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In this paper, an extended immersed boundary method is used to study the convection of heat from two rotating hot cylinders in a square cold cavity containing air with Pr = 0.7 . The variables in this study are the rotation scenario, Rayleigh and Richardson numbers. The computations have been carried out for three different rotation scenarios and a range of Rayleigh and Richardson numbers, i.e. Ra = 10 4 , 10 5 and 10 6 and Ri = 0.1 , 1 , 10 , 100 . The pure natural convection case, i.e. Ri → ∞ , has also been considered. Isotherms, streamlines, local and average Nusselt numbers on all solid boundaries are reported in each test case. It is found that the Rayleigh and Richardson numbers are the dominant variables. Rotation scenario is also important and the rotation may significantly increase the heat transfer rate from the cylinders compared to the corresponding buoyancy-induced convection case. Unstable, periodic flow patterns are observed in some test cases at Ra = 10 6 . [ABSTRACT FROM AUTHOR]

The natural convection heat transfer flow of temperature dependent thermal conductivity on an electrically conducting fluid along a vertical flat plate with heat generation have been investigated in this paper. The governing equations with associated boundary conditions for this phenomenon are converted to dimensionless forms using a suitable transformation. The transformed non-linear equations are then solved using the implicit finite difference method. Numerical results of the velocity and temperature profiles for Prandtl number and heat generation parameter, skin friction and local rate of heat transfer profiles for different values of the thermal conductivity variation parameter, Prandtl number and heat generation parameters are presented graphically. Detailed discussion is given for the effects of the aforementioned parameters. Significant effects are found in velocity and temperature profiles for Prandtl number. Remarkable effects are found in skin friction and heat transfer for heat generation parameter. Also significant effect is found in heat transfer for thermal conductivity variation parameter. [ABSTRACT FROM AUTHOR]

Abstract: Convection in a layer of fluid with a free surface due to a combination of thermocapillary stresses and buoyancy is one of the classic problems of fluid mechanics. Although extensively studied, it is still not fully understood. In particular, neither the effect of phase change nor the thermal boundary conditions at the liquid–vapor interface have been properly described. These two intimately related issues have a significant impact on the stability of the flow and transitions between different convective patterns. The objective of this paper is to develop and validate a comprehensive numerical model which properly describes both heat transfer and phase change at the liquid–vapor interface, as well as the transport of heat and vapor in the gas layer, which is ignored by the vast majority of theoretical studies with minimal justification. We present a numerical investigation of convection in a long cell filled with a volatile fluid and air, and investigate the changes in convective patterns due to with changes in the applied horizontal temperature gradient. We also explore how variations in the wetting properties of the fluid and lateral confinement (three-dimensionality) affect the flow. While the numerical results have been found to be in general agreement with existing experimental observations, we have also discovered an unexpected phenomenon: a region of evaporation near the cold wall and a region of condensation near the hot wall. [Copyright &y& Elsevier]

Abstract: In this paper, effect of magnetic field on free convection heat transfer in an enclosure filled with nanofluid is studied. KKL (Koo-Kleinstreuer-Li) correlation is used for simulating effective thermal conductivity and viscosity of nanofluid. The inner cylinder is maintained at uniform heat flux and the outer cylinder has constant temperature. The governing equations are solved via Control Volume based Finite Element Method. The heat transfer between cold and hot regions of the enclosure cannot be well understood by using isotherm patterns so heatline visualization technique is used to find the direction and intensity of heat transfer in a domain. Effect of Hartmann number, volume fraction of nanoparticle, Rayleigh number and aspect ratio on streamline, isotherm and heatline are examined. The results show that as Hartmann number increases Nusselt number decreases while opposite trend is observed as nanoparticles volume fraction, Rayleigh number and aspect ratio increase. Domination of conduction mechanism causes heat transfer enhancement to increase. So enhancement in heat transfer increases with increase of Hartmann number and aspect ratio while it decreases with augment of Rayleigh number. [Copyright &y& Elsevier]

Abstract: The steady laminar boundary layer flow along a vertical stationary plate with convective surface boundary condition is investigated in this paper. The heat transfer coefficient is considered either constant or variable along the plate and the problem is either non-similar or similar. The results are obtained with the direct numerical solution of the governing equations. The problem is governed by Prandtl number and a convective parameter and the influence of these parameters on the results are presented in tables and figures. There are differences in the results between the non-similar and similar case at low values of the convective parameter but as this parameter increases the differences decrease and the flow tends to the classical natural convection along a vertical isothermal plate. [Copyright &y& Elsevier]

