Simulation of turbulent boundary layers for flows characterized by unsteady driving conditions is important for solving complicated engineering problems such as combustion, blood flow in stenosed arteries, and flow over immersed structures. These flows are often dominated by complex vortical structures, regions of varying turbulence intensities, and fluctuating pressure fields. Pulsating channel flow is one such case that presents a unique set of challenges for newly developed and existing turbulence models used in computational fluid dynamics (CFD) solvers. In the present study, performance of the dynamic hybrid RANS-LES model (DHRL) with exponential time averaging (ETA) is evaluated against Monotonically Integrated Large Eddy Simulation (MILES) and a previously documented LES study for a fully developed channel flow with a time-periodic driving pressure gradient. Results indicate that MILES over predicts mean streamwise velocity for all forcing frequencies while the DHRL model with ETA provides a method for improved results, especially for the lower frequencies. It is concluded that a hybrid RANS-LES model with ETA is a useful alternative to simulate unsteady non-stationary flows but further work is needed to determine the appropriate filter width for ETA to significantly improve the predictive capabilities of the DHRL model.

Reducing turbulent skin-friction drag is a subject of great interest due to the potential benefits. These benefits are reflected in applications such as aircraft and vehicles for which skin-friction drag constitutes a significant fraction of the total drag. For example, commercial airliners have up to 50% of their fuel consumption associated with turbulent drag. Thus, any drag reduction would result in substantial savings with regards to the operational cost of the airline industry. In this study, we investigated the effects of a spanwise body force on reducing skin-friction drag in turbulent channel flows. To this end, we performed direct numerical simulations (DNS) of turbulent channel flows with an applied spanwise body force. The body force consists of four control parameters: the amplitude of excitation, penetration depth, period of oscillation, and wavelength. A series of DNS were performed to investigate the effect of these parameters on drag reduction. We observed different levels of drag reduction and the magnitude of skin-friction varied considerably. The DNS results showed that the skin friction is reduced by as much as 20% with values for penetration lengths from 0.03 to 0.09 and periods between 10 and 20. An optimal combination of the four adjustable control parameters is yet to be concluded. In addition to skin-friction reduction, we found an intriguing observation from a time series of wall shear stress. When the wall shear stress is sufficiently lower than its mean value (i.e., low-drag intervals), the spanwise body force appears to significantly affect turbulent dynamics to make the wall shear stress not as chaotic as in other intervals. Specifically, the standard deviations of the peak-to-peak magnitudes of the wall shear stress during low-drag intervals are significantly lower than that of other intervals. This observation could be crucial in that it may lead to a further fundamental understanding of the drag reduction process. Moreover, it may aid in the development of more effective control schemes by way of anticipating that low-drag intervals are promising targets for drag reduction.

Three-dimensional steady state Computational Fluid Dynamics (CFD) analyses were performed for a pre-designed micro-hydrokinetic turbine to investigate the blockage ratio effect on turbine performance. Simulations were conducted using a physical turbine rotor geometry rather than low fidelity, simplified actuator disk or actuator lines. The two-equation k-ω Shear Stress Transport (SST) turbulence model was employed to predict turbulence in the flow field. The turbine performance at the best efficiency point was studied for blockage ratios of 0.49, 0.70 and 0.98 for three different free stream velocities of 2.0 m/s, 2.25 m/s and 2.5 m/s. Distinct blockage ratio results at a free stream velocity of 2.25 were compared to a previous numerical study incorporating the same rotor geometry within an infinite flowing medium. The pressure gradient between turbine upstream and turbine downstream for blocked channel flows elevated the turbine performance. The increment in blockage ratio from 0.03 to 0.98 enhanced power coefficient from 0.437 to 2.254 and increased power generation from 0.56 kW to 2.86 kW for the present study.

In this experimental work, a flow field test system was installed to investigate the impact of vortex generators on the flow structure and heat transfer of air flow in a horizontal channel. Three different configurations of vortex generators, a small single delta winglet pair, a large single delta winglet pair, and two delta winglet pairs developed in a V-formation array were fitted vertically on an aluminum plate and tested in a small wind path system of open circuit with horizontal test section of dimensions 70 mm (width) × 35 mm (height) × 1600 mm (length). An axial AC fan was used to supply the flow of air through the test section. The air flow was cooling the flat plate which had embedded electric heating constructed as a layered structure. Temperature distributions along the heated plate were measured using thermocouples to obtain the Nusselt numbers. The effect of three different attack angles, 15°, 30°, and 45° of the selected VGs were investigated in this work. The experimental results showed that under the tested Reynolds number of 10145, the presence of vortex generators had considerable effect on temperature distribution, pressure drop and heat transfer augmentation in the channel flow. Compared with the plain channel; the heat transfer rate was enhanced by (31.9% – 51.0%), (30.8% – 53.7 %), and (18.2 % – 36.2%) while the pressure drop increased by (1.8% – 11.0%), (4.5% – 35.4%), and (6.0 % – 30.0%) with the small single delta winglet pair, the large single delta winglet pair, and two pairs deployed in a V-formation array, respectively.

