Umi Nadrah Hussein¹, Najiyah Safwa Khashi’ie^1,*, Norihan Md Arifin², Ioan Pop³

Frontiers in Heat and Mass Transfer, Vol.23, No.2, pp. 383-395, 2025, DOI:10.32604/fhmt.2025.063023 - 25 April 2025

Abstract This study investigates the heat transfer and flow dynamics of a ternary hybrid nanofluid comprising alumina, copper, and silica/titania nanoparticles dispersed in water. The analysis considers the effects of suction, magnetic field, and Joule heating over a permeable shrinking disk. A mathematical model is developed and converted to a system of differential equations using similarity transformation which then, solved numerically using the bvp4c solver in Matlab software. The study introduces a novel comparative analysis of alumina-copper-silica and alumina-copper-titania nanofluids, revealing distinct thermal conductivity behaviors and identifying critical suction values necessary for flow stabilization. Dual solutions… More >

Muhammad Zubair Mustafa¹, Sumera Dero¹, Liaquat Ali Lund², Mehboob Ul Hassan³, Umair Khan^4,5,*

CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.1, pp. 499-513, 2025, DOI:10.32604/cmes.2025.061804 - 11 April 2025

Abstract This paper discusses the model of the boundary layer (BL) flow and the heat transfer characteristics of hybrid nanofluid (HNF) over shrinking/stretching disks. In addition, the thermal radiation and the impact of velocity and thermal slip boundary conditions are also examined. The considered hybrid nano-fluid contains silver (Ag) and iron oxide (Fe₃O₄) nanoparticles dispersed in the water to prepare the Ag-Fe₃O₄/water-based hybrid nanofluid. The requisite posited partial differential equations model is converted to ordinary differential equations using similarity transformations. For a numerical solution, the shooting method in Maple is employed. Moreover, the duality in solutions is… More > Graphic Abstract

Nur Syahirah Wahid^1,*, Nor Ain Azeany Mohd Nasir^2,3, Norihan Md Arifin^1,3, Ioan Pop^4,5

CMES-Computer Modeling in Engineering & Sciences, Vol.142, No.2, pp. 1865-1881, 2025, DOI:10.32604/cmes.2024.059508 - 27 January 2025

Abstract Modeling the boundary layer flow of ternary hybrid nanofluids is important for understanding and optimizing their thermal performance, particularly in applications where enhanced heat transfer and fluid dynamics are essential. This study numerically investigates the boundary layer flow of alumina-copper-silver/water nanofluid over a permeable stretching/shrinking sheet, incorporating both first and second-order velocity slip. The mathematical model is solved in MATLAB facilitated by the bvp4c function that employs the finite difference scheme and Lobatto IIIa formula. The solver successfully generates dual solutions for the model, and further analysis is conducted to assess their stability. The findings More >

Muhammad A. Sadiq^1,2,*, Nadeem Abbas³, Haitham M. S. Bahaidarah⁴, Mohammad Amjad⁵

FDMP-Fluid Dynamics & Materials Processing, Vol.19, No.2, pp. 471-486, 2023, DOI:10.32604/fdmp.2022.021133 - 29 August 2022

Abstract We present the results of an investigation into the behavior of the unsteady flow of a Casson Micropolar nanofluid over a shrinking/stretching curved surface, together with a heat transfer analysis of the same problem. The body force acting perpendicular to the surface wall is in charge of regulating the fluid flow rate. Curvilinear coordinates are used to account for the considered curved geometry and a set of balance equations for mass, momentum, energy and concentration is obtained accordingly. These are turned into ordinary differential equations using a similarity transformation. We show that these equations have More >

Iskandar Waini^1,2, Anuar Ishak^2,*, Ioan Pop³

CMC-Computers, Materials & Continua, Vol.68, No.3, pp. 3255-3269, 2021, DOI:10.32604/cmc.2021.017643 - 06 May 2021

Abstract This study examines the stagnation point flow over a stretching/shrinking sheet in a hybrid nanofluid with homogeneous-heterogeneous reactions. The hybrid nanofluid consists of copper (Cu) and alumina (Al₂O₃) nanoparticles which are added into water to form Cu-Al₂O₃/water hybrid nanofluid. The similarity equations are obtained using a similarity transformation. Then, the function bvp4c in MATLAB is utilised to obtain the numerical results. The dual solutions are found for limited values of the stretching/shrinking parameter. Also, the turning point arises in the shrinking region (λ < 0). Besides, the presence of hybrid nanoparticles enhances the heat transfer rate,… More >

Liaquat Ali Lund^1,2, Zurni Omar¹, Sumera Dero^1,3, Yuming Chu^4,5, Ilyas Khan^6,*, Kottakkaran Sooppy Nisar⁷

CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1963-1975, 2021, DOI:10.32604/cmc.2020.011976 - 26 November 2020

Abstract The unsteady magnetohydrodynamic (MHD) flow on a horizontal preamble surface with hybrid nanoparticles in the presence of the first order velocity and thermal slip conditions are investigated. Alumina (Al₂O₃) and copper (Cu) are considered as hybrid nanoparticles that have been dispersed in water in order to make hybrid nanofluid (Cu − Al₂O₃/water). The system of similarity equations is derived from the system of partial differential equations (PDEs) by using variables of similarity, and their solutions are gotten with shooting method in the Maple software. In certain ranges of unsteadiness and magnetic parameters, the presence of dual solutions More >

Izyan Syazana Awaludin^{1, 2}, Anuar Ishak^2,*, Ioan Pop³

CMES-Computer Modeling in Engineering & Sciences, Vol.120, No.1, pp. 203-214, 2019, DOI:10.32604/cmes.2019.06594

Abstract The present study considers the magnetohydrodynamic (MHD) stagnation point flow with chemical reaction effect over a permeable stretching/shrinking sheet. The partial differential equations are reduced to a set of ordinary differential equations using a similarity transformation. The transformed equations are then solved numerically by employing the bvp4c function available in the MATLAB software. The numerical results illustrate the effects of several parameters on the skin friction coefficient, local Nusselt number and the local Sherwood number. Dual solutions are obtained for a certain range of parameters. The temporal stability analysis is carried out to determine which More >

C. S. K. Raju^a , N. Sandeep^a, J. Prakash^b,1

Frontiers in Heat and Mass Transfer, Vol.7, pp. 1-8, 2016, DOI:10.5098/hmt.7.14

Abstract In this study, we analyzed the effects of nonlinear thermal radiation and induced magnetic field on steady two-dimensional incompressible flow of Jeffrey fluid flow past a stretching/shrinking surface in the presence of homogeneous-heterogeneous reactions. For physical relevance in this study we analyzed the behavior of homogeneous and heterogeneous profiles individually. The transformed governing equations with the help of similarity variables are solved numerically via Runge-Kutta and Newton’s method. We obtained better accuracy of the present results by differentiating with the existed published literature. The effect of pertinent parameters on velocity, induced magnetic field, temperature and More >