Constant Heat Flux Boundary Condition Research Articles

DNS vs. LES: Turbulent flow in square duct with heated foil boundary

Turbulent heat transfer in a square duct, where a finite section of a single duct boundary is heated with an infinitely thin foil, was analyzed with LES and DNS approaches. Both computations were performed with OpenFOAM code with passive scalar approximation, using second order accurate schemes. Results are obtained for the key velocity and temperature statistics in the duct, with an emphasis on the temperature profiles and temperature fluctuations at the foil boundary, which appear due to the imposed constant heat flux boundary condition at the foil. Comparison of DNS and standard LES-WALE model show 20% higher foil temperatures and temperature fluctuations in LES results. These differences are explained with detailed analysis of the LES-WALE model near-wall behavior. It has been demonstrated that LES-WALE yields highly accurate results only when employed with a finely resolved mesh. However, the computational costs associated with such refinement may not be necessarily justified especially with respect to DNS.

Heat transfer inside a horizontal circular enclosure with a heated semi-circular cylinder at different orientations

Natural convection inside a cylindrical enclosure is important in many industrial applications. Laminar natural convective heat transfer in the annular space between heated semi-circular cylinder in a horizontal concentric cylindrical enclosure, which has relevance to cooling of electronic components, is studied in this work. Constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions are considered on the inner cylinder, whereas the outer cylindrical enclosure is maintained at a fixed lower temperature. The Finite Volume Method (FVM) is used for the computations. The effect of the Rayleigh number ( Ra = 10 2 to 10 5 ) and the angular orientation of the semi-circular cylinder on the convective heat transfer is investigated. The fluid flow, temperature profile, and heat flow are visualized via streamlines, isotherms, and heatlines. Further, the overall heat transfer is explained based on the local and average Nusselt number on the inner cylinder wall. The effect of the angular orientation of the inner cylinder is noticeable for Ra ≥ 10 3 . The angular orientation ϕ = 90 ° greatly enhances the heat transfer as compared to all other orientations for all Ra ≥ 10 3 for both CWT and CWHF boundary conditions. The correlation between the average Nusselt and Rayleigh numbers for a particular orientation is proposed.

Thermal entropy generation and exergy efficiency analysis of rGO/water nanofluid in a tube under turbulent regime using experimental and fully connected neural network

Analyzing entropy generation is one of the most effective methods for examining how well thermal systems operate. To determine the ideal operating conditions, numerous researchers have examined the entropy generation of thermal systems. In this work, the effects of concentrations of reduced graphene oxide (rGO) nanoparticles on the formation of entropy in water-rGO nanofluid flow through a circular pipe with a constant wall heat flux boundary condition in turbulent regimes are investigated experimentally. rGOs were prepared from Hummer's technique. Experiments are conducted at particle volumes from 0.5 % to 2.0 %, mass flow rates from 0.0333 kg/s to 0.25 kg/s, and Reynolds numbers from 1800 to 21,000, respectively. Later, estimated data points were anticipated with a convolutional neural network (CNN). The model was analyzed through several performances like root-mean-square-error (RMSE), mean-square-error (MSE), mean-absolute-percentage-error (MAE), and the coefficient of determination (R2). Results indicated, with used by 2.0 vol% of nanofluid, entropy generation-thermal is reduced to 39.24 %, entropy generation-frictional is higher by 16.92 %, entropy generation-total is decreased by 37.82 %, and second law efficiency is augmented to 34.17 % at Reynolds number of 13,705, against base fluid data. The correlation coefficient R2 evaluated from CNN for thermal entropy generation, frictional entropy generation, total entropy generation, and exergy efficiency are 0.99297, 0.99924, 0.9989, and 0.99273, respectively.

Experimentally determining the thermophysical properties, heat transfer and friction factor Fe3O4-TiO2 magnetic hybrid nanofluids in a mini-heat sink under magnetic field: Proposing new correlations

