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The aim of this paper is to study two-dimensional numerical simulations of the flow and temperature fields inside the bend (turn) part of a U-duct.

Several turbulence models based on two and five equations were used to solve the momentum and energy equations inside the bend (turn) part of the U-duct. For two-equation models, both the renormalization group and realizable k-ɛ turbulence models were implemented. The five-equation model used is a Reynolds stress model with different wall boundary conditions. Standard, non-equilibrium and enhanced wall functions were used in parallel with the two- and five-equation models to treat the turbulent flow near the duct walls.

Several turbulence models were used to simulate the flow and temperature fields along the bend part of a U-duct with different inlet and thermal boundary conditions. The numerical results indicate that the renormalization and realizable k-ɛ turbulence models with standard wall function treatment gave the best results when compared with experimental data obtained for similar conditions.

For heat transfer analysis, two different thermal boundary conditions, i.e. constant wall temperature and constant heat flux at the wall are implemented. The results are calculated for Reynolds number equal 20,000.

The results can be used in designing heat exchangers, piping and duct systems, and internal passage cooling of gas turbine blades.

The numerical results obtained here concentrate on the detailed investigation of flow and temperature field at the outer wall of the bend part. Different boundary conditions at the inlet and the outer bend walls of the U-duct were applied to study how these boundary conditions affect the flow and temperature fields.

The purpose of this paper is to investigate the effect of the viscous dissipation of laminar flow through a straight regular polygonal duct on forced convection with constant axial wall heat flux with constant peripheral wall temperature using the boundary element method (BEM).

Both the wall heating case and the wall cooling case are considered. Applying the velocity profile obtained for the duct laminar flow and the energy equation with the viscous dissipation term is solved exactly for the constant wall heat flux using the BEM. The numerical values are obtained by means of a computer program, written by the authors in Fortran. The results of the BEM approach are verified by analytic models. Nusselt numbers are obtained for flows with a different number of sides of a regular polygonal duct and Brinkman numbers.

When the difference in temperature between the wall temperature and the fluid bulk temperature changes the sign, then the functions of the Nusselt number with the Brinkman number generated some singularities (Br_qLs). For the Brinkman number referring to the total wall linear power, with the increasing value of the number of sides of a regular polygonal duct, Br_qLs decreases in the range of 3 ≤ n < ∞. If the Br_qL < Br_qLs, it is possible to note that, in general, the Nusselt number is higher for cross-sections having a lower value of the number of sides of a regular polygonal duct. For Br_qL > Br_qLs, this rule is reversed.

This paper illustrates the effects of viscous dissipation on laminar forced convective flow in regular polygon ducts with a different number n of sides. A compact relationship for the Nusselt number vs the Brinkman number referring to the temperature difference between the wall temperature and the fluid bulk temperature and the Brinkman number, which is based on the total wall linear power, have been proposed.

This study aims to investigate numerically a two-dimensional fully developed mean turbulent fluid flow, and heat transfer in a circular duct is numerically investigated using FORTRAN 95 code that applies the finite difference method to solve the thermal problem for the two thermal boundary conditions, constant surface temperature, constant heat and steady, axisymmetric flow. Several important results have been drawn and discussed from thermal analysis. Finally, the numerical results of the model developed in the document have been validated in good accuracy by comparing them with some correlation results available in the specialized literature.

The methodology of solving the thermal problem is based on the equation of energy for a fluid of constant properties while taking into consideration the hypothesis of the axisymmetric and fully developed pipe flow in steady state. The global equation and the initial and boundary conditions acting on the problem have been configured here in dimensionless form to predict the turbulent behavior of the fluid inside the tube. Thus, using Thomas' algorithm, a program in FORTRAN version 95 was developed to numerically solve the discretized form of the system of equations describing the problem.

The profiles of the solutions are provided from which the authors infer that the numerical and literature correlation agreed very well. Another result that they obtained from this study is the number of Nusselt in the thermal entrance region to which a parametric study based on Reynolds and Peclet numbers, and the longitudinal coordinate, was carried out and discussed well for the impact of the scientific contribution.

