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The conception of a heat function, just like the stream function used in a laminar two dimensional incompressible flow field visualization, has been introduced to visualize the convective heat transfer or the flow of energy around a sphere when the sphere is either being cooled or heated by a stream of fluid flowing around it. The heat function is developed in a spherical polar coordinate and is used to generate the heat lines around the sphere. The heat lines essentially show the magnitude and direction of energy transfer around the sphere with and without the existence of a finite radial velocity at the surface. The steady state hydrodynamic field around the sphere is numerically obtained up to a maximum Reynolds number of 100 and the corresponding thermal field has been obtained by solving the steady state energy equation. The field properties thus obtained are utilized to form the heat function, which becomes an effective tool for visualization of convective heat transfer.

To study quantitatively the effects of combined temperature dependent thermodynamics and transport fluid properties on the heat transfer rate, heat function fields and profiles in a fluid filled square enclosure.

Navier‐Stokes equations in two‐dimensions, which are the flow governing equations, were transformed into stream function and vorticity transport equations. These equations together with the energy and heat function equations were cast into their non‐dimensional forms. Numerical solutions of the resulting equations were done by the use of finite‐difference method.

The numerical investigations conducted covered the Rayleigh and Prandtl numbers in the range 10³≤Ra≤10⁶ and 0.01≤Pr≤450, respectively, and expansion parameter ε=(T_h−T_c)/T_R in the range 0.05≤ε≤1. Results show that Boussinesq‐approximation is not sufficient to simulate natural convective flow when the difference between T_h and T_c is high and close to the reference state temperature. The effects of the other fluids properties other than density can be disregarded in computation without significant loss of accuracy. Combined fluid properties have very strong effects on the heat transfer, heat function fields and profiles.

The results of this study will serve as baseline information to designers of heat transfer or process equipment in which fluid at very high temperature occurs.

The concept of a heat function is introduced to visualize the path of heat flow in a buoyancy‐driven turbulent flow heated vertical flat plate. The velocities and the temperature field near the vertical plate are predicted numerically, using an algebraic flux model of turbulent heat transport. As an accurate prediction of the turbulent heat flux is required in order to predict the heat function in the flow field, the use of an algebraic flux model for the turbulent heat transport θu_i, is made as compared with a simple eddy diffusivity hypothesis. The algebraic flux expression was closed with a low‐Re‐number‐k‐ε — θ² —_θ model. The solution ofthe 4 equation low‐Re‐number‐k‐ε — θ² — ε_θ model predicts very well the local Nusselt number along the plate height as well as the velocity and the temperature field near the wall when compared with the experiments. Then the partial differential equation for the heat function is numerically solved to show the true path of heat flow in the buoyancy‐driven turbulent flow field near a heated vertical plate.

The purpose of this work is to study the effect of surface-radiation on the phenomenon of natural convection flow of a Newtonian fluid in a non-Darcian porous media cavity. The study is mainly focused on the interaction between the inertial resistance of the fluid layers and the surface radiation.

For numerical simulation of transient vorticity transport and energy equations, the paper uses the alternate direct implicit method. Forward Time Central Space descretization is used for the transient and diffusion terms in the alternate direct implicit method, whereas for the convective terms, the method is modified using second upwind differencing technique. ADI method is adopted here, since this technique is unconditionally stable as a complete sweep and is second-order accurate in time for low velocity changes. The stream function equation is solved using the successive over relaxation technique with residual tolerance of order 10-5.

It was found that despite the reduction of flow, the heat transfer increases as the Forschheimer resistance is increased. Further, with the increase in the Planck number, the heat transfer from the bottom radiating wall increases. Darcy drag parameter did not have a significant impact on flow properties except a slight reduction in the flow. Nevertheless, the increase in temperature ratio has a significant impact on flow properties.

The analysis is valid for unsteady, two-dimensional natural convection flow in a fluid-saturated non-Darcy porous medium enclosed by non-isothermal walls. As a first case, the study is conducted for square cavity. An extension to three-dimensional flow case and the study of Darcy-Forschheimer medium with effect of viscous dissipation is left as a part of future work.

The approach is applicable to the modeling of geothermal systems where the inertial resistance to flow also comes into act with the non-uniform temperature distribution. The method is very useful to analyze solar receiver systems, fire research, electronic cooling, brake housing of an aircraft and many environmental geothermal processes.

The study may be of some interest to engineers interested in heat transfer in ventilated rooms or enclosures, the industrial waste, water and atmospheric pollution.

This study aims to investigate the influence of wall curvature in a semicircular thermal annular system on magneto-nanofluidic flow, heat transfer and entropy generation. The analysis is conducted under constant cooling surface and fluid volume constraints.

The mathematical equations describing the thermo-fluid flow in the semicircular system are solved using the finite element technique. Four different heating wall configurations are considered, varying the undulation numbers of the heated wall. Parametric variations of bottom wall undulation (f), buoyancy force characterized by the Rayleigh number (Ra), magnetic field strength represented by the Hartmann number (Ha) and inclination of the magnetic field (γ) on the overall thermal performance are studied extensively.

This study reveals that the fluid circulation strength is maximum in the case of a flat bottom wall. The analysis shows that the bottom wall contour and other control parameters significantly influence fluid flow, entropy production and heat transfer. The modified heated wall with a single undulation exhibits the highest entropy production and thermal convection, leading to a heat transfer enhancement of up to 21.85% compared to a flat bottom. The magnetic field intensity and orientation have a significant effect on heat transfer and irreversibility production.

Further research can explore a wider range of parameter values, alternative heating wall profiles and boundary conditions to expand the understanding of magneto-nanofluidic flow in semicircular thermal systems.