The heat transfer and friction factor for the Fe3O4-TiO2/water nanofluids circulating in a mini-heat sink of comparable magnitude to personal computer or electronic gadgets with and without a magnetic field have been estimated experimentally. The Fe3O4-TiO2 nanomaterial was prepared using chemical coprecipitation and sol–gel technique. Synthesized Fe3O4-TiO2 nanoparticles were characterized by X-ray diffraction, and vibrating sample magnetometer. The water-based hybrid nanofluids were then used in a series of experiments for assessing heat transfer, and friction factor of a mini-heat sink assembly of five circular channels with 4 mm in diameter and 50 mm in length. The experiments were performed in the operating range: 238.66 < Re < 1873.36; 0 <ϕ < 2 %; and 0 < Gauss < 1000, respectively. Constant heat flux boundary condition was maintained at the bottom surface of the heat sink and an external magnetic field was provided with an electromagnet. Results indicate that, by using the Fe3O4-TiO2 hybrid nanofluid of 2 % vol. the Nusselt number, with no magnetic field, is enhanced over that of water by 38.16 %, and by 88.93 % when the magnetic field of 1000 gauss is applied. However, the hybrid nanofluid of 2 vol% imposed a penalty in increase in friction factor of 25.87 % without magnetic field, and 67.64 % when magnetic field of 1000 G is applied at a Reynolds number of 1873.33 over water data. The experimental data were used to develop generalized Nusselt number and friction factor correlations for a mini-heat sink subjected to an external magnetic field.

Lattice Boltzmann Method Simulation of Nanofluid Natural Convection Heat Transfer in a Square Cavity with Constant Heat Flux at Walls

AbstractIn this study, for the first time, a nanofluid's natural convection heat transfer in a two-dimensional square cavity has been numerically investigated by use of the lattice Boltzmann method with the constant heat flux boundary condition. The horizontal walls of the cavity are insulated, and the vertical walls are kept at a constant heat flux. The diameters of the nanoparticles inside the cavity are the same and have a homogeneous distribution, and there is no chemical reaction between the particles. The flow is also assumed to be the steady state and two-dimensional. Constant temperature, streamlines, velocity, and average Nusselt have been investigated for different nanoparticle volume fractions and Rayleigh numbers. The results showed that the lattice Boltzmann method efficiently analyzes the natural heat transfer of nanofluids; moreover, by use of nanofluid in the cavity increases the heat transfer rate. With the increase in the nanoparticle volume fraction, the average Nusselt number on the right wall of the cavity increased. For a volume fraction of 20% with Grashof number 105, the average Nusselt number increased by almost 50% compared to the base fluid at the same Grashof number. It has been observed that as the volume fraction of nanoparticles in the fluid increases, the fluid’s viscosity also increases; consequently, the velocity of the fluid is found to decrease.

Effects of different cross-sections of Body Centered Cubic cells on pressure drop and heat transfer of additively manufactured heat sinks

In many industrial applications, heat loads management requires the design and production of compact heat exchangers which are expected to handle high thermal loads with acceptable pressure losses, while assuring good mechanical performances. These challenging targets can be achieved by filling the cavities where the cool/hot fluid circulates with lattice structures promoting the heat exchange between the fluid and the cavity boundaries. Such lattice structures can be only produced through Additive Manufacturing due to their high geometric complexity. Recent experimental investigations proved the effectiveness of some kinds of lattice structures having a circular cross section. Here the aerothermal behaviour of Body-Centred Cubic (BCC) lattice stagger arrays in a rectangular channel was experimentally investigated by considerably extending the previous studies to higher Reynolds numbers (up to 30′000) and to new types of lattice structures. Specifically, three new BCC structures having a cam-like, drop-like and elliptical cross section were explored in this work and compared against those having circular cross section. All the samples were manufactured by means of Laser Powder Bed Fusion and made from AlSi10Mg. At first, the heat exchangers were comprehensively characterized by means of optical non-destructive methods. Successively they were tested in a dedicated rig by imposing constant heat flux boundary conditions. The characteristics of the transitional or fully turbulent approaching flow to the test section are also reported thanks to dedicated flow field measurements performed by Particle Image Velocimetry. According to the obtained results, the BCC structure with the circular cross section of larger diameter is the most effective in terms of heat transfer, although it is largely penalized by the pressure losses. Similar heat transfer performances were achieved by the tapered cross section of elliptical shape with the advantage of a considerably lower friction factor. Pressure losses resulted almost identical for all the tapered cross sections but lower than those of the circular one having an equal frontal dimension. When considering the thermal performance factor the circular shape becomes unfavourable for Re>20′000, while the elliptical cross section is the best choice to efficiently promote heat transfer up to Re=30′000.