The novelty of the work is the application of the finite difference method programed on the FORTRAN code, as a sequential numerical method of an ODEs system, to determine the number of Nusselt in both uniform wall temperature and wall heat flux uniform.

Jet impingement onto surface finds wide application in industry. In laser processing an assisting gas jet is introduced either to shield the surface from oxidation reactions or initiating exothermic reaction to increase energy in the region irradiated by a laser beam. When an impinging gas jet is used for a shielding purpose, the gas jet enhances the convective cooling of the cavity surface. The convective cooling of the laser formed cavity surface can be simulated through jet impingement onto a cavity with elevated wall temperatures. In the present study, gas impingement onto a slot is considered. The wall temperature of the cavity is kept at elevated temperature similar to the melting temperature of the substrate material. A control volume approach is used to simulate the flow and temperature fields. The Reynolds Stress Turbulence model (RSTM) is employed to account for the turbulence. To examine the effect of cavity depth on the heat transfer characteristics, the depth is varied while keeping the cavity width constant. It is found that impinging jet penetrates into a cavity, which in turn, results in a stagnation region extending into the cavity. An impinging gas jet has considerable effect on the Nusselt number along the side walls of the cavity while the Nusselt number monotonically changes with varying cavity depth.

This study aims to methodologically investigate heat transfer effects on reacting flow inside a liquid-fueled, swirl-stabilized burner. Furthermore, particular attention is paid to turbulence modeling and the results of Reynolds-averaged Navier–Stokes and large eddy simulation approaches are compared in terms of velocity field and flame temperature.

Simulations consist liquid fuel distribution using Eulerian–Lagrangian approach. Flamelet-Generated Manifold combustion model, which is a mixture fraction-progress variable formulation, is used to obtain reacting flow field. Discrete ordinates method is also added for modeling radiation heat transfer effect inside the burner. As a parametric study, different thermal boundary conditions namely: adiabatic wall, constant temperature and heat transfer coefficient are applied. Because of the fact that the burner is designed for operating with different materials, the effects of burner material on heat transfer and combustion processes are investigated. Additionally, material temperatures have been calculated using 1 D method. Finally, soot particles, which are source of luminous radiation in gas turbine combustors, are calculated using Moss-Brookes model.

The results show that the flow behavior is obviously different in recirculation region for both turbulence modeling approach, and this difference causes change on flame temperature distribution, particularly in the outer recirculation zone and region close to swirler. In thermal assessment of the burner, it is predicted that material of the burner walls and the applied thermal boundary conditions have significant influence on flame temperature, wall temperature and flow field. The radiation heat transfer also makes a strong impact on combustion inside the burner; however, luminous radiation arising from soot particles is negligible for the current case.

These types of burners are widely used in research of gas turbine combustion, and it can be seen that the heat transfer effects are generally neglected or oversimplified in the literature. This parametric study provides a basic understanding and methodology of the heat transfer effects on combustion to the researchers.

In laser drilling applications, hole wall remains almost the melting temperature of the substrate material and the thermodynamic pressure developed at high temperature molten surface vicinity influences the heat transfer rates and the skin friction at the surface of the hole wall. This effect becomes complicated for the holes drilled in coated substrates. In this case, melting temperatures of the coating and base materials are different, which in turn modifies the flow field in the hole due to jet impingement. Consequently, investigation of the heat transfer rates from the hole wall surfaces and the skin friction at the hole surface becomes essential. The paper aims to discuss these issues.

Numerical solution for jet impingement onto a hole with high wall temperature is introduced. Heat transfer rates and skin friction from the hole wall is predicted. The numerical model is validated with the experimental data reported in the open literature.

The Nusselt number attains high values across the coating thickness and it drops sharply at the interface between the coating and the base material in the hole. Since fluid temperature in the vicinity of the substrate surface is higher than that of the wall temperature, heat transfer occurs from the fluid to the substrate material while modifying the Nusselt number along the hole wall. This results in discontinuity in the Nusselt variation across the coating-base material interface. The Raighly line effect enhances the flow acceleration toward the hole exit while increasing the rate of fluid strain. Consequently, skin friction increases toward the hole exit. The influence of average jet velocity on the Nusselt number and the skin friction is significant.