This paper presents a new hybrid model that seeks to combine the strengths of Reynolds–averaged Navier-Stokes (RANS) and large eddy simulation (LES) methods. The new model is based on a recently proposed version of a dynamic hybrid RANS-LES (DHRL) framework that addresses several deficiencies inherent in most current hybrid models, including explicit grid dependence, boundary layer model stress depletion, and delayed shear layer breakdown. The DHRL framework is highly generalized, allowing coupling of any desired LES model with any given RANS model. In this study, a recently proposed four-equation eddy-viscosity model (EVM) capable of predicting both flow transition from laminar-to-turbulent (T) and rotation and/or streamline curvature (RC) effects is used for the RANS component, and a monotonically-integrated LES (MILES) scheme is used for the LES component. The new model (DHRL with T-RC effects) is implemented into a commercial computational fluid dynamics (CFD) code and investigated against three different flow configurations. The test cases include nonrotating and rotating channel flow, zero-pressure-gradient (ZPG) boundary layer flow over a flat plate, and flow over a circular cylinder. Results obtained from the numerical simulations indicate that the new hybrid model produces significant levels of turbulent fluctuations in the flowfield and successfully resolves T-RC effects. The results show improved accuracy compared to RANS models and are obtained at a significant reduction of computational cost compared to full LES models. Further investigation on complex test cases is warranted before commenting on the accuracy and potential usage of the model as a practical tool.

The field of control and stabilization of distributed parameter systems described by partial differential equations has recently seen an increasing number of results published by very respected researchers in excellent control engineering and applied mathematics journals. This paper presents a survey of control and stabilization results with emphasis on controls. Various distributed parameter dynamic control and stabilization problems have been studied corresponding to heat conduction, wave propagation, Schrodinger equation, crowd (swarm) dynamics, magneto-hydro-dynamic channel flow, string and beam equations, viscous Burger equation, and general diffusion equations. Various techniques have been used for control and stabilization of such systems: Lyapunov stabilization, backstepping, gain scheduling, singular perturbations, sliding mode control, observer driven controller, tracking control, sampled-data control, neural networks. The field still remains widely open for future research. Applications of surveyed results to various areas including robots, aircraft, networks, transmission lines, electrochemical processes in energy systems are indicated.

Translationally oscillating blades, called agitators, can be used to thoroughly mix the flow inside heat exchanger channels such as those in an electronics module heat sink. Generally, throughflow is provided with an induction fan. Agitation is implemented inside the channel by using either multiple agitator blades, agitator blades with notched edges, full-length long-blade agitators or short-blade agitators. The power needed to drive the agitator blades is dependent on the agitation velocity, geometry and mass. The performance features of a 50mm long agitator blade operating at an oscillation frequency of 500Hz, a 15mm short agitator blade operating at a frequency of 1000Hz, and two blades of length 15mm operating at a frequency of 500 Hz have been compared. Also, runs with other geometric changes, like those with added notches at the tip of the agitator, are made to explore their benefits. The intent is that the notches generate additional vorticity at the channel inlet, which is convected downstream enhancing heat transfer as it passes. Thus, this study numerically finds directions toward optimal agitator configurations and geometries that would give heat transfer augmentation without excessive power input. It was found that a multiple agitator blade configuration containing two short blade agitators operating at frequency 500Hz gives the best performance in terms of heat transfer augmentation when power consumption is considered. Heat flux plots on the channel wall and turbulence kinetic energy plots within the channel have been used to explain the mechanisms of heat transfer augmentation for the various cases.

