Mujahid Islam¹, Fateh Ali^1,*, Xinlong Feng^1,*, M. Zahid², Sana Naz Maqbool¹

CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.3, pp. 3511-3561, 2025, DOI:10.32604/cmes.2025.073678 - 23 December 2025

Abstract Roll coating is a vital industrial process used in printing, packaging, and polymer film production, where maintaining a uniform coating is critical for product quality and efficiency. This work models non-isothermal Carreau fluid flow between a rotating roll and a stationary wall under fixed boundary constraints to evaluate how non-Newtonian and thermal effects influence coating performance. The governing equations are transformed into non-dimensional form and simplified using lubrication approximation theory. Approximate analytical solutions are obtained via the perturbation technique, while numerical results are computed using both the finite difference method and the BVP-Midrich technique. Furthermore, More >

Farzad Mohebbi^*

Frontiers in Heat and Mass Transfer, Vol.23, No.5, pp. 1417-1441, 2025, DOI:10.32604/fhmt.2025.069024 - 31 October 2025

Abstract An inverse analysis is presented to estimate line heat source in two-dimensional steady-state and transient heat transfer problems. A constant heat source is considered in the steady-state heat transfer problem (a parameter estimation problem) and a time-varying heat source is considered in the transient heat transfer problem (a function estimation problem). Since a general irregular 2D heat conducting body is considered, a body-fitted grid generation is used to mesh the domain. Then governing equations and associated boundary and initial conditions are transformed from the physical domain to the computational domain and finite difference method is… More >

Khadija Ibaararen, Mhammed Zaimi, Khadija El Ainaoui, El Mahdi Assaid^*

Energy Engineering, Vol.122, No.9, pp. 3487-3505, 2025, DOI:10.32604/ee.2025.067422 - 26 August 2025

Abstract This study investigates the complex heat transfer dynamics in multilayer bifacial photovoltaic (bPV) solar modules under spectrally resolved solar irradiation. A novel numerical model is developed to incorporate internal heat generation resulting from optical absorption, grounded in the physical equations governing light-matter interactions within the module’s multilayer structure. The model accounts for reflection and transmission at each interface between adjacent layers, as well as absorption within individual layers, using the wavelength-dependent dielectric properties of constituent materials. These properties are used to calculate the spectral reflectance, transmittance, and absorption coefficients, enabling precise quantification of internal heat… More >

Saykat Poddar¹, Jui Saha¹, Badhan Neogi¹, Mohammad Sanjeed Hasan¹, Muhammad Minarul Islam¹, Giulio Lorenzini^2,*, Md. Mahmud Alam³

FDMP-Fluid Dynamics & Materials Processing, Vol.21, No.2, pp. 233-252, 2025, DOI:10.32604/fdmp.2025.056131 - 06 March 2025

Abstract This study presents a numerical analysis of the steady-state solution for transient magnetohydrodynamic (MHD) dissipative and radiative fluid flow, incorporating an induced magnetic field (IMF) and considering a relatively high concentration of foreign mass (accounting for Soret and Dufour effects) over a vertically oriented semi-infinite plate. The governing equations were normalized using boundary layer (BL) approximations. The resulting nonlinear system of partial differential equations (PDEs) was discretized and solved using an efficient explicit finite difference method (FDM). Numerical simulations were conducted using MATLAB R2015a, and the developed numerical code was verified through comparison with another… More >

Tsung-Han Li^1,*, Chia-Ming Fan¹, Po-Wei Li²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.32, No.1, pp. 1-1, 2024, DOI:10.32604/icces.2024.012120

Abstract The generalized finite difference method (GFDM), which cooperated with the fictitious-nodes technique, is proposed in this study to accurately analyze three-dimensional boundary value problems, governed by high-order partial differential equations. Some physical applications can be mathematically described by boundary value problems governed by high-order partial differential equations, but it is non-trivial to analyze the high-order partial differential equations by adopting conventional mesh-based numerical schemes, such as finite difference method, the finite element method, etc. In this study, the GFDM, a localized meshless method, is proposed to accurately and efficiently solve boundary value problems governed by… More >

