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A finite‐difference scheme is developed for solving the boundary layer equations governing the unsteady laminar free convection flow in open ended vertical concentric annuli. The initial condition considered for the creation of the thermal transient corresponds to a step change in temperature at the inner annulus boundary while the outer wall is maintained adiabatic. Numerical results for a fluid of Pr = 0.7 in an annulus of radius ratio 0.5 are presented. The results show the developing velocity and pressure fields with respect to space and time. Also, the important relationship between the annulus height and the induced flow rate is presented for various values of the time parameter starting from quiescence to the final steady state.

To explore the effect of the annulus geometrical parameters on the induced flow rate and the heat transfer under the conjugate (combined conduction and free convection) thermal boundary conditions with one cylinder heated isothermally while the other cylinder is kept at the inlet fluid temperature.

A finite‐difference algorithm has been developed to solve the bipolar boundary‐layer equations for the conjugate laminar free convection heat transfer in vertical eccentric annuli.

Numerical results are presented for a fluid of Prandtl number, Pr=0.7 in eccentric annuli. The geometry parameters of NR₂ and E (the fluid‐annulus radius ratio and the eccentricity, respectively) have considerable effects on the results.

Applications of the obtained results can be of value in the heat‐exchanger industry, in cooling of underground electric cables, and in cooling small vertical electric motors and generators.

The paper presents results that are not available in the literature for the problem of conjugate laminar free convection in open‐ended vertical eccentric annular channels. Geometry effects having been investigated by considering fluid annuli having radii ratios NR₂=0.1 and 0.3, 0.5 and 0.7 and four values of the eccentricity E=0.1, 0.3, 0.5 and 0.7. Moreover, practical ranges of the solid‐fluid conductivity ratio (KR) and the wall thicknesses that are commonly available in pipe standards have been investigated. Such results are very much needed for design purposes of heat transfer equipment.

An analysis of steady laminar mixed convection boundary layer flow along a vertical cone of constant wall temperature is presented. A mixed convection parameter ξ, as proposed by Lin and Chen, is used to serve as a controlling parameter that determines the relative importance of the forced and the free convection flows. New coordinates and dependent variables are then defined in terms of ξ, so that the transformed non‐similar boundary layer equations give computationally efficient numerical solutions which are valid over the entire range of mixed convection flow from the forced convection limit to the free convection limit for fluids of any Prandtl number. The effects of the mixed convection parameter ξ and the Prandtl number Pr on the velocity and temperature profiles as well as on the skin friction and heat transfer coefficients are shown for both cases of buoyancy assisting and buoyancy opposing flow conditions.

The fully developed laminar mixed convection flow in inclined tubes subject to axially and circumferentially uniform heat flux has been studied numerically for a Boussinesq fluid. Dual solutions characterized by a two‐ and a four‐vortex secondary flow structure in a cross‐section normal to the tube’s longitudinal axis have been found for different combinations of the Grashof number Gr and of the tube inclination α for all Prandtl numbers between 0.7 and 7. In the two‐parameter space defined by Gr and α dual solutions occur: at a given α, if the Grashof number exceeds a critical value Gr_ℓ (for horizontal tubes Gr_ℓ is approximately 5.5 × 10⁵, 1.7 × 10⁵ and 1.7 × 10⁴ respectively for Pr = 0.7, 7 and 70); at a given Gr, if the tube inclination is below a critical value α_c (for Gr = 10⁶ this critical angle is approximately 62.5° and 83.5° respectively for Pr = 0.7 and 7). Numerical experiments carried out for developing flows indicate that the two‐vortex solution is the only stable flow structure.

The effects of tube inclination and Grashof number on the fully developed hydrodynamic and thermal fields are investigated numerically for laminar ascending flow of air and water in uniformly heated circular tubes. The effects of the buoyancy induced secondary flow on the hydrodynamic and thermal fields are complex and strongly dependent on the Grashof number, the Prandtl number and the tube inclination. The influence of these parameters on the intensity of the secondary flow, on the distortion of the axial velocity profile and of the temperature field from the corresponding distributions for pure forced flow, as well as on the circumferential variation of the local shear stress and of the local Nusselt number are analysed. The average shear stress is higher than for pure forced flow and it increases with both the tube inclination and with the Grashof number. The average Nusselt number is higher than for pure forced flow and increases with the Grashof number. For a given fluid and Grashof number there exists an optimum tube inclination which maximizes the average Nusselt number. Correlations for the average Nusselt number in terms of Gr and Pr are presented for four different tube inclinations.

