Natural convection heat transfer in partially open inclined square cavities

A numerical study has been carried out on inclined partially open square cavities, which are formed by adiabatic walls and a partial opening. The surface of the wall inside the cavity facing the partial opening is isothermal. Steady-state heat transfer by laminar natural convection in a two dimensional partially open cavity is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10³ to 10⁶, dimensionless aperture size from 0.25 to 0.75, aperture position at high, center and low, and inclination of the opening from 0° (facing upward) to 120° (facing 30° downward). It is found that the volume flow rate and Nusselt number are an increasing function of Rayleigh number, aperture size and generally aperture position. Other parameters being constant, Nusselt number is a non-linear function of the inclination angle. Depending on the application, heat transfer can be maximized or minimized by selecting appropriate parameters, namely aperture size, aperture position and inclination angle at a given operation Rayleigh number.     

Conjugate natural convection heat transfer in an inclined square cavity containing a conducting block

The present work is concerned with computation of natural convection flow in a square enclosure with a centered internal conducting square block both of which are given an inclination angle. Finite volume method through the concepts of staggered grid and SIMPLE algorithm have been applied. Deferred QUICK scheme has been used to discretize the convective fluxes and central difference for diffusive fluxes. The problem of conjugate natural convection has been taken up for validating the code. The abrupt variation in the properties at the solid/fluid interface are taken care of with the harmonic mean formulation. Solution has been performed in the computational domain as a whole with proper treatment at the solid/fluid interface. Computations have been performed for Ra = 10³–10⁶, angle of inclination varying from 15° to 90° in steps of 15° and ratio of solid to fluid thermal conductivities of 0.2 and 5.0. Results are presented in terms of streamlines, isotherms, local and average Nusselt number.     

Conjugate forced convection heat transfer from a flat plate by laminar plane wall jet flow

An analytical solution is investigated for forced convection heat transfer from a laminar plane wall jet as conjugate case. For Re ? 1, boundary layer theory is used for the investigation. The problem has been solved for two classic cases such as Pr ? 1 and Pr ? 1. The conjugate model consists of considering the full Navier-Stokes equation in the fluid medium and coupling of energy equations in the fluid and the slab through the interface boundary conditions. Closed-form relations are found for Nusselt number (Nu), average Nusselt number and conjugate interface boundary temperature (θ_b). The effects of the Reynolds number (Re), the Prandtl number (Pr), the thermal conductivity ratio (k) between the slab and the fluid medium and the slab aspect ratio (λ) are investigated on the heat transfer characteristics. The analytical results are compared with the full numerical results.     

Conjugate conduction-natural convection heat transfer in a hollow building block

Conjugate heat transfer across a hollow block is investigated numerically. Conduction heat transfer in the block material and natural convection in the cavity are considered. Results show that increasing the number of cavities while keeping the block width constant decreases the heat loss (increases the R-value) significantly. A maximum number of six cavities can fit the building block without compromising the strength. With this number of cavities, no insulation would be needed to fill the cavities as a result of the reduced effect of natural convection. This study may provide guidelines for engineers toward better design and selection of building materials for higher thermal resistance.     

Numerical analysis of conjugate heat transfer in a partially open square cavity with a vertical heat source

Conjugate heat transfer in partially open square cavity with a vertical heat source has been numerically studied. The cavity has an opening on the top with several lengths and three different positions. The other walls of cavity were assumed adiabatic. The heat source was located on the bottom wall of cavity and it has got a width such as Printed Circuit Boards (PCB). Steady state heat transfer by laminar natural convection and conduction is studied numerically by solving two dimensional forms of governing equations with finite difference method. The results were reported for various governing parameters such as Rayleigh number (10³ ≤ Ra ≤ 10⁶), conductivity ratio, opening position, opening length, PCB distance and PCB height. The numerical results were discussed with streamlines, isotherms, Nusselt number and velocity profiles on x- and y-directions. It is found that ventilation position has a significant effect on heat transfer.     

Laminar natural convection in inclined open shallow cavities

Laminar steady state natural convection in inclined shallow cavities has been numerically studied. The side facing the opening is heated by a constant heat flux, sides perpendicular to the heated side are insulated and the opening is in contact with a fluid at constant temperature and pressure. Equations of mass, momentum and energy are solved using constant properties and Boussinesq approximation and assuming an approximate boundary conditions at the opening. Isotherms and streamlines are produced, heat and mass transfer is calculated for Rayleigh numbers from 10³ to 10¹⁰, cavity aspect ratio A=H/L from 1 to 0.125. The results show that flow and heat transfer are governed by Rayleigh number, aspect ratio and the inclination. Heat transfer approaches asymptotic values at Rayleigh numbers independent of the aspect ratio. The asymptotic values are close to that for a flat plate with constant heat flux. The effect of elongation of open cavities is to delay this asymptotic behavior. It is also found that the inclination angle of the heated plate is an important parameter affecting volumetric flow rate and the heat transfer.     

