Analysis of water based Casson hybrid nanofluid (NiZnFe2O4+MnZnFe2O4) flow over an electromagnetic actuator with Cattaneo–Christov heat-mass flux: A modified Buongiorno model by S. Baskaran, R. Sowrirajan, S. Divya, S. Eswaramoorthi, K. Loganathan

“…Using suitable variables, the governing coupled nonlinear partial differential equations are transformed into ordinary differential equations, which are solved using MATLABs bvp4c solver. …”
Get full text

Chemical reaction and Soret impacts on MHD heat and mass transfer Casson hybrid nanofluid (MoS2+ZnO) flow based on engine oil across a stretching sheet with radiation by M. Radhika, Y. Dharmendar Reddy

“…The relevant similarity variables convert the governing nonlinear partial differential equations to ordinary differential equations (ODEs). …”
Get full text

Impact of nanoparticles shapes and fuzzy volume fraction on Al2O3 – H2O nanofluid flow past an unsteady expandable surface by Adnan Saeed Butt, Naveed Yaqoob, Sameea Akbar, Gul M. Shaikh, Adeeba Farhat, Fouzia Amir, Mohamed R. Ali

“…The goal is to simplify the nonlinear partial differential equations (PDEs) through appropriate transformations, converting them into ordinary differential equations (ODEs). …”
Get full text

Displacement of hydrocarbon liquids by water using the models of zonally heterogeneous deformable formations by Marat Ya. Khabibullin, Rustem I. Suleymanov, Razifa R. Stepanova, Alina Az. Gizzatullina, Arsen M. Khabibullin

“…It is known that the motion of two-phase hydrocarbon systems in deformable reservoirs is represented by complex nonlinear partial differential equations. An analytical solution of such equations is possible only with the use of special approaches. …”
Get full text

Exploring novel solitary wave phenomena in Klein–Gordon equation using $$\phi ^{6}$$ ϕ 6 model expansion method by Yasir A. Madani, Khidir Shaib Mohamed, Sadia Yasin, Sehrish Ramzan, Khaled Aldwoah, Mohammed Hassan

“…The $$\phi ^{6}$$ ϕ 6 model expansion technique is exceptionally adaptable and may be utilised for a wide array of nonlinear partial differential equations. Despite its versatility, the technique may not be applicable to all nonlinear PDEs, especially those that do not meet the specified requirements or structures manageable by this technique. …”
Get full text

Chemical reactions with the Casson nanofluid flow by the bioconvective behavior of microorganisms over a spinning disc by Prabhakar Sagadevan, Umadevi Raju, Meganathan Murugesan, Unai Fernandez-Gamiz, Samad Noeiaghdam

“…Using the right variables to change the nonlinear partial differential equations (PDEs) that govern the problem into a system of ordinary differential equations (ODEs) is a key step toward finding numerical solutions. …”
Get full text

Boundary layer flow of a non-Newtonian fluid over an exponentially stretching sheet with the presence of a heat source/sink by Vinod Y．, K.R. Raghunatha, Suma Nagendrappa Nagappanavar, Nodira Nazarova, Manish Gupta, Sangamesh

“…The governing equations, formulated as nonlinear partial differential equations, capture the Casson fluid's properties, magnetic field effects, and radiative heat transfer. …”
Get full text

Non Linear Thermal Radiation Analysis of Electromagnetic Chemically Reacting Ternary Nanofluid Flow over a Bilinear Stretching Surface by Shobha V, Hasan Mulki, Baskar P, S. Suresh Kumar Raju, Saleh Mahmoud, Mostafa Abdrabboh, S.V.K. Varma

“…Methodology: The governing nonlinear partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using similarity transformations. …”
Get full text