Generalised Lie similarity transformations for the unsteady flow and heat transfer under the influence of internal heating and thermal radiation
December 09, 2023
Shuguang Li, Muhammad Safdar, Safia Taj, Muhammad Bilal, Shoaib Ahmed, M Ijaz Khan, Maimona Rafiq, Sherzod Shukhratovich Abdullaev,
Pramana-Journal of Physics - Volume:97, Issue:4, Article Number: 203,
Comparative analysis of analytical and numerical approximations for the flow and heat transfer in mixed convection stagnation point flow of Casson fluid
August 04, 2023
M. Tanzeel-ur-Rehman Siddiqi, Muhammad Safdar, Hina Muneer Dutt, Safia Taj, M. Ijaz Khan, Barno Sayfutdinovna Abdullaeva, Reem Altuijri, Ahmed M. Hassan,
Results in Physics - Volume 52, Article Number 106819
Numerical approximations for fluid flow and heat transfer in the boundary layer with radiation through multiple Lie similarity transformations
July 24, 2023
Muhammad Bilal, Muhammad Safdar, Shoaib Ahmed, Karam Dad, Muhammad Umair Ali, Amad Zafar, Kwang Su Kim, Jong Hyuk Byun,
Frontiers in Physics - Volume 11, Article Number 1210827
Heat transfer in MHD thin film flow with concentration using lie point symmetry approach
July 16, 2023
Ghani Khan, Muhammad Safdar, Safia Taj, Riaz Ahmad Khan, Reham A. Alahmadi, Ilyas khan, Sayed M Eldin,
Case Studies in Thermal Engineering - Volume 49, Article Number 103238
Analytical Solutions for Unsteady Thin Film Flow with Internal Heating and Radiation
May 12, 2023
Ahsan Ali Naseer, Muhammad Safdar, Safia Taj, Muhammad Umair Ali, Amad Zafar, Kwang Su Kim, Jong Hyuk Byun,
Journal of Mathematics - Volume 2023 | Article ID 5612023
Multiple Lie symmetry solutions for effects of viscous on magnetohydrodynamic flow and heat transfer in non-Newtonian thin film
May 10, 2023
Muhammad Safdar, Safia Taj, Muhammad Bilal, Shoaib Ahmed, Muhammad Ijaz Khan, Sana Ben Moussa, Bandar M. Fadhl, Basim M. Makhdoum, Sayed M. Eldin,
Open Physics - Volume 21, Issue 1, Pages 1-14
Analytic similarity solutions for fully resolved unsteady laminar boundary layer flow and heat transfer in the presence of radiation
April 01, 2023
Muhammad Bilal, Muhammad Safdar, Shoaib Ahmed, Riaz Ahmad Khan,
Heliyon - Volume 9, Issue 4, Article Number e14765
Reduce-Order Modeling and Higher Order Numerical Solutions for Unsteady Flow and Heat Transfer in Boundary Layer with Internal Heating
December 07, 2022
Muhammad Bilal, Muhammad Safdar, Safia Taj, Amad Zafar, Muhammad Umair Ali, Seung Won Lee,
Mathematics - Volume 10, Issue 24, Article Number 4640
One-dimensional optimal system of Lie sub-algebra and analytic solutions for a liquid film fluid flow
August 01, 2022
Fuzhang Wang, Muhammad Safdar, Bisma Jamil, Muhammad Ijaz Khan, Safia Taj, M.Y. Malik, A.S. Alqahtani, Ahmed M. Galal,
Chinese Journal of Physics - Volume 78, Pages 220-223
Lie symmetry analysis of heat transfer in a liquid film over an unsteady stretching surface with viscous dissipation and external magnetic field
June 13, 2022
Safia Taj, Muhammad Ijaz Khan, Muhammad Safdar, Samia Elattar, Ahmed M. Galal,
Waves in Random and Complex Media - Pages 1-16
Analytic solutions for the MHD flow and heat transfer in a thin liquid film over an unsteady stretching surface with Lie symmetry and homotopy analysis method
May 16, 2022
Muhammad Safdar, Muhammad Ijaz Khan, Riaz Ahmed Khan, Safia Taj, Faizan Abbas, Samia Elattar, Ahmed M. Galal,
Waves in Random and Complex Media - Pages 1-19
Construction of similarity transformations and analytic solutions for a liquid film on an unsteady stretching sheet using lie point symmetries
September 01, 2021
Muhammad Safdar, M. Ijaz Khan, Safia Taj, M.Y. Malik, Qiu-Hong Shi,
Chaos, Solitons and fractals - Volume 150, Article Number 111115
Reduction of systems of two nonlinear parabolic type partial differential equations to solvable forms using differential invariants
September 01, 2021
M.H. Yaseen, Muhammad Safdar, M. Ijaz Khan, M.Y. Malik, Qiu-Hong Shi,
Chaos, Solitons and Fractals - Volume 150, Article Number 111107
Comparison of Noether Symmetries and First Integrals of Two-Dimensional Systems of Second Order Ordinary Differential Equations by Real and Complex Methods
September 17, 2019
Muhammad Safdar, Asghar Qadir, Asghar Qadir, Muhammad Umar Farooq,
Symmetry - Volume 11, Issue 9
Linearization criteria for two-dimensional systems of third-order ordinary differential equations by complex approach
September 01, 2019
Hina Munir Dutt, Muhammad Safdar, Asghar Qadir,
Arabian Journal of Mathematics - Volume 8, Issue 3, Pages 163-170, Part 1
Optimal systems and their group invariants solutions to geodesic equations
September 01, 2019
Bismah Jamil, Tooba Feroze, Muhammad Safdar,
International Journal of Geometric Methods in Modern Physics - Volume 16, Issue 9, Article Number 1950135
Linearization of Two Dimensional Complex-Linearizable Systems of Second Order Ordinary Differential Equations
January 01, 2015
Hina Munir Dutt, Muhammad Safdar,
Applied Mathematical Sciences - Volume 9, No. 58, Pages 2889-2900
Linearization from Complex Lie Point Transformations
November 19, 2014
Sajid Ali, Muhammad Safdar, Asghar Qadir,
Journal of Applied Mathematics - Volume 2014, Article ID 793247, 8 pages
Ibragimov-type invariants for a system of two linear parabolic equations
August 01, 2012
F.M.Mahomed, Muhammad Safdar, J. Zama,
Communications in Nonlinear Science and Numerical Simulation - Volume 17, Issue 8, Pages 3140–3147
Linearizability of Systems of Ordinary Differential Equations Obtained by Complex Symmetry Analysis
October 20, 2011
Muhammad Safdar, Asghar Qadir, Sajid Ali,
Mathematical Problems in Engineering - Volume 2011, Article ID 171834, 17 pages
Linearization of systems of four second order ordinary differential equations
September 01, 2011
M SAFDAR, S Ali, F M Mahomed,
PRAMANA-journal of physics - Volume 77, Issue 3, Pages 581-594, Special Issue SI