MATHEMATICAL ANALYSIS OF NATURAL CONVECTION HEAT TRANSFER IN NANOFLUIDS WITHIN A VERTICAL ANNULUS UNDER THERMAL RADIATION EFFECTS

MATHEMATICAL ANALYSIS OF NATURAL CONVECTION HEAT TRANSFER IN NANOFLUIDS WITHIN A VERTICAL ANNULUS UNDER THERMAL RADIATION EFFECTS

Mathematical Analysis of Natural Convection Heat Transfer in Nanofluids within a Vertical Annulus under Thermal Radiation Effects

^1*MKPEDEM K. A; ²Nyah R; ³FADEPO J. T
1. *Department of Mathematics, University of Abuja, Nigeria.
2.Faculty of Chemical and Process Engineering, Universiti Malaysia Pahang Al-Sultan Abdullah.
3. Department of Industrial Mathematics, Federal University of Science and Technology, Minna. Niger State. Nigeria.
Corresponding author: *kufremkpedem@gmail.com, olayiwola.rasaq@Futminna.edu.ng, fadepoj@gmail.com

Abstract
This study presents a mathematical analysis of convective heat transfer mechanisms relevant to nanofluid flow systems, with particular emphasis on applications in vertical annular geometries subjected to thermal radiation effects. The work examines the fundamental principles of forced convection, dimensional analysis, Reynolds analogy, and heat exchanger effectiveness as essential tools for understanding thermal transport phenomena in nanofluids. Dimensionless parameters including the Reynolds number, Prandtl number, Nusselt number, Stanton number, and Number of Transfer Units (NTU) are derived and analyzed to establish generalized heat-transfer correlations. The influence of nanoparticle concentration on effective thermophysical properties and subsequent heat-transfer enhancement is discussed through modified Reynolds analogy and heat exchanger formulations. The study demonstrates how nanoparticle dispersion improves thermal conductivity, convective heat-transfer coefficients, and overall thermal performance. Furthermore, the effectiveness–NTU method is employed to evaluate heat exchanger performance under varying operating conditions. The developed mathematical framework provides a foundation for predicting and optimizing heat transfer in nanofluid-filled annular systems and advanced thermal engineering applications.

Keywords: Forced Convection, Nanofluids, Reynolds Analogy, Dimensional Analysis, Heat Exchanger Effectiveness, Heat Transfer Enhancement.

DOI: https://doi.org/10.46654/ijaar.v6n12.61244