Ph.D, MSc

Dr. Murali Krishna P. currently serves as Assistant Professor (Sr. Gr.) in the Department of Mathematics, School of Engineering, Coimbatore Campus. His areas of research include Finite Element Methods with B-Splines. He has also completed PGDST.


Publication Type: Journal Article

Year of Publication Title


C. Dhivya and Murali Krishna Panthangi, “Quasi-linearized B-spline collocation method for coupled nonlinear boundary value problems”, Journal of Physics: Conference Series, vol. 1139, p. 012083, 2018.[Abstract]

A collocation method with B-splines as shape functions is introduced to solve acoupled system of nonlinear boundary value problems in four unknowns and four equations.The proposed method uses the quasilinearization technique to linearize the nonlinear problems.Based on the order of derivative of each unknown in the given system, the approximation ofeach unknown is expressed as linear combination of B-spline functions of different degree. Uponimposing the boundary conditions to these approximations the shape functions take a new form.With the revised approximation collocation method is implemented for the linearized system.To test the efficiency of the method a real time problem from literature is considered and solvedby the proposed method. Results obtained by the proposed method are in good agreement withthe actual one

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C. Ramreddy and Murali Krishna Panthangi, “Effects of First and Second Order Velocity Slips on Melting Stretching Surface in a Thermally Stratified Nanofluid: Tiwari and Das' Model”, Journal of Nanofluids, vol. 6, pp. 155-163, 2017.[Abstract]

This article emphasizes the heat transfer of thermally stratified nanofluid towards a melting stretching surface with first and second-order velocity slips for the first time. The model used for the nanofluid incorporates the effect of volume fraction parameter. The boundary layer equations governed by a nanofluid, which are partial differential equations of motion and energy, are converted to a set of non-linear ordinary differential equations using a set of non-dimensional transformations. Then the reduced equations are solved numerically using Shooting method along with Runge-Kutta fourth order technique. The interesting features of the results for alumina-water and copper-water nanofluids includes (i) the velocity and temperature reduces but, skin friction and Nusselt number enhances with increase of Melting parameter in the presence and/or absence of stratification, (ii) it can be noticed that for both types of thermally stratified nanofluids, the skin friction enhances and Nusselt number reduces with increase of solid volume fraction parameter , and (iii) the skin friction and heat transfer rate are more with existence of second order velocity slip and are less in the absence of the second order velocity slip for both types of thermally stratified nanofluids.

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Murali Krishna Panthangi, “Fem Based Collocation Method For Solving Eighth Order Boundary Value Problems Using B-Splines”, ARPN Journal of Engineering and Applied Sciences, vol. 11, pp. 13594 – 13598, 2016.[Abstract]

An easy to implement FEM based collocation method is proposed to solve a special case eighth order boundary
value problem. By the proposed method, numerical results canbe obtained not only for the solution but also for derivatives
of the solution. Ninth degree B-splines are used as basis functions to approximate the solution. These functions are
changed into a set of new functions with the help of boundary conditions. The proposed method with the new set of Bsplines gives a stable system of linear equation in the unknown parameters which are used to approximate the solution and
its derivatives. To test the efficiency of the method, some numerical examples which are available in literature are solved
using the proposed method. The obtained results are in good agreement with the exact solutions.

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