IMPACT OF MEASUREMENTS TECHNIQUES ON HEAT TRANSFER CHARACTERISTICS IN AIR JET ARRAYS

Air impact processes have diverse applications in engineering, including backflow welding, textile drying, and gas turbine blade and combustion liner cooling. This research examines the influence of experimental methodologies and measurement tools on convective heat transfer in adjustable air jet assemblies. The experiment involves the use of heated targets made of thin stainless steel foil with constant heat flux boundary conditions. Thermography measures target surface temperatures by analyzing how internal passage cross-flow affects convective heat transfer via outflow adjustments. The experiments involve two arrays of jet nozzles: inline and staggering, each comprising 44 impingement jet nozzles arranged in 4 rows with 11 jet holes in each row. The study presents unsteady time average local and spatial Nusselt numbers as functions of jet Reynolds number (4630-14000) and explores their dependence on the jet nozzle diameter. Cross-flow levels significantly affect spatial and local Nusselt numbers in both local and span-wise averaged values, regardless of the Reynolds number. Strong cross-flow (single configuration) distributes flow causing turbulence and uneven heat distribution, reducing Nusselt numbers. In contrast, moderate cross-flow (double configuration) improves heat transfer and increases Nusselt numbers. The study emphasizes the crucial role of experimental techniques in heat transfer evaluation and demonstrates agreement with prior studies within a standard error below 5%.

PARAMETRIC STUDY AND DEVELOPMENT OF A CORRELATION FOR NUSSELT NUMBER IN NANOFLUID JET IMPINGEMENT

Numerical simulations for nanofluid ( water with Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt; nanoparticles) jet impinging perpendicularly on a flat circular heated p late have been performed. A heated p late is subjected to constant heat flux boundary condition. A two-phase modified mixture mo del was used for the prediction of heat transfer coefficient, and comparisons are made with standard mixture model. Present results for average Nusselt number are validated with experimental data available in the literature. Though a standard mixture model predicted heat transfer with accepted accuracy, it was found that accuracy of modified mixture model is better (around 5&amp;#37; improvement) compared to standard mixture model. Thereafter, parametric study was performed considering nozzle exit Reynolds number (Re), spacing ratio (&lt;i&gt;H/D&lt;/i&gt;), nanoparticle volume fraction (&amp;phi;), and nanoparticle diameter (dp) on heat transfer prediction. The results reveal that particle diameter in the range 10-100 nm has no effect on the Nusselt number, Furthermore, heat transfer increased with increasing Reynolds number and volume fraction. However, spacing ratio shows first increasing and then, decreasing trend (similar to a log-normal distribution curve) in the prediction of heat transfer. Finally, a new correlation was developed for Nusselt number using nonlinear regression analysis. In the correlation, a two-phase multiplier was used, which is the ratio between two-phase Nusselt number (Nu&lt;sub&gt;nf&lt;/sub&gt; ) and single-phase Nusselt number (Nu&lt;sub&gt;sp&lt;/sub&gt;). The simplified correlation is found to predict data with maximum error of 8.9&amp;#37;, average error of 2.74&amp;#37; and &lt;i&gt;R&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt; &amp;#61; 0.955.

The use of variable coil pitch of helical tube on the hydro-thermal performance improvement

The use of helical tubes in heat transfer appliances is desirable due to their better heat transfer characteristics, but the higher pressure drop decreases the overall performance. The variation of pitch design of a helical tube is proposed to alleviate this situation so that the pitch number does not remain constant in the total tube length. A total of six variable pitch numbers with three different diameters are proposed and investigated on the thermal and fluid characteristics. To better understand the helical tube efficiency, PEC (performance evaluation criteria) is selected as a performance indicator in the present work and simulations are performed in a laminar regime (100 ≤ Re≤ 1600) at a constant heat flux boundary condition using computational fluid dynamics. The numerical results show that variable radial pitch has higher effects on the overall performance than variable axial pitch, and it can intensify the helical tube performance by up to 10%. The results also indicate that increasing the tube diameter leads to heat transfer and friction factor increment while increasing the Reynolds number deteriorates the overall performance.

Effects of buoyancy in a laminar flow of supercritical carbon dioxide in a horizontal microchannel at different gravities