Bingrui Ju^1,2, Wenxiang Sun², Wenzhen Qu^1,2,*, Yan Gu²

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 267-280, 2024, DOI:10.32604/cmes.2024.052159 - 20 August 2024

Abstract In this study, we propose an efficient numerical framework to attain the solution of the extended Fisher-Kolmogorov (EFK) problem. The temporal derivative in the EFK equation is approximated by utilizing the Crank-Nicolson scheme. Following temporal discretization, the generalized finite difference method (GFDM) with supplementary nodes is utilized to address the nonlinear boundary value problems at each time node. These supplementary nodes are distributed along the boundary to match the number of boundary nodes. By incorporating supplementary nodes, the resulting nonlinear algebraic equations can effectively satisfy the governing equation and boundary conditions of the EFK equation. More >

Chunlei Ruan^1,2,*, Cengceng Dong¹, Zeyue Zhang¹, Boyu Chen¹, Zhijun Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.3, pp. 2707-2728, 2024, DOI:10.32604/cmes.2024.050003 - 08 July 2024

Abstract Transient heat conduction problems widely exist in engineering. In previous work on the peridynamic differential operator (PDDO) method for solving such problems, both time and spatial derivatives were discretized using the PDDO method, resulting in increased complexity and programming difficulty. In this work, the forward difference formula, the backward difference formula, and the centered difference formula are used to discretize the time derivative, while the PDDO method is used to discretize the spatial derivative. Three new schemes for solving transient heat conduction equations have been developed, namely, the forward-in-time and PDDO in space (FT-PDDO) scheme,… More >

P. Pai Nityanand, B. Devaki, G. Bhat Pareekshith, V. S. Sampath Kumar^*

Frontiers in Heat and Mass Transfer, Vol.22, No.2, pp. 655-673, 2024, DOI:10.32604/fhmt.2024.050237 - 20 May 2024

Abstract The study in this manuscript aims to analyse the impact of thermal radiation on the two-dimensional magnetohydrodynamic flow of upper convected Maxwell (UCM) fluid between parallel plates. The lower plate is porous and stationary, while the top plate is impermeable and moving. The equations that describe the flow are transformed into non-linear ordinary differential equations with boundary conditions by employing similarity transformations. The Homotopy Perturbation Method (HPM) is then employed to approach the obtained non-linear ordinary differential equations and get an approximate analytical solution. The analysis includes plotting the velocity profile for different Reynolds number… More >

Dewi Puspitasari¹, Diah Kusuma Pratiwi¹, Pramadhony Amran², Kaprawi Sahim^1,*

Frontiers in Heat and Mass Transfer, Vol.22, No.1, pp. 305-315, 2024, DOI:10.32604/fhmt.2023.041882 - 21 March 2024

Abstract The natural convection from a vertical hot plate with radiation and constant flux is studied numerically to know the velocity and temperature distribution characteristics over a vertical hot plate. The governing equations of the natural convection in two-dimension are solved with the implicit finite difference method, whereas the discretized equations are solved with the iterative relaxation method. The results show that the velocity and the temperature increase along the vertical wall. The influence of the radiation parameter in the boundary layer is significant in increasing the velocity and temperature profiles. The velocity profiles increase with More >

Ziqiang Bai¹, Wenzhen Qu^2,*, Guanghua Wu^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.3, pp. 2955-2972, 2024, DOI:10.32604/cmes.2023.031474 - 15 December 2023

Abstract In the past decade, notable progress has been achieved in the development of the generalized finite difference method (GFDM). The underlying principle of GFDM involves dividing the domain into multiple sub-domains. Within each sub-domain, explicit formulas for the necessary partial derivatives of the partial differential equations (PDEs) can be obtained through the application of Taylor series expansion and moving-least square approximation methods. Consequently, the method generates a sparse coefficient matrix, exhibiting a banded structure, making it highly advantageous for large-scale engineering computations. In this study, we present the application of the GFDM to numerically solve More >