Mixed Convection Conditions Research Articles

Fluid-structure interaction induced mixed convection characteristics in a lid-driven square cavity with non-Newtonian power law fluids

The present study aims to numerically explore Fluid-Structure Interaction (FSI) induced mixed convection characteristics in a square cavity filled with a non-Newtonian power-law fluid. The side walls of the cavity under consideration are subjected to constant low temperature having motion in opposite directions while the insulated top wall and the bottom hot wall are kept stationary. A flexible fin is mounted on the bottom wall that essentially serves as a passive flow modulator. To solve the transient flow, thermal, and stress fields, the FSI problem is presented in an arbitrary Lagrangian-Eulerian framework employing the Galerkin finite element method. Different non-Newtonian fluids are represented by the power-law index (n) varied within the range, of 0.6 ≤ n≤ 1.4. Besides, the dynamic as well as mixed convection condition of the flow is analyzed by variation of Reynolds number (100 ≤ Re ≤ 300) and Richardson number (0.1 ≤ Ri ≤ 10.0) respectively. System characteristics have been evaluated in terms of streamline and isotherm contours, spatial and time-averaged Nusselt number as well as Normalized Nusselt number in regard to the “No Fin” case. The outcome of the present study reveals that the efficacy of a flexible fin for a given system depends on both the system dynamic condition (Re) and the mixed convection regime (Ri). The presence of a flexible fin has been found to have positive impact on heat transfer performance for both the shear-thinning and shear-thickening fluids for higher values of Re and Ri. However, for lower values of Re, the inclusion of a flexible fin has been found to adversely affect the heat transfer performance for shear-thickening fluids. Moreover, the thermal field exhibits periodic oscillation properties at Ri = 10, which can be attributed to the induced motion of the flexible fin. This phenomenon has been further elucidated through Power Spectrum Analysis. Results obtained in the present study might provide valuable insights into FSI-induced mixed convection with non-Newtonian fluids having versatile industrial applications such as solar thermal collectors with strategically positioned passive flexible flow modulators.

MHD viscoelastic nanofluid flow across an extended plate using mixed convection and thermal radiation

Opportunities for magnetohydrodynamic mixed convection include modeling firefighting, combustion engineering, and cooling of electronic components. Nanotechnology has just provided a novel passive technique for improving heat transfer. Structured colloidal suspensions of magnetite nanoparticles in a base fluid are known as magneto nanofluids, and they are intended for use in thermal transfer uses, such as micro device cooling mechanisms. The current model is intended for examination of the nanofluid stagnation point flow using magnetohydrodynamics. A stretched sheet was exposed to magnetic strength and thermal radiation effects with outstanding results on heat transfer enhancements under mixed convection conditions. Furthermore, over the boundary effects of thermal slip and velocity are considered. The persuading system of partial differential equations of the governed fluid model is transformed into a scheme of coupled non-linear ordinary differential equations and expounded using a suitable numerical method. The fluid’s velocity, temperature, and concentration of nanoparticles are discussed graphically for a range of newly emerging parametric values. It has been noted that when there is a magnetic field, the fluid’s temperature increases, but its velocity decreases. After obtaining the numerical solution, parameters characterizing the flow, such as the local skin friction coefficient, local Sherwood number, and local Nusselt number, are thoroughly investigated.

Direct Numerical Simulation of liquid metal forced and mixed convection in a square rod bundle

This paper reports results of Direct Numerical Simulations of fully developed, forced and mixed convection of Liquid Lead Bismuth Eutectic (LBE) around four vertical cylindrical rods arranged in a square lattice at Pr = 0.031. The solutions provided here are placed in a context where very few data are available for low-Prandtl flows, especially in mixed convection conditions, and can hence be useful for the development and validation of advanced turbulent heat transfer models. The equations are discretized using a Finite Volume implementation of a second order projection method. The irregular cylindrical boundaries are handled with an original Immersed Boundary technique. A single friction Reynolds number value is set (Reτ = 180) and buoyancy effects are accounted for by imposing the Rayleigh number, under the Boussinesq approximation. A Ra-value Ra = 2.5 ×104 is selected in order to investigate the main differences between forced and mixed convection at low Prandtl number values. Time-averaged velocity and temperature fields are shown, in order to discuss the main features of the flow and thermal fields. First order statistics are also presented, highlighting the effect of aiding buoyancy on turbulent heat and momentum transport.