Conjugate heat transfer analysis of copper staves and sensor bars in a blast furnace for various refractory lining thickness

Lining erosion is the most important factor for determining the campaign life of a blast furnace. To provide information about the heat transfer of the copper stave in the belly of the No. 1 blast furnace at CSC (China Steel Corporation), a conjugate heat transfer model, including the heat transfer of the stave and sensor bar in thermal conduction and radiation transmission from the gas temperature inside the blast furnace and convection heat transfer in cooling pipe, was developed for the steady state process. The simulations focus specifically on the effects of the gas temperature, the geometric thickness of the cooling stave, the slag layer thickness and the material and diameter of the sensor bar. The results show that the refractory lining and the slag shell provide significant protection for the stave body. A copper sensor bar can be used to measure the residual lining thickness of the cooling stave. To estimate a more reasonable stave thickness, several key factors, such as the diameter and material of the sensor bar, were examined in this study. The results can serve as important reference information for blast furnace operation and the prediction of its campaign life.     

Parametric study on mixed convection heat transfer in an inclined arc-shape cavity

This paper presents a parametric study on mixed convection heat transfer in an inclined arc-shape cavity subjected to a moving lid. The governing equations for the inclined arc-shape cavity were derived with the incorporation of inertia and buoyant force terms and solved by using the finite-volume method and numerical grid generation scheme. The parametric study considered three physical parameters including inclination angle, Reynolds number and Grashof number, and explored the effect of these parameters on the flow field and heat transfer characteristics. Computations were conducted for the Reynolds number ranging from 100 to 1500, Grashof number from 10⁵ to 10⁷ and inclination angle from 15⁰ to 60⁰. The numerical results show that the flow pattern becomes inertia-dominant and the strength of the primary vortex generally increases as the Reynlods number increases. As the Grashof number increases, the strength of the inertial-induced vortex decreases and the strength of the buoyancy-induced vortex increases. The strength of the vortexes decreases with the increasing inclination angle and the buoyancy-induced flow becomes more dominant. The average Nusselt number increases as the Grashof number increases for all the inclination angles studied here. The local friction increases with the increasing inclination angle, and becomes significant as the Grashof number increases.     

Conjugate heat transfer characterization in cooling channels

Cooling technology of gas turbine blades,primarily ensured via internal forced convection,is aimed towards withdrawing thermal energy from the airfoil.To promote heat exchange,the walls of internal cooling passages are lined with repeated geometrical flow disturbance elements and surface non-uniformities.Raising the heat transfer at the expense of increased pressure loss;the goal is to obtain the highest possible cooling effectiveness at the lowest possible pressure drop penalty.The cooling channel heat transfer problem involves convection in the fluid domain and conduction in the solid.This coupled behavior is known as conjugate heat transfer.This experimental study models the effects of conduction coupling on convective heat transfer by applying iso-heat-flux boundary condition at the external side of a scaled serpentine passage.Investigations involve local temperature measurements performed by Infrared Thermography over flat and ribbed slab configurations.Nusselt number distributions along the wetted surface are obtained by means of heat flux distributions,computed from an energy balance within the metal domain.For the flat plate experiments,the effect of conjugate boundary condition on heat transfer is estimated to be in the order of 3%.In the ribbed channel case,the normalized Nusselt number distributions are compared with the basic flow features.Contrasting the findings with other conjugate and convective iso-heat-flux literature,a high degree of overall correlation is evident.     