The effects of buoyancy were generally neglected in convective heat transfer inside horizontal microchannels because gravitational effects diminish compared to inertial and viscous forces with diminishing length scale. However, buoyancy effects can be significant for supercritical carbon dioxide (sCO2) slightly above the critical condition in microchannels, and the heat transfer coefficient can peak because of abrupt changes in the fluid's thermophysical properties. Previous studies considered buoyancy in channels with hydraulic diameter above 500 μm at a constant surface heat flux boundary condition. These effects were not well understood for microchannels with a hydraulic diameter as small as 100 μm, particularly with constant wall temperature boundary condition, but they hold great potential in the design of micro heat exchangers.This study numerically investigated the effects of buoyancy inside a 100-μm hydraulic diameter square microchannel with a total length of 27 mm and a heated length of 25 mm for laminar flow of sCO2. A total of 180 cases were analyzed to predict the effects of surface temperature ranging from 310 to 350 K, pressure ranging from 8 to 10 MPa, Reynolds numbers from 100 to 500, and gravitational acceleration from 0 g to 3 g, on the heat transfer. It was revealed that gravity has a significant effect on the heat transfer coefficient and on the thermal entrance length. The average heat transfer coefficient was increased by up to 138% on the bottom surface of the channel for 3 g compared to 0 g. The thermal entrance length showed a mixed behavior, such as it was increased for certain conditions while decreased for other conditions. For some cases, it was also observed that the pressure drop increased slightly with increasing gravity, and it was directly proportional to the wall shear stress. Finally, it was concluded that the gravity had a significant effect on the flow and heat transfer characteristics but was negligible for Richardson number below 10−4.

Enhanced laminar heat transfer via magnetically driven ferrofluids

Many industries, such as microelectronics and power electronics, face challenges in removing large amounts of heat from small areas to prevent overheating. Recent research has shown that microchannel flow of ferrofluids driven by an external magnetic field (MF) has the potential to deliver efficient cooling systems for modern electronics. Despite this potential, robust optimisation of the MF has not been undertaken. This paper addresses this shortcoming by reporting the effect of the MF produced by three permanent magnets in various configurations on the heat transfer of ferrofluids undergoing laminar flow through a microchannel under constant heat flux boundary conditions at Peclét number Pe=73. Observations from numerical simulation show that the rate of convective heat transfer varies strongly with position and orientation of the magnets. We show that for the optimum magnet configuration, the maximum and average Nusselt numbers increase by more than 146% and 51% over the unperturbed flow, some of the highest values reported in the literature. These results show that significantly accelerated heat transfer is possible in magnetically driven ferrofluids, with potential for further enhancement with more rigorous optimisation.

An analytical method for quickly evaluating the performances of refractory alloys in sCO2 Brayton cycle applications

An analytical method has been developed to quickly evaluate structure materials' performances in sCO2 power cycle applications. This analytical method combines a conjugate heat transfer model for a tube with constant heat flux boundary conditions with its corresponding mechanical model to obtain the allowable working fluid temperatures and minimum required wall thickness. Three refractory alloys, Inconel 617, Haynes 230, and SS 253 MA, have been selected for implementing this analytical method by comparing their allowable working fluid temperatures and minimum required wall thicknesses under various boundary conditions. The allowable working fluid temperature has been observed not to change with the external surface temperature of the tube monotonically but with a peak. In general, Nickel based alloys (Inconel 617 and Haynes 230) have better performances than the SS 253 MA, but the difference becomes insignificant for low working fluid temperature and low heat flux applications. Besides, Inconel 617 can offer slightly higher allowable working fluid temperature than Haynes 230 in most work conditions, but the minimum required wall thickness is also significantly larger than that of Haynes 230. In addition, the minimum required wall thickness can be significantly reduced when the allowable working fluid temperature is set slightly lower than its peak value due to the rapid decrease of the maximum allowable stresses at high temperatures, which will be useful in potential techno-economic optimization for heat exchanger designs.

Heat transfer, exergoeconomic performance and sustainability impact of a novel CuO + MgO + GO/Water ternary nanofluid

This paper describes an experimental investigation of heat transport, exergy, economic, sustainability, and environmental impact of a ternary nanofluid applied in a circular conduit under 5.36 kW/m2 constant heat flux boundary condition. The experiments are undertaken in fully developed turbulent flow with a Reynolds number range of 12,500–35,000. A stable ternary nanofluid is prepared by dispersing MgO, CuO and GO (graphene oxide) nanopowders into water in the presence of GA (Gum Arabic) surfactant applying ultrasonication. The nanopowder concentration is varied by 0.10, 0.30 and 0.50 wt%. The thermal conductivity with 0.50 wt% is the highest and 24.23 % greater than the value with water. The maximum Nusselt number, which is abnormally 148.23 % greater than water, is obtained with 0.50 wt%. The friction factor of nanofluid gradually decreases with increasing Reynolds number and they are average 3 % higher than water. Ternary nanofluid with 0.5 wt% and 0.30 wt% delivers the highest energy and exergy efficiencies of 96.51 % and 59.68 % respectively at 35,000 Reynolds number. The cost of exergy destruction is reduced by ternary nanofluid application. The analysis of improvement potential (IP) demonstrates the advantage of ternary nanofluid over water. Further, the result depicts that the use of ternary nanofluid can increase sustainability up to 81.10 % and reduces the harmful impact of energy loss on the environment maximum by 52.32 %. Finally, the authors recommend ternary nanofluids as working fluids for future heat transfer and energy applications.

