Effect of heater location and wall waviness on buoyant convection in a porous wavy cavity using heat function approach

Huey Tyng Cheong; Sivasankaran  Sivanandam

doi:10.59400/adecp4147

Effect of heater location and wall waviness on buoyant convection in a porous wavy cavity using heat function approach

Huey Tyng Cheong
School of Mathematical Sciences, Sunway University, Sunway City 47500, Malaysia
Sivasankaran Sivanandam
Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia; Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences (SIMATS), Chennai 602105,India

Article ID: 4147

DOI: https://doi.org/10.59400/adecp4147

Keywords: heat function; natural convection; wavy cavity; porous medium; localized heating

Abstract

Natural convection and thermal transport in a porous square cavity with a wavy cold wall and a localized heat source on the left sidewall are numerically examined in this work. The cavity is filled with a fluid-saturated porous medium and is governed by the Darcy model under steady, laminar flow conditions with the Boussinesq approximation. A heater of fixed length is mounted on the left sidewall at three different points, namely the lower, center, and upper positions, while the right sidewall is maintained at a constant cold temperature and modeled with varying waviness in terms of amplitude and number of undulations. The remaining walls are considered adiabatic. The governing dimensionless equations for energy and stream functions are discretized using the finite difference technique and solved iteratively for various heater positions, right sidewall waviness, and Darcy–Rayleigh values after transforming the physical wavy domain into a rectangular computational domain. Results are presented in the form of Nusselt numbers, isotherms, streamlines, and heatlines. The findings indicate that the heater position has a significant influence on the convection flow, and heat transfer performance. The averaged heat transmission rate is improved by the right sidewall’s increased waviness. Among the heater placements, lower heating produces the highest averaged heat transfer for higher Darcy–Rayleigh numbers, whereas center heating is more effective under weak convection conditions. This study provides useful insight into the thermal design of porous systems involving non-uniform heating, such as solar air conditioning, ventilation, and heating systems.

Published

2026-04-30

How to Cite

Cheong, H. T., & Sivanandam, S. (2026). Effect of heater location and wall waviness on buoyant convection in a porous wavy cavity using heat function approach. Advances in Differential Equations and Control Processes, 33(2). https://doi.org/10.59400/adecp4147

Download Citation

Issue

Vol. 33 No. 2 (2026) in progress:

Section

Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

[1]Upreti H, Pandey A, Gupta T. Exploring the Flow Dynamics of MHD Hybrid Nanofluid over a Non-Flat Porous Surface Using Neural Network Approach. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería. 2025; 41(2). doi: 10.23967/j.rimni.2025.10.64380

[2]Sharma PK, Sharma BK, Kumar A. Mathematical Analysis of Chemically Reacting Species and Radiation Effects on MHD Free Convective Flow Through a Rotating Porous Medium. Acta Mechanica et Automatica. 2024; 18(2): 193–203. doi: 10.2478/ama-2024-0023

[3]Murthy PVSN, Kumar BVR, Singh P. Natural Convection Heat Transfer from a Horizontal Wavy Surface in a Porous Enclosure. Numerical Heat Transfer, Part A: Applications. 1997; 31(2): 207–221. doi: 10.1080/10407789708914033

[4]Rathish Kumar BV, Shalini. Free convection in a non-Darcian wavy porous enclosure. International Journal of Engineering Science. 2003; 41(16): 1827–1848. doi: 10.1016/S0020-7225(03)00113-7

[5]Das PK, Mahmud S, Humaira Tasnim S, et al. Effect of surface waviness and aspect ratio on heat transfer inside a wavy enclosure. International Journal of Numerical Methods for Heat & Fluid Flow. 2003; 13(8): 1097–1122. doi: 10.1108/09615530310501975

[6]Misirlioglu A, Baytas AC, Pop I. Free convection in a wavy cavity filled with a porous medium. International Journal of Heat and Mass Transfer. 2005; 48(9): 1840–1850. doi: 10.1016/j.ijheatmasstransfer.2004.12.005

[7]Chen XB, Yu P, Winoto SH, et al. Free Convection in a Porous Wavy Cavity Based on the Darcy-Brinkman-Forchheimer Extended Model. Numerical Heat Transfer, Part A: Applications. 2007; 52(4): 377–397. doi: 10.1080/10407780701301595

[8]Mansour MA, El-Aziz MMA, Mohamed RA, et al. Numerical Simulation of Natural Convection in Wavy Porous Cavities Under the Influence of Thermal Radiation Using a Thermal Non-equilibrium Model. Transport in Porous Media. 2011; 86(2): 585–600. doi: 10.1007/s11242-010-9641-5

[9]Sojoudi A, Saha SC, Khezerloo M, et al. Unsteady Natural Convection Within a Porous Enclosure of Sinusoidal Corrugated Side Walls. Transport in Porous Media. 2014; 104(3): 537–552. doi: 10.1007/s11242-014-0347-y

