In this paper pin-fin cooling by Mixed Convection has been considered. The system consisting of a pin-fin heat sink and a chimney is presented for increasing heat transfer and draft force. The flow regime is laminar. The results is applied to problems in which the size of the overall system is constrained. For a given heat dissipation and total system size optimal values of the pin-fin diameter and heat sink porosity are obtained. It is shown hat the optimum occur for systems with and without chimney. The pin-fin array is modeled as a Forchheimer-flow porous medium (Non Darcy-flow). The results of optimization are compared with existing data in literature. Also it is shown that the results obtained grom Forchheimer-flow porous model agree much better with the experimental results compared with the natural Convection dary model.

The present paper investigates, numerically, the effect of the Grashof number to a Reynolds number ratio (Gr/Re), on fluid flow and heat transfer within a vertical channel for two cases: Mixed (natural-forced) Convection and combined Mixed Convection-radiation. The flow in the channel is assumed to be two-dimensional, laminar and steady. The wall temperature is defined as a linear function of the channel height. When dealing with the combined Mixed Convection-radiation case, radiational properties have been taken into account, both for the walls and the fluid. The fluid has a Prandtl number of 0.71 and it is radiationally assumed as a participating medium. A comparison between the two cases at a constant Gr/Re is reported, so as to investigate the influence of radiation, as one of the heat transfer modes, more clearly. To solve the governing equations (i.e., mass continuity, momentum and energy) the Finite Volume method is employed and the SIMPLE algorithm is adopted to couple the velocity and pressure fields. The radiative transfer equation is solved using the Discrete Ordinates Method, by adopting its $S_4$ order quadrature scheme. The results for both cases are presented as the profiles of axial velocity across the channel width, axial centerline velocity, bulk temperature and pressure versus channel height.

A combined Convection process between two parallel vertical infinite walls, containing an incompressible viscous fluid layer and a fluid saturated porous layer has been presented analytically. There is a vertical axial variation of temperature in the upward direction along the walls. The Brinkman extended Darcy model is applied to describe the momentum transfer in the porous region. The viscosity of the fluid layer and the effective viscosity of the porous layer are assumed to be different. Also the thermal conductivities of both fluid and porous layers are assumed to be different. The graphs and tables have been used to distinguish the influence of distinct parameters on the velocity and skin-friction. It is determined that the velocity is intensified on making greater the temperature difference between the walls while increment in the viscosity ratio (porous/fluid) parameter diminishes the velocity of the fluid. It has been observed that the numerical values of the skin-frictions have an increasing tendency with the increment in the values of temperature difference between the walls while decreasing tendency with the increment in the viscosity ratio parameter (porous/fluid).

In this study, stability of unsteady Mixed Convection in a horizontal annulus between two concentric cylinders was investigated numerically. The surfaces of the cylinders were considered to be at fixed temperatures and it was assumed that the hot inner cylinder is rotating at a constant angular velocity. The buoyancy forces were formulated utilizing the Boussinesq approximation. The governing equations of fluid flow and heat transfer in the annulus were solved with a finite element method for different values of the geometric (radius ratio) and transport parameters (Rayleigh number and Reynolds number). Development of the convective flow and heat transfer was expressed by the average Nusselt number for the outer cylinder. The results show that, for a narrow gap annulus, convective flow induces flow bifurcation and becomes unstable for high values of the Rayleigh number. Flow becomes more unstable with an increase in the Reynolds number. For a wide gap annulus, flow is stable for all values of the Rayleigh number if the rotation effects are small. On the other hand, convective flow becomes unstable for the modest and high values of the Ra number with an increase in the Re number.

A numerical investigation of unsteady laminar Mixed Convection heat transfer in a lid driven cavity of aspect ratio of 5 is performed. The forced convective flow inside the cavity is attained by a mechanically induced sliding lid, which is set to oscillate horizontally. The natural Convection effect is sustained by subjecting the bottom wall to a higher temperature than its top counterpart. In addition, the two vertical walls are kept insulated. Discretization of the governing equations is achieved through a finite volume method. Fluid flow and heat transfer characteristics are examined in the domain at Richardson number, Grash of number and dimensionless lid oscillation frequency of: 10-3 £ Ri £103 , Gr = 104, and S=0.001, 01, respectively the working fluid is assigned a Prandtl number of 0.7 throughout this investigation. Temporal variations of streamlines, isotherms, and Nusselt number are presented for various dimensionless groups. The results show that with decreasing the value of oscillation frequency, while Ri<1, the amplitude and the period of the rate of heat transfer oscillations increase.