Hierarchic modeling of heat transfer processes in heat exchangers

An alternate approach based on hierarchic modeling is proposed to simulate fluid and heat flow in heat exchangers. On the first level, the direct simulations have been performed for the geometry that is similar to a segment of the examined heat sink. Based on the obtained results, the Reynolds number dependencies of the scaling factors f and StPr^2/3 have been established. On the second level, the integral model of the whole heat sink has been built using the volume averaging technique (VAT). The averaging of the transport equations leads to a closure problem. The direct model Reynolds number dependencies f and StPr^2/3 have been used to calculate the local values of the drag coefficient and the heat transfer coefficient , which are needed in the integral model. The example calculations have been performed for 14 different pressure drops across the aluminum heat sink. The whole-section drag coefficient and Nusselt number have been calculated and compared with the experimental data [M. Rizzi, M. Canino, K. Hu, S. Jones, V. Travkin, I. Catton, Experimental investigation of pin fin heat sink effectiveness, in: Proc. of the 35th National Heat Transfer Conference Anaheim, California, 2001]. A good agreement between the modeling results and the experiment data has been reached with same discrepancies in the transitional regime. The constructed computational algorithm offers possibilities for geometry improvements and optimization, to achieve higher thermal effectiveness.     

A numerically-based parametric study of heat transfer off an inclined surface subject to impinging airflow

Impinging jets may be used to achieve enhanced local heat transfer for convective heating, cooling, or drying. The issuing jet may contact the surface normally or obliquely. Factors such as jet attachment, surface angle, jet angle and size, separation distance between jet orifice and surface of impingement, and trajectory influence heat transfer dramatically. This study addresses the thermal problem of jet impingement on an inclined surface and is motivated by the practical application of air jets issuing out of a defroster’s nozzles and impinging on the inclined windshield surface of a vehicle. The effects of incoming fluid velocity, openings’ geometry (circular vs. rectangular), number of openings, angle that the inclined surface makes with the horizontal plane and angle of impinging jet on heat transfer are examined. Fluid mechanics and heat transfer characteristics are exhibited in details for a configuration with three rectangular openings. A comparative study for other configurations is also featured. The results are correlated in terms of governing dimensionless parameters through numerically-based correlations that are useful for predicting heat transfer on an inclined surface subject to impinging airflow.     

Numerical simulation of fluid flow and heat transfer in a microchannel heat sink with offset fan-shaped reentrant cavities in sidewall

The paper is focused on the investigation of fluid flow and heat transfer characteristics in a microchannel heat sink with offset fan-shaped reentrant cavities in sidewall. In contrast to the new microchannel heat sink, the corresponding conventional rectangular microchannel heat sink is chosen. The computational fluid dynamics is used to simulate the flow and heat transfer in the heat sinks. The steady, laminar flow and heat transfer equations are solved in a finite-volume method. The SIMPLEX method is used for the computations. The effects of flow rate and heat flux on pressure drop and heat transfer are presented. The results indicate that the microchannel heat sink with offset fan-shaped reentrant cavities in sidewall improved heat transfer performance with an acceptable pressure drop. The fluid flow and heat transfer mechanism of the new microchannel heat sink can attribute to the interaction of the increased heat transfer surface area, the redeveloping of the hydraulic and thermal boundary layers, the jet and throttling effects and the slipping over the reentrant cavities. The increased heat transfer surface area and the periodic thermal developing flow are responsible for the significant heat transfer enhancement. The jet and throttling effects enhance heat transfer, simultaneously increasing pressure drop. The slipping over the reentrant cavities reduces pressure drop, but drastically decreases heat transfer.     

Conjugate heat transfer in open cavities with a discrete heater at its optimized position

In this article, we determined optimum position of a discrete heater by maximizing the conductance and then studied heat transfer and volume flow rate with the discrete heater at its optimum position in open cavities. Continuity, Navier–Stokes and energy equations are solved by finite difference-control volume numerical method. The relevant governing parameters were: the Rayleigh numbers from 10⁶ to 10¹², the Prandtl number, Pr = 0.7, the cavity aspect ratio, A = H/L from 0.5 to 2, the wall thickness l/L from 0.05 to 0.15, the heater size h/L from 0.15 to 0.6, and the conductivity ratio k_r from 1 to 50. We found that the global conductance is an increasing function of the Rayleigh number, the conductivity ratio, and a decreasing function of the wall thickness. Best thermal performance is obtained by positioning the discrete heater at off center and slightly closer to the bottom. The Nusselt number and the volume flow rate in and out the open cavity are an increasing function of the Rayleigh number and the wall thickness, and a decreasing function of the conductivity ratio. The Nusselt number is a decreasing function of the cavity aspect ratio and the volume flow rate is an increasing function of it.     

Conjugate heat transfer analysis of film cooling flows

The objective of this study is to evaluate the potential of various grids to satisfactorily simulate the development of a cooling film, using a coupled computation that takes into account the full geometry. Detailed computations of a single row of 30 degrees round holes on a flat plate are presented for blowing ratios of 0.764,1.01 and 1.54. The simulation results are compared well with experimental data. The two-layer model gave more accurate results but consumed much more computational time than the standard wall functions. The k-e turbulence model with wall functions with appropriate values of y is suitable for practical use. The results show the importance of the conjugate calculation for accurately describing the influence of the heat transfer within the cooling film.     