[10]Prakash O, Barman P, Rao PS, et al. MHD free convection in a partially open wavy porous cavity filled with nanofluid. Numerical Heat Transfer, Part A: Applications. 2023; 84(5): 449–463. doi: 10.1080/10407782.2022.2132330

[11]Armaghani T, Rashad AM, Togun H, et al. Hybrid Nanofluid Unsteady MHD Natural Convection in an Inclined Wavy Porous Enclosure with Radiation Effect, Partial Heater and Heat Generation/Absorption. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering. 2024; 48(3): 971–988. doi: 10.1007/s40997-023-00720-3

[12]Tanveer A, Sami-ul-Haq, Ashraf MB, et al. Thermal analysis of nonlinear mixed convection effects within wavy enclosure. Case Studies in Thermal Engineering. 2024; 63: 105322. doi: 10.1016/j.csite.2024.105322

[13]Chuhan IS, Li J, Guo Z, et al. Entropy optimization of MHD non-Newtonian fluid in a wavy enclosure with double diffusive natural convection. Numerical Heat Transfer, Part A: Applications. 2024; 85(16): 2703–2723. doi: 10.1080/10407782.2023.2228482

[14]Mandal DK, Mondal MK, Biswas N, et al. Convective heat transport in a porous wavy enclosure: Nonuniform multi-frequency heating with hybrid nanofluid and magnetic field. Heliyon. 2024; 10(9): e29846. doi: 10.1016/j.heliyon.2024.e29846

[15]Sivasankaran S, Cheong HT, Aasaithambi T. Effect of Localized Heater Position and Length on Buoyant Convection in an Oblique Porous cavity Using Heatlines Approach. International Journal of Applied and Computational Mathematics. 2025; 11(5): 181. doi: 10.1007/s40819-025-01996-6

[16]Hansda S, Majhi D, Hussein AK, et al. Magento-double diffusive natural convection in a partially heated wavy porous cavity filled with a radiative hybrid nanofluid. Journal of Thermal Analysis and Calorimetry. 2025; 150(13): 10489–10512. doi: 10.1007/s10973-025-14398-z

[17]Parmar D, Murthy SVSSNVGK, Kumar BVR, et al. Numerical simulation of fractional order double diffusive convective nanofluid flow in a wavy porous enclosure. International Journal of Heat and Fluid Flow. 2025; 112: 109749. doi: 10.1016/j.ijheatfluidflow.2025.109749

[18]Barman P, Kumar BVR. FEA of entropy generation due to free convection of hybrid-nanofluid in a partially heated tilted porous enclosure with wavy wall. International Journal of Numerical Methods for Heat & Fluid Flow. 2025; 35(9): 3029–3052. doi: 10.1108/HFF-09-2024-0723

[19]Roy NC, Rumpa SH, Amin A. Natural convective ternary nanofluid flow in a trapezoidal wavy enclosure with multiple cold obstacles. International Journal of Heat and Fluid Flow. 2026; 117: 110139. doi: 10.1016/j.ijheatfluidflow.2025.110139

[20]Sankar M, Bhuvaneswari M, Sivasankaran S, et al. Buoyancy induced convection in a porous cavity with partially thermally active sidewalls. International Journal of Heat and Mass Transfer. 2011; 54(25–26): 5173–5182. doi: 10.1016/j.ijheatmasstransfer.2011.08.029

[21]Sivasankaran S, Bhuvaneswari M. Effect of thermally active zones and direction of magnetic field on hydromagnetic convection in an enclosure. Thermal Science. 2011; 15: 367–382. doi: 10.2298/TSCI100221094S

[22]Chen TH, Chen LY. Study of buoyancy-induced flows subjected to partially heated sources on the left and bottom walls in a square enclosure. International Journal of Thermal Sciences. 2007; 46(12): 1219–1231. doi: 10.1016/j.ijthermalsci.2006.11.021

[23]Zhao FY, Liu D, Tang GF. Free convection from one thermal and solute source in a confined porous medium. Transport in Porous Media. 2007; 70(3): 407–425. doi: 10.1007/s11242-007-9106-7

[24]Zhao FY, Liu D, Tang GF. Natural convection in a porous enclosure with a partial heating and salting element. International Journal of Thermal Sciences. 2008; 47(5): 569–583. doi: 10.1016/j.ijthermalsci.2007.04.006

[25]Sivasankaran S, Do Y, Sankar M. Effect of Discrete Heating on Natural Convection in a Rectangular Porous Enclosure. Transport in Porous Media. 2011; 86(1): 261–281. doi: 10.1007/s11242-010-9620-x

