http://repository.must.ac.ke/handle/123456789/29 Thu, 07 May 2026 10:40:22 GMT 2026-05-07T10:40:22Z http://repository.must.ac.ke/handle/123456789/1545 Mathematical Modelling of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surface of a Vertical Cylinder Ong'era, Omariba Geofrey; Sigey, Johana Kibet; Okelo, Jeconia Abonyo; Karanja, Stephen Mbugua Turbulent natural convection in cylindrical enclosures is a significant phenomenon in most engineering and industrial applications, such as thermal insulation, electronics cooling, and building climate control. An explicit understanding of the transition of flow from laminar to turbulent and its influence on heat transfer is essential in terms of optimizing system performance. The study solves two major objectives: Model the governing equations of turbulent natural convection in a cylindrical enclosure using K-Omega turbulence model, and compute the effective thermal conductivity, turbulence intensity, and streamline distribution as functions of Rayleigh number. The enclosure that has been considered is an insulated vertical sidewall enclosure with a top wall at 298 K and a bottom wall at 320 K. The mathematical formulation consists of the Reynolds-Averaged Navier–Stokes (RANS) equations, the energy equation, and transport equations for turbulence, subject to the Boussinesq approximation to model buoyancy. A low-Reynolds-number two-equation model is used to model turbulence close to the walls, and the Prandtl number is set to 0.71 to model air as the working fluid. Numerical solutions are achieved by the use of the finite difference technique and verified by simulations done in ANSYS Fluent. The simulation identifies how structures flow and mechanisms of heat transfer change with increasing Rayleigh numbers. At small Rayleigh numbers, the flow is steady, conduction-dominated, with smooth streamlines and little or no turbulence. It is noted that as the Rayleigh number increases, buoyancy-driven convection becomes more significant, leading to the formation of vortices, intensified turbulence, and enhanced mixing, which collectively improve the effective thermal conductivity. The streamline distribution becomes increasingly complex and disordered, reflecting the transition to chaotic flow. These results demonstrate that the Rayleigh number is a key parameter influencing thermal and flow characteristics in cylindrical enclosures. The study provides practical insights in designing and optimizing systems involving buoyancy-induced turbulent heat transfer. Fri, 04 Jul 2025 00:00:00 GMT http://repository.must.ac.ke/handle/123456789/1545 2025-07-04T00:00:00Z http://repository.must.ac.ke/handle/123456789/624 A numerical investigation of the effect of curvature and Reynolds number to radial velocity in a curved porous pipe Mwangi, Daniel Mathaia; Karanja, Stephen; Kimathi, Mark Different irrigation methods are being used in agriculture. However, due to scarcity of water, irrigation methods that use water efficiently are needed. The motivation of this study is the increasing use of porous pipes to meet this requirement. The objective of this study is to investigate the effect of curvature and Reynolds number on radial velocity profile of water across a porous wall of a curved pipe with circular cross-section, constant permeability k and porosity ϕ. The momentum equations of the two dimensional flow are written in toroidal coordinates. The main flow in the pipe is only characterized by δ and Re as the only non-dimensional groups of numbers. We also considered the flow to be fully developed, unsteady, laminar and irrotational. Darcy law is used to analyse the flow across the porous membrane. The main flow was coupled with the flow through the porous wall of the pipe. The equations were solved using finite difference method. It was observed that effect of curvature on the velocity across the pipe wall is negligible while an increase in Reynolds number leads to an increase in the radial velocity. The findings of this study are important in the design of porous pipes and also in their use during irrigation. Sun, 01 Jan 2017 00:00:00 GMT http://repository.must.ac.ke/handle/123456789/624 2017-01-01T00:00:00Z http://repository.must.ac.ke/handle/123456789/623 Modeling Open Channel Fluid Flow with Trapezoidal Cross Section and a Segment Base Marangu, Philip Karobia.; Mwenda, Eustace Kirima; Theuri, DM This study investigates the suitability of trapezoidal cross-section with segment base in drainage system design. The study has considered steady uniform open channel flow. The saint-Venant partial differential equations of continuity and momentum governing free surface flow in open channels have been solved using finite difference approximation method. We investigate the effects of the channel radius, area of the cross section, the flow depth and the manning coefficient on the flow velocity. The flow variables are velocity and the flow depth while the flow parameters are cross section area of flow, channel radius, slope of the channel and manning coefficient. The study has established that increase in cross section area of flow leads to a decrease in flow velocity. Further, increase in channel radius and cross section area of flow leads to a decrease in flow velocity and increase in roughness coefficient cause flow velocity to decrease. Additionally, increase in flow depth increases velocity. The physical conditions of the flow channel have been applied to conservation equations to arrive at specific governing equations. The results of the study have been presented graphically. Fri, 01 Jan 2016 00:00:00 GMT http://repository.must.ac.ke/handle/123456789/623 2016-01-01T00:00:00Z http://repository.must.ac.ke/handle/123456789/51 Classical construction of angles in general Kimuya, Alex M. The construction of angles in general is a classical problem in mathematics. The early mathematicians failed to redress the problem under the stated restrictions because they did not have a bearing to approach the problem from. Eventually, the classical problem was assumed impossible. This paper contributes the interest in solving this crucial problem by presenting a very straight forward methodology of constructing angles in general. Several geometrical constructions were carried out to answer the questions; what methodology would generalize the construction of all angles measurable using the protractor? What approach would lead to the construction of some regular polygons whose the angle subtended at their center would only be estimated? The methods revealed in this work responded to these two questions in a simple but a more fashionable way. Two smart chords were generated which helped construct any angle a multiple of both five or two, and both five and two. The methodology involved relating the angles at a difference of ten degrees from each other in their descending order. The idea yielded excellent results. Linear simultaneous equations were used to confirm the accuracy of the two developed chords. The chords were therefore considered to form the base for constructing angles in general. Fri, 01 Jan 2016 00:00:00 GMT http://repository.must.ac.ke/handle/123456789/51 2016-01-01T00:00:00Z