Abstract: In this paper, a new boundary-domain integral equation for solving energy equation in convective heat transfer problems is derived. The derived integral equation accounts for fluid velocity which is computed using the velocity boundary-domain integral equations presented in [2,3] (X.W. Gao, 2004, 2005). Numerical implementation of these integral equations is discussed for steady incompressible fluid flows, in which the velocity and pressure integral equations are uncoupled from the temperature equation, and thus can be solved separately. By substituting the velocity, velocity gradient, and pressure integral equations into the energy integral equation, temperatures can be computed without iterative processes. Two numerical examples for 2D problems are given to validate the proposed method. [Copyright &y& Elsevier]

Abstract: This paper reports an analytical and numerical study of natural convection in a shallow enclosure filled with a non-Newtonian fluid. Thermal boundary conditions of the Neumann type are applied on the horizontal walls of the enclosure while the vertical walls are assumed adiabatic. A power law model is used to characterize the non-Newtonian fluid behavior of the fluid. The governing parameters for the problem are the thermal Rayleigh number Ra, power-law index n, Prandtl number Pr and cavity aspect ratio A. An analytical solution, valid for an infinite layer, is derived on the basis of the parallel flow approximation. Rigid–rigid, free–free and rigid–free hydrodynamic boundary conditions are considered. It is demonstrated that, for shear-thinning fluids, the onset of convection is subcritical. For shear thickening fluids, convection is found to occur at a supercritical Rayleigh number equal to zero. The effects of the non-Newtonian behavior on the fluid flow, temperature field and heat transfer are discussed. A good agreement is found between the analytical predictions and the numerical results obtained by solving the full governing equations. [Copyright &y& Elsevier]

Abstract: This paper considers the heat and mass transfer characteristics of some nanofluid flows past a vertical infinite flat plate. The radiation effect for two distinct types of thermal boundary conditions is also taken into account. Derivation of exact analytical solutions are aimed for different water-based nanofluids containing Cu, Ag, CuO, Al2O3, and TiO2. The velocity and temperature profiles, skin friction coefficient and Nusselt number are easily examined and discussed via the closed forms obtained which may be further used to verify the validity of obtained numerical solutions for more complicated transient free convection nanofluid flow problems. [Copyright &y& Elsevier]

Abstract: This paper discusses the problem of blade cooling system optimization connected with conjugate heat transfer (CHT) analysis for reliable thermal field prediction within a steam cooled component. Since the full CHT solution, which involves the main flow, blade material and the coolant flow domains is computationally expensive from the point of view of optimization process, it was decided to reduce the problem by fixing the boundary conditions at the blade surface and solving the task for the interior only (both solid material and coolant). Such assumption, on one hand, makes the problem computationally feasible, and on the other, provides more reliable thermal field prediction than it used to be with the empirical relationships. The analysis involves shape optimization of internal cooling passages within an airfoil. The cooling passages are modeled with a set of four Bezier splines joined together to compose a closed contour. Each passage is fed with cooling steam of constant parameters at the inlet. In the present study the airfoil profile is taken as aerodynamically optimal. The search problem is solved with evolutionary algorithm and the final configuration is to be found among the Pareto optimal cooling candidates. [Copyright &y& Elsevier]

Abstract: In this paper, mixed convection flow and heat transfer around a long cylinder of square cross-section under the influence of aiding buoyancy are investigated in the vertical unconfined configuration (Reynolds number, Re =1–40 and Richardson number, Ri =0–1). The semi-explicit finite volume method implemented on the collocated grid arrangement is used to solve the governing equations along with the appropriate boundary conditions. The onset of flow separation occurs between Re =1–2, between Re =2–3 and between Re =3–4 for Ri =0, 0.5 and 1, respectively. The flow is found to be steady for the range of conditions studied here. The friction, pressure and total drag coefficients are found to increase with Richardson number, i.e., as the influence of aiding buoyancy increases drag coefficients increase at the constant value of the Reynolds number. The temperature field around the obstacle is presented by isotherm contours at the Prandtl number of 0.7 (air). The local and average Nusselt numbers are calculated to give a detailed study of heat transfer over each surface of the square cylinder and an overall heat transfer rate and it is found that heat transfer increases with increase in Reynolds number and/or Richardson number. The simple expressions for the wake length and average cylinder Nusselt number are obtained for the range of conditions covered in this work. [Copyright &y& Elsevier]