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 aim of this article is to present the results of a parametric analysis of the entropy generation due to mixed convection in the entry‐developing region between two differentially heated isothermal vertical plates.

The entropy generation was estimated via a numerical solution of the mass, momentum and energy conservation equations governing the flow and heat transfer in the vertical channel between the two parallel plates. The resultant temperature and velocity profiles were used to estimate the entropy generation and other heat transfer parameters over a wide range of the operating parameters. The investigated parameters include the buoyancy parameter (Gr/Re), Eckert number (Ec), Reynolds number (Re), Prandtl number (Pr) and the ratio of the dimensionless temperature of the two plates (θ_T).

The optimum values of the buoyancy parameter (Gr/Re) optimum at which the entropy generation assumes its minimum for the problem under consideration have been obtained numerically and presented over a wide range of the other operating parameters. The effect of the other operating parameters on the entropy generation is presented and discussed as well.

The results of this investigation are limited to the geometry of vertical channel parallel plates under isothermal boundary conditions. However, the concept of minimization of entropy generation via controlling the buoyancy parameter is applicable for any other geometry under any other thermal boundary conditions.

The results presented in this paper can be used for optimum designs of heat transfer equipment based on the principle of entropy generation minimization with particular focus on the optimum design of plate and frame heat exchanger and the optimization of electronic packages and stacked packaging of laminar‐convection‐cooled printed circuits.

This paper introduces the entropy generation minimization via controlling the operating parameters and clearly identifies the optimum buoyancy parameter (Gr/Re) at which entropy generation assumes its minimum under different operating conditions.

The interaction of variable property convection and surface radiation in a differentially heated square cavity is considered. Effect of surface radiation on natural convection has been studied from the point of view of flow structure and isotherm patterns. Wherever possible, a comparative study has been invoked between the outcome of the present work and the constant property formulation. The finite element method has been used in the present work and associated formulation schemes have been described in detail.

The paper seeks to focus on obtaining the transient torque required to rotate the inner cylinder in open ended vertical concentric annuli for a fluid of Pr = 0.7 in the laminar natural convection flow regime over a wide range of the controlling parameter Gr²/Ta. The inner wall is heated and subjected to an impulsive rotation while the outer one is stationary and maintained adiabatic.

The governing transient boundary‐layer equations are numerically solved using an iterative linearized finite‐difference scheme.

The transient induced flow rate and absorbed heat for different annulus heights are presented. High rotational speed (i.e. low values of Gr²/Ta) increases the flow rate and heat absorbed in short annuli. However, for considerably tall annuli, Gr²/Ta has slight effect on the flow and heat absorbed. The steady‐state time is tangibly influenced by Gr²/Ta in considerably short annuli and very slightly affected for considerably tall annuli.

The investigated problem can simulate the start‐up period of naturally cooled small vertical electric motors.

The paper presents results not available in the literature for the effect of Gr²/Ta on the developing velocities, pressure, flow‐rate induced, absorbed heat by fluid and required torque in vertical concentric annuli with impulsively rotated inner walls under the transient free‐convection heat transfer mode.

The paper utilizes a boundary‐layer model in bipolar coordinates to study the developing laminar free convection in vertical open‐ended eccentric annuli with one of the boundaries uniformly heated while the other boundary is cooled and kept isothermal at the ambient temperature. This model has been solved numerically using finite‐difference techniques. Results not available in the literature are presented for a fluid of Prandtl number 0.7 in an annulus of radius ratio 0.5 for three values of the dimensionless eccentricity, namely, 0.1, 0.5 and 0.7. These results include the developing velocity profiles and the pressure along the annulus, the channel heights required to naturally induce different flow rates and the variation of the total heat absorbed by the fluid with the channel height.