Modified correlations for the Nusselt numbers at the boundaries of a bottom-heated molten metal layer in a stratified corium melt pool and an assessment of heat transfer conditions during a severe accident

The paper discusses new correlations for the Nusselt numbers at the side and bottom surfaces of a bottom-heated molten steel layer under the conditions of mixed natural convection of the melt at Rayleigh (Ra) numbers from ∼ 106 to 1012. The melt layer under consideration is characterized by radial non-uniformity of the temperature distribution, when the averaged temperatures of the top and side surfaces of the layer show a difference in value. This thermal pattern of the molten metal layer is typical when a stratified corium molten pool forms during a severe accident (SA). Upper metallic melt layer goes above the oxide phase of corium pool, and it is heated along its bottom surface. For an adequate prediction of heat transfer at the side and bottom surfaces of a layer in a SA, we developed special correlations for the Nu numbers. They take into account Rayleigh number and additional factors that determine geometric parameters of the layer and the temperature conditions at the bottom, side and top surfaces of the layer. Parameters in the developed correlations for the Nu numbers were determined via CFD simulation and mathematical processing of the simulation results. CFD simulations by means of the ANES code were completed in accordance with a specially developed experiments matrix. Two-parameter k-ω turbulence model by Wilcox, which includes Menter’s improved near wall functions, has been implemented in the CFD code and applied accordingly. To evaluate the accuracy and predictability of the developed correlations we ran a comparative analysis of the Nu numbers at the sidewall and bottom surfaces of the melt layer, as defined on the basis of the developed correlations for the Nu numbers and as defined in CFD simulation. The comparison showed a strong correspondence of the results within a wide range of Rayleigh number values of ∼ 106 < Ra < 1012. The analysis of the developed correlations allowed shaping a number of critical arguments that define heat transfer conditions at the melt layer boundaries. It was found that the Nu numbers at the side and bottom surfaces are largely dependent on the difference in the temperatures of the top and side surfaces of the layer. As the difference between the these temperatures widens, the Nu numbers increase drastically (by tens of percent or more) in comparison to similar Nu numbers defined on the basis of the well-known correlations. It is specified that when the temperatures at the top and side surfaces of the layer are equal, the heat transfer conditions at the side surface are defined by “Globe and Dropkin” correlation used for the horizontal surfaces of the layer. We also evaluated the significance of the geometric parameters on the Nu values for the sidewall and bottom surfaces of the melt layer. Multiplicative effect of this parameter and of the parameter for temperature conditions at the boundaries of the layer mentioned above may lead to a significant (by times) increase of the Nu values. That must be considered in the thermal analysis of the corium pool and the processes of the SA.

Assessment of advanced RANS models to predict the heat transfer for supercritical fluids in vertical tubes

The extreme thermophysical property changes of fluids near the pseudocritical point lead to strong buoyancy and acceleration effects, posing challenges for turbulence modelling. This paper aims to assess the performance and applicability of various turbulence models, with the intention of providing a useful reference for quickly selecting appropriate models and for models’ further improvement. Additional Favre-averaged turbulence models were implemented through user-defined scalars in ANSYS Fluent and compared to published experimental and high-fidelity simulation data. This study found that the tested turbulence models have different sensitivities to molecular Prandtl numbers, buoyancy effects, and flow acceleration. For forced convection, all turbulence models can be applied in the case of the flow acceleration number Kv<1.37×10−8, and the ZXY model has the widest application range. None of the tested turbulence models showed generalizability under mixed convective conditions. The Lien-PSA model qualitatively reproduced the wall temperature trends for all tested cases.

Computational analysis of radiative nanofluid flow past an inclined cylinder with slip effects using the Yamada–Ota model

The notion of the paper is to analyse the flow attributes of a carbon nanotube-based hybrid nanofluid over an inclined cylinder. This study accounts for the impacts of mixed convection, thermal radiation, suction/blowing, and slip boundary conditions. The solution of the governing equations is obtained using the "bvp4c solver", and presented through graphs and tables. The obtained results are validated by comparing them with published work. The study reports that increasing the temperature slip parameter led to a reduction in both velocity and temperature distributions. The presence of an electric parameter contributed to an increase in nanofluid flow, while the temperature of the nanofluid exhibited a decrease. Moreover, increasing the Hartmann number from 0.2 to 1.1 results in a 1.39% increase in the heat transfer rate within the hybrid nanofluid model. However, the pure fluid model demonstrates a more substantial enhancement, with a significant 3.8% rise in the heat transfer rate.