In this paper, we consider the three dimensional flow of granular materials and a viscous fluid in a channel. We use Mixture Theory to treat this problem as a two-component system [1]: One component is the solid particles (granular materials), such as sand, coal particles or red blood cells; the solid particles are modeled as a generalized Reiner-Rivlin type fluid derived by Massoudi [2], which not only considers the effects of volume fraction but also has a viscosity which is shear rate dependent. The other component, the host fluid, is assumed to behave as a linear viscous fluid, such as water, oil or plasma. For the interaction forces, the effect of different hindrance functions for the drag force is studied; moreover a generalized form of the expression for the hindrance function is suggested. For studying this two-component system numerically, a three dimensional CFD solver based on OpenFOAM® has been developed. Applying this solver, a specific problem (blood flow) has been studied for which our numerical results and experimental data [3] show good agreement.

In the present paper, six new types of rectangular channels with elliptic scale-roughened walls for heat transfer enhancement, which include elongated scale cases ( P t /P l = 0.3, 0.5, 0.7) and squeezed scale cases ( P t /P l = 1.43, 2, 3.33), are proposed. Heat transfer and fluid flow characteristics for sixteen different scale-roughened models (with the scale height varying in the range from 1mm to 2.5mm) are predicted numerically using commercial CFD code, Ansys CFX, with the Reynolds number ranging from 5000 to 15000. The turbulent model employed is the k-ω based Shear-Stress-Transport (SST) model with automatic wall function treatment. It is found that the elliptic scales with their long axis oriented perpendicular to the flow direction enhance the heat transfer performance considerably, while the scales elongated in the flow direction have lower Nusselt numbers and pressure drops compared to the circular scale-roughened channels. It is also found that the scale-shaped roughness strongly spins the flow in the spanwise direction, which breaks the near wall boundary layers continuously and enhances the bulk flow mixing. With the flow marching in a spiral pattern, Nusselt number ratios between the squeezed scale-roughened and smooth channel flows ( Nu/Nu ∞ ) could be augmented to be within the range of 6.1 to 8.1, which is a 50% improvement over the circular scale-roughened channels.

A parametric study is conducted using numerical experimentation to construct an empirical Nusselt number correlation in terms of Richardson and Prandtl numbers for laminar mixed convection in a square cavity. The square cavity under study is assumed to be filled with a compressible fluid. The bottom of the cavity is insulated and stationary where as the top of the cavity (the lid) is pulled at constant speed. The vertical walls of the cavity are kept at constant but unequal temperatures. A two-dimensional, mathematical model is adopted to predict the momentum and heat transfer inside this rectangular cavity. This physics based mathematical model consists of conservation of mass, momentum (two-dimensional, unsteady Navier-Stokes equations for compressible flows) and energy equations for the enclosed fluid subjected to appropriate boundary and initial conditions. The compressibility of the working fluid is represented by an ideal gas relation. The thermodynamic and transport properties of the working fluid are assumed to be constant. The governing equations are discretized using second order accurate central differencing for spatial derivatives and second order finite differencing (based on Taylor expansion) for the time derivatives. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns of the problem. Grid independence and time convergence studies were carried to determine the accuracy of the square mesh adopted for the present study. Two benchmark cases (driven cavity and rectangular channel flows) were studied to verify the accuracy of the CMSIP. Numerical experiments were then carried out to simulate the heat transfer characteristics of mixed convection flow for different Richardson numbers in the range of 0.036<Ri<1.00 where the Reynolds number is kept less than 2000 to ensure laminar flow conditions inside the cavity. The velocity vector field maps (circulation patterns) and temperature contours, and temperature profiles along the horizontal axes were generated for different Prandtl numbers ranging from 0.3 to 1. Wall heat fluxes and Nusselt numbers were determined for each parametric study. The collected data from the numerical experiments were then used to construct an empirical Nusselt number correlation in terms of Richardson and Prandtl numbers.

Air cooling of electronic equipment continues to hold many advantages over liquid cooling in terms of simplicity, reliability, cost, etc. Many active and passive air cooling techniques have been developed to meet the thermal challenges of modern, high-power electronics. Active cooling includes such features as piezoelectric flapping fans and synthetic jets that could directly break down and thin the thermal boundary layers on heated surfaces. A microchannel bank of fins, micro pin-fin surfaces, etc. are passive methods for increasing heat transfer area. In the current study, both active and passive methods, piezoelectric translational agitators and micro pin fin arrays, are employed to dramatically enhance convective heat transfer rates. A piezoelectric stack actuator coupled with an oval loop shell displacement amplifier was utilized to generate high-frequency and large-displacement translational agitation over the micro pin fin surface. Two different micro pin-fin surfaces were fabricated using copper and the LIGA process. Heat transfer experiments were performed in a single channel that houses a one-sided, heated surface with attached micro pin fins. The piezoelectric translational agitator oscillates at a high frequency of 596 Hz with a large displacement of up to 1.8 mm. The heat transfer coefficients on the micro pin-fin surface cooled by the agitator and various channel through-flows were compared with those of plain surfaces under the same channel flow rates. A maximum improvement of 222% in the heat transfer rate was achieved when the agitator was operated, the micro pin-fin surface was in place and the channel flow velocity was 11.6 m/sec, compared to that of a non-agitated plain surface case with the same flow rate.