The findings are very useful to analyze the flow field in the hole at different wall temperature. In the simulations hole diameter is fixed in line with the practical applications. However, it may be changed to examine the influence of hole diameter on the flow field and heat transfer. However, this extension be more toward academic study than the practical significance.

The complete modeling of turbulent flow jet flow impinging onto a hole is introduced and boundary conditions are well defined for the numerical solutions. The method of handing the physical problem will be useful for those working in the area of heat transfer and fluid flow. In addition, the importance of heat transfer rates and skin friction at the hole wall is established, which will benefit the practical engineers and the academicians working in the specific area of laser machining.

The findings are useful for those working to improve the laser technology in the machining area.

The work presented is original and never being published anywhere else. The findings are reported in detail such that academicians and engineers are expected to benefit from this original contribution.

This study aims to undertake a comprehensive examination of heat transfer by convection in porous systems with top and bottom walls insulated and differently heated vertical walls under a magnetic field. For a specific nanofluid, the study aims to bring out the effects of different segmental heating arrangements.

An existing in-house code based on the finite volume method has provided the numerical solution of the coupled nondimensional transport equations. Following a validation study, different explorations include the variations of Darcy–Rayleigh number (Ra_m = 10–10⁴), Darcy number (Da = 10^–5–10^–1) segmented arrangements of heaters of identical total length, porosity index (ε = 0.1–1) and aspect ratio of the cavity (AR = 0.25–2) under Hartmann number (Ha = 10–70) and volume fraction of φ = 0.1% for the nanoparticles. In the analysis, there are major roles of the streamlines, isotherms and heatlines on the vertical mid-plane of the cavity and the profiles of the flow velocity and temperature on the central line of the section.

The finding of a monotonic rise in the heat transfer rate with an increase in Ra_m from 10 to 10⁴ has prompted a further comparison of the rate at Ra_m equal to 10⁴ with the total length of the heaters kept constant in all the cases. With respect to uniform heating of one entire wall, the study reveals a significant advantage of 246% rate enhancement from two equal heater segments placed centrally on opposite walls. This rate has emerged higher by 82% and 249%, respectively, with both the segments placed at the top and one at the bottom and one at the top. An increase in the number of centrally arranged heaters on each wall from one to five has yielded 286% rate enhancement. Changes in the ratio of the cavity height-to-length from 1.0 to 0.2 and 2 cause the rate to decrease by 50% and increase by 21%, respectively.

Further research with additional parameters, geometries and configurations will consolidate the understanding. Experimental validation can complement the numerical simulations presented in this study.

This research contributes to the field by integrating segmented heating, magnetic fields and hybrid nanofluid in a porous flow domain, addressing existing research gaps. The findings provide valuable insights for enhancing thermal performance, and controlling heat transfer locally, and have implications for medical treatments, thermal management systems and related fields. The research opens up new possibilities for precise thermal management and offers directions for future investigations.

This study aims to perform a numerical study of air convection in a rectangular enclosure with two isothermal blocks and oscillating bottom wall temperature under laminar flow conditions. The geometry of the enclosure contains two isothermal blocks placed equidistant along the streamwise direction. The top wall is assumed to be cold (low temperature). The bottom wall temperature is either kept as constant or sinusoidally varied with time. The vertical walls are considered as adiabatic. The flow is diagonally upwards and assisted by the buoyancy force. The inlet is positioned at the bottom of the left wall, and the outlet is placed at the top of the right wall. The parameters considered in this paper are Rayleigh number (104-106), Prantdl number (0.71), amplitude of temperature oscillation (0-0.5) and the period (0.2). The effects of these parameters on heat transfer and fluid flow inside the open cavity are studied. The periodic results of fluid flow are illustrated with streamlines and the heat transfer is represented by isotherms and time-averaged Nusselt number. By virtue of increasing buoyancy, the heat transfer accelerates with an increase in the Rayleigh number. Also, the heat transfer is intensive with an increase in the bottom wall temperature.