This study introduces a constraint-based analysis of magneto-nanofluidic thermal behavior in a complex semicircular thermal system, providing insights into the impact of wall curvature on heat transfer performance. The findings contribute to the design and optimization of thermal systems in various applications.

The purpose of this paper is to present novel search formulations in gradient‐type methods for prediction of boundary heat flux distribution in two‐dimensional nonlinear heat conduction problems.

The performance of gradient‐type methods is strongly contingent upon the effective determination of the search direction. Based on the definition of this parameter, gradient‐based methods such as steepest descent, various versions of both conjugate gradient and quasi‐Newton can be distinguished. By introducing new search techniques, several examples in the presence of noise in data are studied and discussed to verify the accuracy and efficiency of the present strategies.

The verification of the proposed methods for recovering time and space varying heat flux. The performance of the proposed methods via comparisons with the classical methods involved in its derivation.

The innovation of the present method is to use a hybridization of a conjugate gradient and a quasi‐Newton method to determine the search directions in gradient‐based approaches.

This paper aims to investigate the thermal performance of equivalent square and circular thermal systems and compare the heat transport and irreversibility of magnetohydrodynamic (MHD) nanofluid flow within these systems.

The research uses a constraint-based approach to analyze the impact of geometric shapes on heat transfer and irreversibility. Two equivalent systems, a square cavity and a circular cavity, are examined, considering identical heating/cooling lengths and fluid flow volume. The analysis includes parameters such as magnetic field strength, nanoparticle concentration and accompanying irreversibility.

This study reveals that circular geometry outperforms square geometry in terms of heat flow, fluid flow and heat transfer. The equivalent circular thermal system is more efficient, with heat transfer enhancements of approximately 17.7%. The corresponding irreversibility production rate is also higher, which is up to 17.6%. The total irreversibility production increases with Ra and decreases with a rise in Ha. However, the effect of magnetic field orientation (γ) on total EG is minor.

Further research can explore additional geometric shapes, orientations and boundary conditions to expand the understanding of thermal performance in different configurations. Experimental validation can also complement the numerical analysis presented in this study.

This research introduces a constraint-based approach for evaluating heat transport and irreversibility in MHD nanofluid flow within square and circular thermal systems. The comparison of equivalent geometries and the consideration of constraint-based analysis contribute to the originality and value of this work. The findings provide insights for designing optimal thermal systems and advancing MHD nanofluid flow control mechanisms, offering potential for improved efficiency in various applications.

The purpose of this study is to investigate the influence of enclosure shape on magnetohydrodynamic (MHD) nanofluidic flow, heat transfer and irreversibility in square, trapezoidal and triangular thermal systems under fluid volume constraints, with the aim of optimizing thermal behavior in diverse applications.

The study uses numerical simulations based on a finite element-based technique to analyze the effects of the Rayleigh number (Ra), Hartmann number (Ha), magnetic field orientation (γ) and nanoparticle concentration (ζ) on heat transfer characteristics and thermodynamic entropy production.

The key findings reveal that the geometrical design significantly influences fluid velocity, heat transfer and irreversibility. Trapezoidal thermal systems outperform square systems, while triangular systems achieve optimal enhancement. Nanoparticle concentration enhances heat transfer and flow strength at higher Rayleigh numbers. The magnetic field intensity has a significant impact on fluid flow and heat transport in natural convection, with higher Hartmann numbers resulting in reduced flow strength and heat transfer. The study also highlights the influence of various parameters on thermodynamic entropy production.

Further research can explore additional geometries, parameters and boundary conditions to expand the understanding of enclosure shape effects on MHD nanofluidic flow and heat transfer. Experimental validation can complement the numerical simulations presented in this study.

This study provides valuable insights into the impact of enclosure shape on heat transfer performance in MHD nanofluid flow systems. The findings contribute to the optimization of thermal behavior in applications such as electronics cooling and energy systems. The comparison of different enclosure shapes and the analysis of thermodynamic entropy production add novelty to the study.

The purpose of this paper is to carry out a comprehensive review of some latest studies devoted to natural convection phenomenon in the enclosures because of its significant industrial applications.

Geometries of the enclosures have considerable influences on the heat transfer which will be important in energy consumption. The most useful geometries in engineering fields are treated in this literature, and their effects on the fluid flow and heat transfer are presented.

A great variety of geometries included with different physical and thermal boundary conditions, heat sources and fluid/nanofluid media are analyzed. Moreover, the results of different types of methods including experimental, analytical and numerical are obtained. Different natures of natural convection phenomenon including laminar, steady-state and transient, turbulent are covered. Overall, the present review enhances the insight of researchers into choosing the best geometry for thermal process.

A comprehensive review on the most practical geometries in the industrial application is performed.

The purpose of this study is the hydrothermal analysis of the natural convection phenomenon within the heat exchanger containing nanofluids using the lattice Boltzmann method (LBM).

The thermal conductivity as well as dynamic viscosity of the CuO–water nanofluid is estimated using the Koo-Kleinstreuer-Li model. The LBM has been used with unique modifications to make it flexible with the curved boundaries. The local as well as total entropy generation assessment, local Nusselt variation, as well as heatline visualization are used.

The solid volume percentage of the CuO–water nanofluid, a range of Rayleigh numbers (Ra) and thermal settings of internal operational fins and bodies are all factors that have been thoroughly researched to determine their effects on entropy production, heat transfer efficiency and nanofluid flow.

The originality of this work is using a novel numerical method (i.e. curved boundary LBM) as well as the local/volumetric second law analysis for the application of heat exchanger hydrothermal analysis.