Analysis of entropy generation and Joule heating effects for MHD peristaltic flow over an asymmetric channel with mixed convective conditions

AbstractThe investigation of entropy generation in peristaltic flow in an asymmetric channel under mixed convective conditions is a contribution to the body of literature. The used transport model includes appropriate boundary conditions along with continuity, momentum, energy, and concentration equations. Under the presumptions of a long wavelength and a low Reynolds number, the analysis is carried out. The analysis takes into account important elements including Joule heating, magnetohydrodynamics (MHD), and heat and mass transmission. An approach using BVP4C is used to analyze the governing system. The research adds to the body of knowledge in the subject by revealing important details about the complex interactions between these variables and how they affect peristaltic flow's creation of entropy. The originality of this work resides in its thorough examination of numerous crucial elements, including MHD, Joule heating, and mass and heat transport. The originality of this research is further enhanced by the analysis of the impacts of various parameters on velocity, temperature, concentration, pressure gradient, and streamlines. This study provides a novel viewpoint and a deeper knowledge of the entropy generation phenomenon in peristaltic flow, opening the door for potential applications in numerous disciplines including fluid dynamics, biomedical engineering, and transport processes.

Baffle effects on enhancing cooling performance of electronic components by nanofluid in a horizontal channel

PurposeThe purpose of this study is to investigate the impact of varying baffle height and spacing distance on heat transfer and cooling performance of electronic components in a baffled horizontal channel, using a Cu-H2O nanofluid under mixed convection and laminar flow.Design/methodology/approachThe mathematical model is two-dimensional and comprises a system of four governing equations, such as the conservation of continuity, momentum and energy. To obtain numerical solutions for these equations, the finite volume method was used for discretization. A validation process was performed by comparing this study’s results with those of previously published studies. The comparison revealed a close agreement. The numerical study was performed for a wide range of key parameters: The baffle height (0 ≤ h ≤ 0.7), the spacing distance between baffle and blocks (0.25 ≤ w ≤ 3), the Grashof and Reynolds numbers are kept equal to 104 and 75, respectively, the channel aspect ratio is L/H = 10, and the volume fraction of Cu nanoparticles is fixed at φ = 5%.FindingsThe results of the study reveal a significant improvement in heat transfer in terms of total Nusselt number of the top and bottom hot components, which exhibited an improvement of 16.89% and 17.23% when the baffle height increases from h = 0 to h = 0.7. Additionally, the study found that reducing the distance between the baffle and the electronic components up to a certain limit can improve the heat transfer rate. Therefore, the optimal height of the baffle was found to be no lower than 0.6, and the recommended distance between the heaters and the baffle was 0.5.Originality/valueThis study provides valuable insights into the optimization of the design of baffled channels for improved heat transfer performance. The findings of study can be used to improve heat exchangers and cooling systems in various applications. The use of Cu-H2O nanofluid under mixed convection and laminar flow conditions in channel with baffle and electronic components is also unique, making this study an original contribution to the field.

Mixed convective-quadratic radiative MoS 2–SiO 2/H 2 O hybrid nanofluid flow over an exponentially shrinking permeable Riga surface with slip velocity and convective boundary conditions: Entropy and stability analysis

In this work, the flow of a hybrid Mo S 2 − Si O 2 /water nanofluid across a porous exponentially diminishing Riga surface with the effects of quadratic heat radiation is taken into account. We also considered the effects of mixed convection, slip velocity, and convective thermal boundary conditions. Before numerically solving the governing partial differential equations, the MATLAB function bvp4c was used to get a comprehensive description of all relevant flow characteristics. The ramifications of physical characteristics concerning fluid flow and thermal profile are investigated using graphs and tables. The primary objective of this study is to investigate the Nusselt number, skin friction coefficient, and entropy production. Using the second law of thermodynamics, the irreversibility factor is computed. For a given value of the mass suction parameter, the findings also indicate the occurrence of dual-nature solutions in the shrinking sheet area, with a stable upper solution branch and unstable bottom solution branch. In addition, the first solution produces a positive minimum eigenvalue, whereas the second solution produces a negative eigenvalue, showing the stability of the first solution. For heat transfer enhancement, the existence of quadratic thermal radiative parameter impacts is more advantageous. With a larger value for the modified Hartman number, the velocity field has expanded. Also, recent research demonstrates that raising the thermal Biot number enhances the thermal gradient. Increases in nanoparticle volume fraction and thermal radiation parameters lead to a commensurate rise in entropy production. Because of these findings, we can better regulate the temperature of various environments by controlling the flow of heat.