Experiments were carried out to investigate the flow characteristics with/without heat exchange in vertical and inclined tube-bundle channels. In the experiments, the influences of flow directions and heat exchange upon the flow characteristics were studied. Experiments showed that the flow friction in tube-bundle channels had relations to the flow directions, and the liquid temperature difference at the inlet and outlet of tube-bundle channels. And these influences were comparatively obvious in the laminar flow regime. In the experiments, the transition from laminar to turbulent flow was carefully observed. The flow characteristics of single phase flow through tube-bundle channels were different from those in circular tubes and those in annular channels. The flow friction in tube-bundle channel is larger than that in normal circular tube. And the transition from laminar flow to turbulent flow in tube-bundle channel is different from that in normal circular tube. The influences of flow direction and heat exchange on the friction were also studied. The results were gained to provide the basis for the further investigations on the two-phase flow in tube-bundle channels.

Convective heat transfer enhancement on a wall of a narrow channel enhanced by high-frequency, translational oscillation of a thin agitator plate is described. The oscillation is realized using a piezoelectric stack actuator. Small amplitudes of the piezoelectric stack actuator were amplified through oval loop shell structures so that large translational amplitudes are provided to the thin plate agitator. Heat transfer tests were conducted with three operating frequencies resulting from three oval loop shell structures operating at their resonance frequencies. For each operating frequency, four different amplitudes (corresponding to different applied voltages to the piezoelectric stacks) were investigated. Three channel flow rates were tested. They represent laminar, transition, and turbulent flow regimes for a non-agitated channel. Running with agitation and channel flow allows a study of the agitation effect with different channel flow rates. The results show that the oscillating plate with a frequency of about 1,140 Hz raises the convective heat transfer coefficient on the heated surface by 93%, compared to a case with channel flow only. The flow rate was 45 LPM, corresponding to the transitional flow regime in an un-agitated channel. The amplitude of oscillation was about 1.1 mm, peak-to-peak. It was found that the effect of cross flow is minimized with high oscillation frequency agitation regardless of channel flow velocity and flow regime of the un-agitated flow. In addition, numerical simulations were performed to support the experimental results and understand underlying phenomena of translational agitation. Numerical simulation results match well with the experiments and provided good explanations of heat transfer enhancement from the translational agitator. The piezoelectrically-driven oscillating agitator plate coupled with traditional fan cooling shows promising potential for advanced air cooling applications.

Air-cooled heat sinks prevail in microelectronics cooling due to their high reliability, low cost, and simplicity. But, their heat transfer performance must be enhanced if they are to compete for high-flux applications with liquid or phase-change cooling. Piezoelectrically-driven agitators and synthetic jets have been reported as good options in enhancing heat transfer of surfaces close to them. This study proposes that agitators and synthetic jets be integrated within air-cooled heat sinks to significantly raise heat transfer performance. A proposed integrated heat sink has been investigated experimentally and with CFD simulations in a single channel heat sink geometry with an agitator and two arrays of synthetic jets. The single channel unit is a precursor to a full scale, multichannel array. The agitator and the jet arrays are separately driven by three piezoelectric stacks at their individual resonant frequencies. The experiments show that the combination of the agitator and synthetic jets raises the heat transfer coefficient of the heat sink by 80%, compared with channel flow only. The 3D computations show similar enhancement and agree well with the experiments. The numerical simulations attribute the heat transfer enhancement to the additional air movement generated by the oscillatory motion of the agitator and the pulsating flow from the synthetic jets. The component studies reveal that the heat transfer enhancement by the agitator is significant on the fin side and base surfaces and the synthetic jets are most effective on the fin tips.