Abstract: This paper aims to study the gravity effects on the mixed convection heat transfer in a microchannel using lattice Boltzmann method. To include these effects, hydrodynamic boundary condition equations are modified. In this problem, cold fluid enters the microchannel and leaves it after cooling the hot walls. For a wide range of inlet Knudsen number (Kn), computations are performed, and for validation, appropriate comparisons between present and previous available results are made. As the results, stream lines, longitudinal variations of friction coefficient, Nusselt number, slip velocity and temperature jump, and velocity and temperature profiles in different cross sections are presented. The results show that lattice Boltzmann method can be used to simulate mixed convection in a microchannel, and the effects of buoyancy forces are important for Kn < 0.05, specially for hydrodynamic properties, and thus should be included. For Kn > 0.05, these effects can be ignored. In addition, it is observed that buoyancy forces generate a rotational cell in the microchannel flow, leading to the negative slip velocity at Kn = 0.005. [Copyright &y& Elsevier]

Abstract: In this paper, the possible optimal thickness of a heat sink base has been explored numerically with different convective heat transfer boundary conditions in a dimensionless three dimensional heat transfer model. From the numerical results, relations among different heat transfer mechanisms (natural or forced, air or liquid), different area ratios of a heat sink to a heating source, and the lowest thermal resistance have been obtained and discussed. Also a simple correlation for these three parameters from data fitting is given for guiding a heat sink design. [Copyright &y& Elsevier]

Abstract: This paper presents a two-step up-scaling approach to determine the jump relations that must be imposed at the interface between a homogeneous porous domain and a free domain. We study convective heat transfer at such an interface under the assumption of local thermal equilibrium. The two-step approach has the capability of providing closed jump relations depending on intrinsic characteristic of the interface. In addition, from the resulting jump relations, it is possible to determine a particular interface location where the condition of continuity are sufficient. Thus, the use of jump or continuity conditions depend only on the interface location inside the fluid–porous transition region. [Copyright &y& Elsevier]

Abstract: In this paper, a theoretical study of laminar forced convection inside ducts, subjected to periodically varying inlet temperature is presented. A thermal diffusion in the duct walls and a boundary condition which accounts for external convection are considered. In the first part, this problem is solved by applying a Generalized Integral Transform Technique (GITT). The complex eigenvalues and coefficients results are listed and compared with the literature. In the second part, the Quasi-steady Approach (QSA) which employs a constant heat transfer coefficient at liquid–solid interface is also investigated and compared with the GITT solution. The bulk temperature, Nusselt number, the damping and phase lag coefficients as function of the inlet temperature frequency are plotted. [Copyright &y& Elsevier]

Abstract: This paper concerns the physical process of heat transfer from hot wires located in the proximity of walls consisting of different thermal conductivities. It points out that it is common practice to calibrate hot wires in a free stream of constant and known velocity, but when utilized for near-wall measurements additional heat losses occur owing to the presence of the wall, resulting in erroneous velocity readings. Therefore, a combined experimental and numerical methodology for heat transfer from a heated wire in a flow field is proposed, taking the effects of wire diameter, overheat ratio, wall thermal conductivity, wall distance, wall thickness and shear rate on the measured velocity into account. The present investigations indicated that the flow under the plate, i.e., the corresponding shear rate at the wall opposite the location of the wire where velocity measurements were taken, changes the thermal boundary conditions around the hot wire. It was also observed that heat diffusivity is dominant in the wall region and plays the major role in heat transfer from the wire rather than convection, especially for highly heat-conducting materials. For highly heat-conducting walls, a universal correction law for the wall influence was given by Durst et al. [F. Durst, E.-S. Zanoun, M. Pashtrapanska, In situ calibration of hot wires close to highly heat-conducting walls, Exp. Fluids 31 (2001) 103–110]. However, for poorly heat-conducting walls, the correction law depends on the wall thickness and the heat transfer from the surface opposite the wall where the hot-wire measurements were performed. [Copyright &y& Elsevier]

Abstract: A Direct Numerical Simulation (DNS) method has been developed to solve the heat transfer equations for the computation of thermal convection in particulate flows. This numerical method makes use of a finite difference method in combination with the Immersed Boundary (IB) method for treating the particulate phase. A regular Eulerian grid is used to solve the modified momentum and energy equations for the entire flow region simultaneously. In the region that is occupied by the solid particles, a second particle-based Lagrangian grid is used, which tracks particles, and a force density function or an energy density function is introduced to represent the momentum interaction or thermal interaction between particle and fluid. The numerical methods developed in this paper have been validated extensively by comparing the present simulation results with those obtained by others. [Copyright &y& Elsevier]