[26]Sivakumar V, Sivasankaran S, Prakash P, et al. Effect of heating location and size on mixed convection in lid-driven cavities. Computers & Mathematics with Applications. 2010; 59(9): 3053–3065. doi: 10.1016/j.camwa.2010.02.025

[27]Malleswaran A, Sivasankaran S, Bhuvaneswari M. Effect of heating location and size on MHD mixed convection in a lid‐driven cavity. International Journal of Numerical Methods for Heat & Fluid Flow. 2013; 23(5): 867–884. doi: 10.1108/HFF-04-2011-0082

[28]Sivasankaran S, Sivakumar V, Hussein AK, et al. Mixed Convection in a Lid-Driven Two-Dimensional Square Cavity with Corner Heating and Internal Heat Generation. Numerical Heat Transfer, Part A: Applications. 2014; 65(3): 269–286. doi: 10.1080/10407782.2013.826017

[29]Malleswaran A, Sivanandam S. A Numerical Simulation on MHD Mixed Convection in a Lid-driven Cavity with Corner Heaters. Journal of Applied Fluid Mechanics. 2016; 9(1): 311–319. doi: 10.18869/acadpub.jafm.68.224.22903

[30]Öztop HF, Estellé P, Yan WM, et al. A brief review of natural convection in enclosures under localized heating with and without nanofluids. International Communications in Heat and Mass Transfer. 2015; 60: 37–44. doi: 10.1016/j.icheatmasstransfer.2014.11.001

[31]Rao PS, Barman P. Natural Convection in an Open and Wavy Porous Cavity Submitted to a Partial Heat Source. International Journal of Applied and Computational Mathematics. 2024; 10(5): 153. doi: 10.1007/s40819-024-01782-w

[32]Tharapatla G, Rajakumari P, Reddy RGV. Heat and mass transfer effects on MHD non-Newtonian fluids flow through an inclined thermally-stratified porous medium. World Journal of Engineering. 2023; 20(1): 117–130. doi: 10.1108/WJE-02-2021-0099

[33]Aastha A, Chand K. Soret and Dufour Effects on Chemically Reacting and Viscous Dissipating Nanofluid Flowing Past a Moving Porous Plate in the Presence of a Heat Source/Sink. Acta Mechanica et Automatica. 2023; 17(2): 263–271. doi: 10.2478/ama-2023-0030

Early fault signals of the rolling bearing in the rotor are weak and present the characteristics of non-periodic and non-stationary; it is more difficult to carry out fault diagnosis on it. In this regard, this paper proposes a weak rolling bearing fault diagnosis algorithm based on whale optimization algorithm, simplistic geometry mode decomposition, and maximum correlated kurtosis deconvolution (WOA-SGMD-MCKD). Firstly, the vibration signal of the rotor platform is obtained, and the Symmetric Geometric Mode Decomposition (SGMD) is used to reconstruct the vibration signal. To obtain the best decomposition effect of the SGMD and overcome modal aliasing, the Whale Optimization Algorithm (WOA) is used to optimize the embedding dimension. Secondly, for the reconstructed vibration signal, the Maximum Correlated Kurtosis Deconvolution (MCKD) is used to extract its impulse component, and the WOA is used to optimize the filter length and deconvolution period of the MCKD so that the frequency envelope spectrum of the vibration signal can be obtained, which can provide the basis for the fault diagnosis of rolling bearings. Finally, the effectiveness and feasibility of the algorithm proposed are verified by a non-periodic and non-stationary simulation platform and rotor maneuvering platform in this paper.

Numerical solution of a 3D mathematical model for the progression of tumor angiogenic factor in a tissue

In this work, the movement of tumor angiogenic factor in a three-dimensional tissue is obtained by the Method of Lines. This method transforms a partial differential equation into a system of ordinary differential equations together with the initial and boundary conditions. The more the number of lines is increased, the more the accuracy of the method increases. This method results in very accurate numerical solutions for linear and non-linear problems in contrast with other existing methods. We present Matlab-generated figures, which are the movement of tumor angiogenic factor in porous medium and explain the biological importance of this progression. The computer codes are also provided.

Mathematical modelling and controllability analysis of fractional order coal mill pulverizer model

This paper investigates the controllability of nonlinear dynamical systems and their applications, with a focus on fractional-order systems and coal mill models. A novel theorem is proposed, providing sufficient conditions for controllability, including constraints on the steering operator and nonlinear perturbation bounds. The theorem establishes the existence of a contraction mapping for the nonlinear operator, enabling effective control strategies for fractional systems. The methodology is demonstrated through rigorous proof and supported by an iterative algorithm for controller design. Additionally, the controllability of a coal mill system represented as a nonlinear differential system, is analyzed. The findings present new insights into the interplay of fractional dynamics and nonlinear systems, offering practical solutions for real-world control problems.