The numerical study proposed is to investigate the effectiveness of delta-winglet vortex generators (VGs) used for heat-transfer enhancement in a horizontal rectangular channel as a typical air passage for fin-and-tube heat exchangers. The effects of four different configurations of vortex generators have been investigated: (1) single pair VGs with a 30 degree attack angle; (2) 2-pair VG array with a 30 degree attack angle; (3) single pair VGs with a 45 attack angle; (4) 2-pair VG array with a 45 attack angle. The numerical results indicate that average Nusselt number increase is 31%–38% and 51%–71% for the channel mounted with VGs with a 30 degree attack angle and a 45 degree attack angle, respectively. The enhancement for single large pair of VGs is higher than that for a V-formation array with 2 small pairs. However, VGs also introduce extra pressure drop penalties to the channel flow, and higher heat-transfer performance is also accompanied by a larger pressure drop penalty. According to the results, a single large pair of VGs with 45 attack angle shows the best overall performance among all the configurations investigated.

Fluid transport with diffusion through micro-/nano-channels is found in many natural phenomena and industrial processes, including fluid transport or diffusion through nano-materials, molecular/atomistic transfer across nuclear pores or in the MEMS devices among other applications. Those nano-pores can be treated as nano-channels in the thin layers of the membranes. The transport phenomena of fluid in such small confined channels, usually in the size of ten molecular diameters or less, differs significantly from its bulk behaviors and cannot be described with continuum theory. In this case, molecular dynamics (MD) simulation, rather than continuum methods, is better suited to study the phenomena. The surface diffusion, related to both the fluid and solid material properties and the flow rate, can be used as a parameter for estimating the adsorbing capacity of a porous nano-material. The transport of fluids through porous materials occurs mainly by diffusion. In this study, a molecular-continuum hybrid scheme is used for the study of the diffusion in a representative Couette flow problem. By varying the velocity of the moving-solid wall, we investigated the effect of the shearing condition on the mass flux going through the pores. The relationship of the physical mechanisms and the transport phenomena (e.g. Fick’s law) were then linked among the different length scales. Activated carbon with its high surface area has been emerging as a promising candidate for an adsorbent due to not only its stable thermodynamic and mechanical properties but also its homogenous and isotropic porous distribution and relatively even pore size. In this study, we focus on the characteristics of the permeation and the adsorption process between different gases and the carbon substrate under various shearing conditions. The investigation of the diffusion process of fluids through the pores of the nano-materials has become an interesting topic in recent decades. This investigation has been divided into two major areas: 1) the diffusivity estimation and 2) the transient diffusion rate. We apply a continuum/MD hybrid scheme to a model problem of various gases transport through a carbon substrate with several pores in a channel flow under different shear rates. Instead of inserting and deleting particles from the control volumes used in the DCV-GCMD method, we keep the number of particles in the simulation system constant. The interactions between fluid/fluid, fluid/solid and solid/solid are all assumed to be under Lennard-Jones potentials. In the modeled Couette flow, the two solid walls are constructed with nano-pores that allow fluids to go through the substrate to study the transient diffusion rate (flux). Before simulating the fluid transport through the nano-pores, we need to validate the natural diffusion properties of the bulk fluid. To do this, a system (as a cube) consisting of pure liquid argon molecules is used to perform the pure MD simulation. The radial distribution function (RDF) is used as the parameter to verify the natural diffusion of the liquid argon fluid in the bulk flow, which is a structural correlation. It describes the spherically averaged local organization around any given molecule. Figure 1 shows a good comparison of the radial distribution functions between the MD prediction and the experimental measurement of Eisenstein and Gingrich (1942). By comparing our calculation to Wu et al. (2008) under similar circumstances, we found that the average (from 8 pores) and corrected mass flux J · ( RTh ) is linearly proportional to the average pressure gradient along the pore. And the slope of this relationship is the transport diffusivity, which is 4.6 × 10 −7 m 2 / s under 273K and 4.9 × 10 −7 m 2 / s under 300K. This indicates that the current simulation follows the Fick’s law exactly. Similarly, for other gases, the same linear relationships can also be obtained. These calculations are listed in Table 1 that shows the transport diffusivity increases with temperature. The mass fluxes of three gases at various pore widths are calculated as shown in Fig. 2. Generally, with larger pores, the mass fluxes increase. However, among three gases, the increase of H 2 is much faster than the other two gases because of hydrogen’s smaller molecular size. In another word, smaller molecules as H 2 have faster diffusion rates during the adsorption process.