The momentum and energy equations are solved simultaneously. The energy equation (3) is initially solved using the alternating direction implicit (ADI) method. The results of the energy equation are updated into the vorticity equation. The unsteady vorticity transport equation is also solved using the ADI method. Dimensionless time step equal to 0.01 is used for high Ra (10⁵ and 10⁶) and 0.001 is used for low Ra (10⁴). Convergence criteria of 10⁻⁵ is used during the vorticity, stream function and temperature calculations, as the sum of error should be very small.

Numerical study of air convection in a rectangular enclosure with two isothermal blocks and oscillating bottom wall temperature is performed under laminar flow condition. The effect of the isothermal blocks on the heat transfer is analyzed for different Rayleigh numbers and the following conclusions are arrived. The hydrodynamic blockage effect is subdued by the isothermal heating of square blocks. Based on the streamline diagrams, it is found that the formation of vortices is greatly influenced by the Rayleigh number when all the walls are exposed to a constant wall temperature. The influence of amplitude on the heat transfer is remarkable on the wall exposed to oscillating temperature and is subtle on the opposite static cold wall. The heat transfer increases with an increase in the Rayleigh number and temperature.

Flow is assumed to be two-dimensional and laminar subject to oscillatory boundary condition. The present investigation aims to study natural convection inside the cavity filled with air whose bottom wall is subject to time-variant temperature. The buoyancy is further intensified through two isothermal square blocks placed equidistant along the streamwise direction at mid-height.

The authors have developed a CFD solver to simulate the situation. Effect of Rayleigh number subject to oscillatory thermal boundary condition is simulated. Streamline contour and isotherm contour are presented. Local and average Nusselt numbers are presented.

This work aims to investigates exact solutions of the classical Glauert’s laminar wall jet mass and heat transfer under wall suction, wall contraction or dilation, and two thermal transport boundary conditions; prescribed constant surface temperature and prescribed constant surface flux in nanofluidic environment.

The flow system arranged in terms of partial dif- ferential equations is non-dimensionalized with suitable dimensionless transformation variables, and this new set of equations is reduced into ordinary differential equations via a set of similarity transformations, where they are treated analytically for closed form solutions.

Exact solutions of nanofluid flow for velocity distributions, momentum flux, wall shear stress and heat transfer boundary layers for commonly studied nanoparticles; namely copper, alumina, silver, and titanium oxide are presented. The flow behavior of alumina and titanium oxide is identical, and a similar behavior is seen for copper and silver, making two pairs of identical traits. The mathematical expressions as well as visual analysis of wall shear drag and temperature gradient which are of practical interest are analyzed. It is shown that wall stretching or shrinking, wall transpiration and velocity slip together influences the jet flow mechanism and extends the original Glauert’s jet solutions. The exact solutions for the two temperature boundary layer conditions and temperature gradients are analyzed analytically. It is found that the effect of nanopar- ticles concentration on thermal boundary layer is intense, causing temperature uplift, whereas the wall transpiration causes a decrease in thermal layers.

The analysis carried out in nanofluid environment is genuinely new and unique, as our work generalizes the Glauert’s classical regular wall jet fluid problem.

Presents a numerical study on heat transfer by natural convection in porous media in vertical enclosures with side wall heating. The model for porous media includes inertia terms and also the Brinkman extension in addition to the Darcy resistance term. A semi‐implicit finite element scheme based on operator splitting method is adopted for solving the time‐dependent system of equations. The first half of the investigations is confined to the low permeability regime where Darcy law holds good. Presents the results for annular and rectangular cavities and proposes correlations for two types of boundary conditions, namely constant wall temperature case and uniform wall heat flux case. In the second half of the investigations, the scheme is applied in a high permeability regime, where the validity of Darcy law becomes questionable. Employs plane rectangular cavities with the two types of boundary conditions mentioned earlier. Highlights the influence of Rayleigh number (Ra) and Darcy number (Da) as separate parameters and proposes correlations for a square cavity for the first time in terms of Ra and Da as separate parameters. Discusses a qualitative study of the effect of aspect ratio on heat transfer as the permeability changes.