Flow and heat transfer over shallow cavities

The flow over a shallow cavity heated with constant heat flux form the bottom side has been studied experimentally and numerically. In the experimental part, pressure coefficient and Nusselt number have been measured along the cavity floor. In the numerical simulation, the conservation equations of mass, momentum, and energy have been solved. The standard k–? turbulence model is used to account for the turbulent fluctuations. In both experimental and numerical part, the effect of changing cavity aspect ratio and Reynolds number has been studied. It is found that, a single elongated eddy has been formed for aspect ratio lower than 7. As the aspect ratio increases the flow impinges with the cavity floor creating two eddies, one beside the upstream cavity side and the second beside the downstream cavity side. Local Nusselt number along the cavity floor is affected mainly by the flow structure inside the cavity and the average Nusselt number has increased with increasing the aspect ratio up to 10 and with increasing Reynolds number. A correlation for the average Nusselt number, as a function of Reynolds number and cavity aspect ratio, is developed.     

Conjugate heat transfer in channels with heat-conducting inclined fins

Conjugate heat transfer in a finned channel with equally spaced fins placed transversely to the flow direction following in-line and staggered arrangements is evaluated. The fins and channel walls are heat-conducting and are fully coupled to a turbulent fluid flow problem. The hydrodynamic and thermal effects of the fin blockage ratio, fin angle, and flow velocity were investigated. The simulations show that the fin arrangement is of paramount importance on the performance of the heat exchanger: the staggered fin configuration provided lower pressure drop and higher heat transfer rate than the in-line fin arrangement for different flow conditions.     

The effect of the inclined perforated baffle on heat transfer and flow patterns in the channel

The effect of a number of inclined perforated baffles on the flow patterns and heat transfer in the rectangular channel with different types of baffles is numerically and experimentally checked out. Reynolds numbers are varied between 23,000 and 57,000. The SST k − ω turbulence model is used in the method to predict turbulent flow. The baffles have the width of 19.8 cm, the square diamond type hole having one side length of 2.55 cm, and the inclination angle of 5°. The results show that the flow patterns around the holes are entirely different with different numbers of holes and it significantly affects the local heat transfer, and two baffles provide greater heat transfer performances than a single baffle.     

The heat transfer and fluid flow of a partially heated microchannel heat sink

Numerical modeling of the conjugate heat transfer in microchannel heat sink is presented. As the most of the cooling applications deals with the partial heated sections, the influence of the heating position on the thermal and hydrodynamic behavior is analyzed. The laminar fluid flow regime and the water as a working fluid are considered. It is observed that partial heating together with variable viscosity has a strong influence on thermal and hydrodynamic characteristics of the micro-heat sink.     

Numerical investigation of laminar heat transfer in a square channel with 45° inclined baffles

A numerical investigation of laminar periodic flow and heat transfer in a three-dimensional isothermal-wall square channel fitted with 45° inclined baffles on one channel wall is carried out in the present work. The finite volume method is introduced and the SIMPLE algorithm has been implemented for all computations. The fluid flow and heat transfer characteristics are presented for Reynolds numbers ranging from 100 to 1200. The 45° baffle mounted only on the lower channel wall has a height of b and an axial pitch length (L) equal to channel height (H). Effects of flow blockage ratios, BR = b/H = 0.1–0.5, on heat transfer and pressure loss in the square channel are examined and also compared with the typical case of the transverse baffle (or 90° baffle). It is found that apart from the rise of Reynolds number, the increase in the blockage ratio with the attack angle (α) of 45° results in considerable increases in the Nusselt number and friction factor values. The use of the 45° baffle can help to generate a streamwise main vortex flow throughout the channel leading to fast and chaotic mixing of flow between the core and the wall regions. In addition, the computational results reveal that the significant increase in heat transfer rate is due to impingement jets induced by a longitudinal vortex pair (P-vortex) of flow, appearing on the upper, lower and baffle trailing end side walls. The appearance of vortex-induced impingement flows created by the baffles leads to the maximum thermal enhancement factor of about 2.2 at BR = 0.4 and Re = 1200. The enhancement factor of the 45° baffle investigated is found to be higher than that of the 90° baffle for all Reynolds numbers and baffle heights.