This work indicates a numerical study on the laminar heat transfer Mixed Convection in a square cavity with two openings (an inlet and an outlet) on vertical walls through which nanofluid flows. Two flow directions are examined: i) ascending flow which enters the bottom opening and exits the upper opening; ii) descending flow which enters the upper opening and exits the bottom opening. The ascending flow contributes to buoyancy forces while for the descending flow, the opposite takes place. The intention is to cool a heat source placed at the center of the geometry. The nanofluid has Copper nanoparticles and water as its base-fluid. The velocity and temperature of the entrance flow are known. Some results are experimentally and numerically validated. A mesh independency study is carried out. Some parameters are ranged as follows: i) the Reynolds number from 50 to 500, the nanofluid volume fraction from 0 to 1%, the Grashof number from 103 to 105. It is noteworthy to mention that in some cases, the fluid is stuck inside the cavity which weakens the heat transfer. The nanoparticles increase the heat transfer of 4% for the ascending primary flow inside the cavity.

Magnetic nanofluids (MNFs) have been the focus of extensive research nowadays owing to their potential usefulness as a transfer medium. This study is concerned with the boundary layer flow and heat transfer of MNF past a rotating vertical cone with the embedment of the porosity regime and Mixed Convection. The buoyancy opposing flow on the combined free and forced Convection is being emphasized in this study to evaluate the behavior of the fluid within this region and predict the point of the boundary layer transition. The initial formulation of the model is simplified appropriately by employing the suitable similarity transformation. The package of bvp4c MATLAB is employed to execute the numerical solutions. Analysis of stability is also reported. Due to the Mixed Convection parameter, the opposing flow contributes towards two different alternative solutions, but the second solution is not stable. A higher local Nusselt number are achieved by increasing the concentration of magnetic nanofluid up to 2% and enlarging the Mixed Convection parameter under the influence of the porosity regime in the vertical rotating cone. It has been established in this study that the addition of cobalt ferrite as the magnetic nanoparticles (MNPs) is proven to have the ability in enhancing the thermal performance of the fluid.

In this paper, Mixed forced and natural Convection heat transfer in a rectangular cavity has been numerically studied. The cavity receives a uniform heat flux from one side and is ventilated with a uniform external flow. The external flow enters the cavity from the heated side and leaves the cavity from the opposite side. The velocity and temperature fields and heat transfer rate are determined by solving the two-dimensional continuity, momentum and energy equations. In this research, steady-state flow with constant Reynolds number, Re=100, is considered. Rayleigh number is in the range of 0£Ra£107. First, the results are presented for a cavity with constant aspect ratio, AR=2, and four different inlet and exit opening positions. Then cases with a fixed opening position and different aspect ratios including 0.1, 0.25, 1, 4 and 10 are modeled. In the cavities with opening in the bottom or cavities with aspect ratios less than one, the results show weak effects of natural Convection on heat transfer. This research has been done for air as a working fluid (Pr = 0.71). In some cases, the results are compared with those from previous studies.

A numerical analysis is carried out to study the performance of Mixed Convection in a rectangular enclosure. Four different placement configurations of the inlet and outlet openings were considered. A constant flux heat source strip is flush-mounted on the vertical surface, modeling an integrated circuit chips affixed to a printed circuit board, and the fluid considered is air. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh elements by a nonlinear parametric solution algorithm. Results are obtained for a range of Richardson number from 0 to 10 at Pr= 0.71 and Re = 100 with constant physical properties. At the outlet of the computational domain a convective boundary condition (CBe) is used. The results indicate that the average Nusselt number and the dimensionless surface temperature on the heat source strongly depend on the positioning of the inlet and outlet. The basic nature of the resulting interaction between the forced external air stream and the buoyancy-driven flow by the heat source is explained by the heat transfer coefficient and the patterns of the streamlines, velocity vectors and isotherms.