Parameter study for oil spray cooling on endwindings of electric machines via Eulerian–Lagrangian simulation

The demand for larger power density and torque for the power traction motors used in electrified transportation puts forward a requirement for better thermal management methods. Spray cooling is a promising direct liquid cooling technique that has been proved to possess high heat removal capability in previous research. This paper investigates the heat transfer characteristics of spray cooling on endwindings of electric machines via numerical simulation through an Eulerian–Lagrangian approach. The utilized numerical models and calculated results are validated with experimentally measured data. The influence of different parameters and options involved in the simulation settings on the final results, like the stream numbers for the spray injector, the constant heat flux versus constant temperature thermal boundary condition, the influence of splashing, the effect of heat conduction in the endwindings and the Saffman lift force, only solving the energy equation for the air after its flow field reaches a steady-state, are evaluated. Parameter analyses are also conducted for operation conditions, configuration of the spray nozzles, and material properties of the coolant liquid. It is found that larger flow rate, smaller droplet size, lower spray height, more nozzle numbers, larger thermal conductivity and smaller viscosity of the coolant liquid tend to increase the overall heat transfer performance.

Entropy generation of Al2O3/water nanofluid in corrugated channels

The flow of nanofluids in a corrugated channel has been shown to have a significant impact on heat transfer performance, and has therefore become an important area of research. The ob-&#x0D; jective of this paper is to understand the thermal behavior of Al2O3/water nanofluid in a sinu-soidal and square channel and to identify ways to optimize heat transfer performance in such configurations. For this purpose, a numerical simulation was conducted using ANSYS-Fluent software 16.0 on entropy generation and thermo-hydraulic performance of a wavy channel with the two corrugation profiles (sinusoidal and square). The analyses were carried out under laminar forced convection flow conditions with constant heat flux boundary conditions on the walls. The influence of various parameters, such as particle concentration (0–5%), particle di-ameter (10nm , 40nm and 60nm), and Reynolds number (200 &lt; Re &lt; 800) on the heat transfer, thermal, and frictional entropy generation, and Bejan number was analyzed. Moreover, the distribution of streamlines and static temperature contours has been presented and discussed, and a correlation equation for the average Nusselt number based on the numerical results is presented. One of the most significant results obtained is that the inclusion of nanoparticles (5% volume fraction) in the base fluid yielded remarkable results, including up to 41.92% and 7.03% increase in average Nusselt number for sinusoidal and square channels, respectively. The sinusoidal channel exhibited the highest thermo-hydraulic performance at Re= 800 and φ= 5%, approximately THP= 1.6.&#x0D; In addition, the increase of nanoparticle concentration from 0% to 5% at Re= 800 and dnp= 10nm, diminishes the total entropy generation by 28.39 % and 22.12 % for sinusoidal and square channels, respectively, but when the nanoparticle diameter decreases from 60nm to 10nm at ϕ= 5% and Re= 800, the total entropy generation in the sinusoidal channel decreases by 34.85%, whereas in the square channel, it decreases by 20.05%. Therefore, rather than using a square channel, it is preferable and beneficial to use small values of nanoparticle diameter and large values for each of ϕ and Re in the sinusoidal wavy channel. Overall, the study of nanofluid flow in a wavy channel can provide valuable insights into the behavior of nanofluids and their potential applications in a variety of fields, including manufacturing, energy produc-tion, mining, agriculture, and environmental engineering.

Fully Developed Laminar Flow of Heat Transfer Non-Newtonian Flow in Ducts with Arbitrary Cross-Sectional Shape

The pressure drop and heat transfer properties of a laminar flow with circular, square, and triangular cross sections and a constant heat flux boundary condition are given by a numerical solution. A 3D Navier-Stokes incompressible flow and energy equation serves as the foundation for the numerical model. Results are tabulated and given visually for the velocity field, Poiseuille number, and Nusselt number product for various power-law indices (0.5 n 1.0). One of the analyzed ducts causes a greater heat transfer intensification along with a significant pressure loss. A different type of duct allows for a better balance between pressure loss and heat transfer. In order to verify the accuracy of the numerical codes created in the current study, critical comparisons with earlier findings in the literature are also carried out.