A numerical study is conducted to identify the unsteady characteristics of momentum and heat transfer in lid-driven cavity flows. The cavity under study is filled with a compressible fluid and is of rectangular shape. The bottom of the cavity is insulated and stationary where as the top of the cavity (the lid) is pulled at constant speed. The vertical walls of the cavity are kept at constant but unequal temperatures. A two-dimensional, mathematical model is adopted to investigate the shear and buoyancy driven circulation patterns inside this rectangular cavity. This physics based mathematical model consists of conservation of mass, momentum (two-dimensional, unsteady Navier-Stokes equations for compressible flows) and energy equations for the enclosed fluid subjected to appropriate boundary and initial conditions. The compressibility of the working fluid is represented by an ideal gas relation and its thermodynamic and transport properties are assumed to be function of temperature. The governing equations are discretized using second order accurate central differencing for spatial derivatives and second order finite differencing (based on Taylor expansion) for the time derivatives. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns of the problem. Grid independence and time convergence studies were carried out to determine the accuracy of the square mesh adopted for the present study. Two benchmark cases (driven cavity and rectangular channel flows) were studied to verify the accuracy of the CMSIP. Numerical experiments were then carried out to simulate the unsteady development of the shear and buoyancy driven circulation patterns for different Richardson numbers in the range of 0.036< Ri <100 where the Re number is kept less than 2000 to assure laminar flow conditions inside the cavity. Simulations start with a stagnant fluid subjected to a sudden increase in one of the walls temperature. At the same time the upper lid of the cavity is accelerated, instantaneously, to a constant speed. The circulation patterns, temperature contours, vertical and horizontal velocity profiles were generated at different times of the simulation, and wall heat fluxes and Nusselt numbers were calculated for the steady state conditions. Only the results for a square cavity are presented in this paper. These results indicate that the heat transfer rates at the vertical walls of the cavity are enhanced with the decrease in Richardson number.

This study investigates experimentally and theoretically both the effects of operating and configuration parameters on convection heat transfer process and fluid flow characteristics for air flowing in transitional regime through parallel plate channel with offset plate segments heated by a radiation heat flux. This configuration is intended to be applied into air heater solar collectors and/or a combined photovoltaic and air heater solar collector system (PV/T). In the experimental measurements, the operating parameters tested were Re values ranging from 2580 to 4650 with combination of incident radiation heat flux (q inc ) values of 400, 700, and 1000 W/m 2 , respectively. The experimental results show that the local Nusselt number (Nu x ) is not unique function in the axial distance. In addition, a linear relationship between Re and apparent friction factor is observed. Moreover, in case of Re = 2600, increasing the incident radiation flux values by 175% and 250% leads to an increase in Nu x values by 20% and 35%, respectively. The theoretical results indicate that, combinations of Re values inside the channel falling within the laminar regime with selections of both the plate’s length and thickness can lead to the convection heat transfer enhancement with avoiding of additional pumping power penalty when the channel flow falls in transitional regime.

Thermal analysis employing a full conjugation model is performed in this study for laminar airflow in a parallel-plate channel with discrete flush-mounted heat sources. The numerical model accounts for mixed convection, surface radiation, and two-dimensional conduction in the substrate. The effects of Reynolds number, surface emissivity of walls and heat sources, as well as thickness and thermal conductivity of the substrate, are analyzed in detail. It is shown that participation of radiation brings the wall temperatures closer, and the trend of temperature variation along the top wall is drastically altered. Such effects are pronounced for black enclosures and diminished for high Reynolds numbers. The influence of substrate conductivity and thickness is very similar in that a large value for both parameters would facilitate redistribution of heat and tend to yield a uniform temperature field in the substrate. For highly conductive or thick substrate, the ‘hot spot’ cools down and may move upstream to the penultimate source. Radiation loss to the ambient increases with substrate conductivity and thickness due to the elevated temperature near the inlet and outlet, yet the total heat transfer over the bottom surface by convection and radiation remains unaltered.

Thermal analysis employing a full conjugation model is performed in this study for laminar airflow in a parallel-plate channel with discrete flush-mounted heat sources. The numerical model accounts for mixed convection, surface radiation, and two-dimensional conduction in the substrate. The effects of Reynolds number, surface emissivity of walls and heat sources, as well as thickness and thermal conductivity of the substrate, are analyzed in detail. It is shown that participation of radiation brings the wall temperatures closer, and the trend of temperature variation along the top wall is drastically altered. Such effects are pronounced for black enclosures and diminished for high Reynolds numbers. The influence of substrate conductivity and thickness is very similar in that a large value for both parameters would facilitate redistribution of heat and tend to yield a uniform temperature field in the substrate. For highly conductive or thick substrate, the ‘hot spot’ cools down and may move upstream to the penultimate source. Radiation loss to the ambient increases with substrate conductivity and thickness due to the elevated temperature near the inlet and outlet, yet the total heat transfer over the bottom surface by convection and radiation remains unaltered.