A case study of heat transmission in a Williamson fluid flow through a ciliated porous channel: A semi-numerical approach by Usman, S. Shaheen, M.B. Arain, Kottakkaran Sooppy Nisar, Ashwag Albakri, MD Shamshuddin, Fouad Othman Mallawi

“…Differential Transform Method (DTM) has been incorporated as an efficient semi-numerical technique to solve these dimensionless coupled nonlinear partial differential equations. The existence of a solution has been established with the DTM, and the outcomes of the boundary layer distribution are found in mathematical and graphical forms. …”
Get full text

A Unifying Numerical Framework for the “Small-Slope” Based Core-Annular Flow Instability Models by Antonio Quevedo, Carlos Fuentes, Carlos Chávez, Enrique González-Sosa, Carlos Mota

“…The models consist of evolution equations; highly nonlinear partial differential equations of fourth order in space and first order in time. …”
Get full text

Thermal features and heat transfer enhancement of a Casson fluid across a porous stretching/shrinking sheet: Analysis of dual solutions by M. Riaz Khan, Mohamed Abdelghany Elkotb, R.T. Matoog, Nawal A. Alshehri, Mostafa A.H. Abdelmohimen

“…This study formulates the nonlinear Partial Differential Equations (PDEs), that are initially transformed into the non-dimensional Ordinary Differential Equations (ODEs) based on the dimensionless variables. …”
Get full text

On the exact soliton solutions and different wave structures to the (2+1) dimensional Chaffee–Infante equation by Chaoyang Zhu, Mawaheb Al-Dossari, S. Rezapour, B. Gunay

“…The methods employed in this study distinguish themselves by their simplicity, reliability, and ability to generate novel solutions for nonlinear partial differential equations within the realm of mathematical physics.…”
Get full text

Stability analysis and dynamics of solitary wave solutions of the (3+1)-dimensional generalized shallow water wave equation using the Ricatti equation mapping method by Naila Nasreen, Muhammad Naveed Rafiq, Usman Younas, Muhammad Arshad, Muhammad Abbas, Mohamed R. Ali

“…The method used distinguishes out for its simplicity, dependability, and ability to generate novel solutions for nonlinear partial differential equations in the area of mathematical physics. …”
Get full text

Unification of all hyperbolic tangent function methods by Gözükızıl Ömer Faruk, Akçağıl Şamil, Aydemir Tuğba

“…Over the last twenty years, several “different” hyperbolic tangent function methods have been proposed to search solutions for nonlinear partial differential equations (NPDEs). The most common of these methods were the tanh-function method, the extended tanh-function method, the modified extended tanh-function method, and the complex tanh-function method. …”
Get full text

Non-Linear Dynamic Movements of CNT/Graphene/Aluminum Oxide and Copper/Silver/Cobalt Ferrite Solid Particles in a Magnetized and Suction-Based Internally Heated Surface: Sensitivit... by C. S. K. Raju, M. Dinesh Kumar, N. Ameer Ahammad, Ahmed A. El-Deeb, Barakah Almarri, Nehad Ali Shah

“…Usually, this helps enhance the heat transfer rate; in this article, using new similarity transformations created by Lie group analysis, the governing nonlinear partial differential equations are transformed into a system of connected nonlinear ordinary differential equations. …”
Get full text

Insights into the thermal characteristics and dynamics of stagnant blood conveying titanium oxide, alumina, and silver nanoparticles subject to Lorentz force and internal heating o... by Li Shuguang, Li Yijie, Al Mesfer Mohammed K., Ali Kashif, Jamshed Wasim, Danish Mohd, Irshad Kashif, Ahmad Sohail, Hassan Ahmed M.

“…Exact unsolvable nonlinear partial differential equations can be transformed into ordinary differential equations that can be solved numerically by similarity transformation. …”
Get full text

Influence of radially magnetic field properties in a peristaltic flow with internal heat generation: Numerical treatment by Imran Haider Qureshi, Muhammad Awais, Saeed Ehsan Awan, Muhammad Nasir Abrar, Muhammad Asif Zahoor Raja, Sayer Obaid Alharbi, I. Khan

“…Mathematical formulations have been performed which results into nonlinear partial differential equations. The suitable variables have been employed to obtain coupled ordinary differential system. …”
Get full text

Numerical analysis of thermophoretic particle deposition in a magneto-Marangoni convective dusty tangent hyperbolic nanofluid flow – Thermal and magnetic features by Li Shuguang, Ali Kashif, Algarni Salem, Alqahtani Talal, Ahmad Sohail, ElSeabee Fayza Abdel Aziz, Ullah Hameed, Jamshed Wasim, Irshad Kashif

“…By using similarity transformations, the resulting system of nonlinear partial differential equations is converted into nonlinear ordinary differential equations. …”
Get full text

Boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity by Hafidzuddin, Mohd Ezad Hafidz, Mohd Nazar, Roslinda, Md. Arifin, Norihan, Pop, Ioan

“…Appropriate similarity variables are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary (similarity) differential equations. …”
Get full text

Hyperbolic tangent fluid model for stagnation flow of hybrid nanofluid over a stretching sheet. by Md. Ali, Zaileha, Ismail, Nur Zahidah, Ilias, Mohd. Rijal, Soid, Siti Khuzaimah, Ishak, Anuar, Md. Basir, Md. Faisal, Norzawary, Nur Hazirah Adilla

“…The boundary layer problem is formulated to nonlinear partial differential equations which is then transformed into ordinary differential equations by using similarity transformation. …”
Get full text

Influence of viscous dissipation on the flow and heat transfer of a Jeffrey fluid towards horizontal circular cylinder with free convection: A numerical study by Syazwani, Mohd Zokri, Nur Syamilah, Arifin, Muhammad Khairul Anuar, Mohamed, Abdul Rahman, Mohd Kasim, Nurul Farahain, Mohammad, Mohd Zuki, Salleh

“…The non-dimensional variables and non-similar transformations are implemented to transform the dimensional partial differential equations into two nonlinear partial differential equations (PDEs). Then, the implicit, unconditionally stable and well-tested Keller-box method is used to solve the PDEs by adding an extra boundary condition at infinity. …”
Get full text

A study of triple-mass diffusion species and energy transfer in Carreau–Yasuda material influenced by activation energy and heat source by Muhammad Sohail, Umar Nazir, Essam R. El-Zahar, Hussam Alrabaiah, Poom Kumam, Abd Allah A. Mousa, Kanokwan Sitthithakerngkiet, Choonkil Park

“…The mathematical model composing transport of momentum, heat and mass species is developed in Cartesian coordinate system under boundary layer investigation in the form of coupled nonlinear partial differential equations. The complex partial differential equations are converted into coupled nonlinear ordinary differential equations by using the appropriate similarity transformation. …”
Get full text

Constructing analytical estimates of the fuzzy fractional-order Boussinesq model and their application in oceanography by Saima Rashid, Mohammed K.A. Kaabar, Ali Althobaiti, M.S. Alqurashi

“…A shallow fluid assumption is illustrated by a series of nonlinear partial differential equations in the framework. Because the waves are scattered over a wide geographical region, this system can precisely replicate atmospheric internal waves. …”
Get full text

Viscous Dissipation and Chemical Reaction on Radiate MHD Casson Nanofluid Past a Stretching Surface with a Slip Effect by Dachapally Swapna, Kamatam Govardhan, Ganji Narender, Santoshi Misra

“…Governing nonlinear partial differential equations are transformed into the dimensionless nonlinear ordinary differential equations by using appropriate transformations. …”
Get full text

Unsteady Coupled Moisture and Heat Energy Transport through an Exterior Wall Covered with Vegetation by Leopold Škerget, António Tadeu, João Almeida

“…The transport of moisture and heat through the support structure, which includes insulation and soil layers, is defined in a series of nonlinear partial differential equations (PDEs). After setting out the model, this article presents and discusses a set of numerical applications. …”
Get full text

Recent progress in Cattaneo-Christov heat and mass fluxes for bioconvectional Carreau nanofluid with motile microorganisms and activation energy passing through a nonlinear stretch... by Umar Farooq, Muhammad Abdul Basit, Sobia Noreen, Nahid Fatima, Abdullah Alhushaybari, Sayed M. El Din, Muhammad Imran, Ali Akgül

“…Methodology: The mathematical model was developed by taking these things into account and getting a model of nonlinear partial differential equations for administering this problem. …”
Get full text

Numerical investigation of magnetized nanofluid flow with thermal radiation and homogeneous/heterogeneous reactions over a vertical cylinder by Muhammad Sami Rashad, Umair Manzoor, Shan Ali Khan, Haihu Liu, Taseer Muhammad

“…The mathematical flow model, based on nonlinear partial differential equations (PDEs), is converted into ordinary differential equations (ODEs) by using suitable similarity transformations that pronounced nonlinear system of ODEs. …”
Get full text

Thermal analysis of a radiative slip flow of an unsteady casson nanofluid toward a stretching surface subject to the convective condition by Jie Liu, Awatef Abidi, M. Riaz Khan, Saim Rasheed, F.M. Allehiany, Emad E. Mahmoud, Ahmed M. Galal

“…In view of these assumptions, a system of nonlinear partial differential equations (PDEs), have been formulated which are primarily converted to the dimensionless ordinary differential equations (ODEs). …”
Get full text