Numerical Investigation of the Hydrothermal Characteristics of Water Flow in Compound Microchannel Heat Sinks

In the present work, three-dimensional numerical simulations of laminar forced convection flow of water in unique compound microchannel heat sinks (MCHSs) were investigated using computational fluid dynamics (CFD) modeling. The newly proposed MCHS is made up of circular microchannels slotted from the top within a trapezoidal shape, and its cooling effectiveness was compared to that of traditional rectangular MCHS. Each MCHS under consideration has the same hydraulic diameter and heat transfer surface area. Water volumetric flow rates (Qin) with a wide range of values are used, ranging from 40 to 90 ml/min, with the fluid inlet temperature set to 20 oC. A constant heat flux boundary condition of 100 W/cm2 is supplied on the MCHS bottom. The results demonstrated that the inclusion of reentrant trapezoidal shapes can disrupt both hydrodynamic and thermal boundary layers, as well as accelerate fluid flow and mixing in the main flow, resulting in a significant heat transfer enhancement. Furthermore, at Qin=90 ml/min, the average Nusselt number (Nuavg) of compound MCHS increased by 2.16%, while total pressure drop and total thermal resistance decreased by 1.73% and 1.57%, respectively, when compared to the straight rectangular counterpart.

Figures-of-Merit Analysis Using the Thermophysical Properties of Water and Ethylene Glycol Based Reduced Graphene Oxide/Nanodiamond Hybrid Nanofluids

The water and ethylene glycol based stable rGO/nanodiamond hybrid nanofluids were prepared and used for thermophysical properties analysis. The thermophysical properties were measured experimentally at various particle loadings from 0.2% to 1.0% and various temperatures ranging from 20 to 60 °C. From the measured thermophysical properties the figures-of-merit were analyzed by assuming constant heat flux and turbulent boundary conditions by using different models, and also by assuming the hybrid nanofluids flows through a tube. Results indicate that the thermal conductivity of water and ethylene glycol based hybrid nanofluids at Φ = 1.0% vol. is enhanced about 27.87% and 18.8% at 60 °C; viscosity of water and ethylene glycol based hybrid nanofluids at Φ = 1.0% vol. is also enhanced by 72.15% and 86.62% compared to their base fluids at 20 °C. The density is also increased with an increase of particle loadings, whereas, the specific heat is decreased with a rise of particle loadings. Experimental thermophysical properties are fitted into regression equations by using multi linear regression method. The figures-of-merit of all the prepared hybrid nanofluids show its value is less than one under the used particle loadings and temperatures.

Effect of Magnetic Field on the Developing Thermal Field in a Duct Filled with Porous Media under Local Thermal Non-Equilibrium with a Nonlinear Flow Model

In this article, the numerical study of the influence of a magnetic field at the laminar forced convection in a thermally developing region coming under the influence of local thermal non-equilibrium (LTNE) of parallel plate channels completely immersed in the porous material is investigated. Constant wall heat flux boundary conditions are applied to the walls of the channel. In the nonlinear flow model, the Darcy-Brinkman-Forchheimer equation governs the flow field in the porous region, which is assumed to be unidirectional. The system is defined by certain well-known parameters, these being Darcy number (Da), thermal conductivity ratio (κ), Forchheimer number (F), Hartmann number (M), and Biot number (Bi). Numerical solutions have been obtained by applying a successive accelerated replacement (SAR) scheme. Exact solutions for the dimensionless temperature and the fully developed Nusselt number in the absence of the Forchheimer number (F = 0), for the fully developed thermal field, are obtained for the linear flow model, the Darcy-Brinkman model. Plots are given for the dimensionless temperature profiles in the fluid and solid phases, wall temperature, as well as the local Nusselt number at the parallel plate channel, which has been displayed. The effect of the magnetic field and the thermal conductivity ratio has a significant effect on the local Nusselt number.

Thermal Convection of an Ellis Fluid Saturating a Porous Layer with Constant Heat Flux Boundary Conditions

The present work analyzes the thermal instability of mixed convection in a horizontal porous channel that is saturated by a shear-thinning fluid following Ellis’ rheology. The fluid layer is heated from below by a constant heat flux and cooled from above by the same heat flux. The instability of such a system is investigated by means of a small-disturbances analysis and the resulting eigenvalue problem is solved numerically by means of a shooting method. It is demonstrated that the most unstable modes on the instability threshold are those with infinite wavelength and an analytical expression for such conditions is derived from an asymptotic analysis. Results show that the non-Newtonian character of the fluid has a destabilizing role.