT). IEEE, Chennai, India, 2016.[Abstract]


Hemodynamics in large human arteries, both in systemic and pulmonary circulation, is analysed. To the best of our knowledge, in pulsatile flow, this is the first theoretical study elaborating on hemodynamic factors such as Wall Shear Stress, Oscillatory Shear Index, Relative Residence Time and their effects on the pathogenesis of atherosclerosis by employing BJR slip at the lumen-wall interface, which takes into account the finite wall thickness of the artery. Also, the physiological pressure gradient waveform taken from the medical literature is modeled realistically by using McDonald's model. All the results reported are in good agreement with the data given in the available medical literature. Our model can predict the biological response of the artery in the normal/abnormal flow regime in a much better way, if the data fixed are subject specific. Our results confirm that low WSS and high OSI need not co-locate and also, explain the significances of OSI and RRT in the formation of atherosclerosis. Further, it emphasizes the need for the appropriate slip condition at the lumen-wall interface in the context of blood flow.

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Publication Type: Conference Paper

Year of Publication Title

2006

K. Ramakrishnan and Dr. Shailendhra K., “Hydromagnetic blood flow through a straight channel with permeable walls covered by porous media”, in Applications of Mathematics in Biotechnology and Managerial Sciences, 2006.

2006

Dr. Shailendhra K., “Application of Z-transform in finding some finite sums”, in Anual Conference of Kerala Mathematical Society, Kerala, 2006.

2005

Dr. Shailendhra K. and Devi, S. P. Anjali, “Temporal and spatial distribution of heat flux in oscillating MHD flow subjected to an axial temperature gradient”, in International Conference on Recent Advances in Mathematics, India, 2005.

Publication Type: Thesis

Year of Publication Title

2002

Dr. Shailendhra K., “Studies on unsteady and enhanced heat transfer in MHD Flows”, Bharathiar , 2002.