Dynamics of Brownian motion and nonlinear mixed convective conditions on thermophoretic slip flow embedded with non-Fourier flux

In this paper, the importance of mass and heat transfer characteristics of mixed convective conditions on nonlinear free convection flow embedded with non-Fourier flux and thermal radiation is numerically investigated. A partial Casson slip and mixed impact of thermophoresis and Brownian motion is considered at the elastic surface. To change the highly nonlinear partial differential equations into ordinary differential system, we used the similarity transformations and then the shooting method is employed to solve resulting equations. The significance of various physical parameters on the velocity, concentration and temperature profiles are investigated for both negative value of ferromagnetic interaction ([Formula: see text]) and positive value of ferromagnetic interaction ([Formula: see text]). The governing physical aspects of coefficient of skin friction, the Sherwood and Nusselt numbers are obtained for various embedded parameters. Our findings concluded that the ferromagnetic interaction is positive and then more mass transfer rate is identified compared to the negative value of ferromagnetic interaction, but whereas in friction and heat transfer rate, it was completely mixed sense (i.e., different effects have different results). Brownian motion has less Nusselt number values in positive ferromagnetism compared to negative ferromagnetism and quite opposite behavior is observed in the presence of thermophoresis, this happened due to nonlinear flux and buoyancy.

Fluid-structure interaction of a thin flexible heater inside a lid-driven cavity

The purpose of this study is to explore the characteristics of fluid-structure interaction and heat transfer enhancement from a hot flexible thin plate during mixed convection. The mixed convection condition of the plate heater is assumed by placing it inside a lid driven cavity with top and bottom cavity walls being fixed and insulated while left and right cavity walls maintained at constant low temperature move in downward and upward direction respectively. The Galerkin Finite Element Approach has been used to numerically solve equations describing unsteady flow, thermal and stress fields in the Arbitrary Lagrangian-Eularian (ALE) framework. Key parameters include Reynolds number ( Re) and Richardson number ( Ri), and Cauchy number ( Ca) which are varied in the range of 100 ≤ Re ≤ 500, 0.1 ≤ Ri ≤10, and 10−4 ≤ Ca ≤ 10−7 respectively. To investigate the effect of the heater’s geometry, the plate length ( l) has been varied within 0.1 ≤ l ≤ 0.7. The results have been presented in terms of the distribution of streamline and isotherm, heat transfer rate from the flexible heater as well as its deformation. The outcomes reveal that heat transfer enhances with the increase in Reynolds number and Richardson number while it degrades with the extension of the heater. Moreover, thermal frequency obtained by Fast Fourier Transform (FFT) indicates dominant peaks at higher Reynolds number and Richardson number although these become insignificant as the plate becomes rigid.

Mixed convection phenomena in tubes with wire coil inserts

A numerical investigation of the flow and heat transfer in a helical coil in laminar and transitional flow regime under mixed convection conditions is presented. The continuous separation and reattachment of the boundary layer caused by the wire coil, that interrupts the flow near the tube all, and the swirl induced by the helical shape of the insert, are identified as the mechanism for heat transfer enhancement. Simulations in the Reynolds number range 200<Re<1500 show the role of mixed convection on heat transfer, as the flow dynamics is sensitive to the buoyancy forced induced by the tube wall heating. The interaction of the secondary swirl flow with the buoyancy motion is investigated in this work, with the aim of clarifying the range where heat transfer could be worsened by the presence of the helical coil. The investigation has been undertaken considering a helical coil of geometrical characteristics e/D=0.071 and p/D=1.5 and water as working fluid. Validation with experimental results of friction factor and Nusselt number is also presented.

An analytical representation of raindrop size distribution in a mixed convective and stratiform precipitating system as revealed by field observations

AbstractThis study investigated a rainfall event under a typhoon influence using a 2D video disdrometer and weather radar observations to characterize raindrop size distribution (DSD) in a mixed convective and stratiform precipitating system. During the time period when both convective and stratiform rainfalls existed, the DSDs generally indicated a monotonically decreasing shape with increasing particle size, with a relatively gradual decrease at intermediate particle size observed at certain times; this feature is attributed to the combined effect of convective and stratiform rainfalls. During the transitional period between convective and stratiform rainfalls, the DSDs exhibited a bimodal shape. The DSDs were well approximated by a newly proposed gamma raindrop distribution combined with exponential (GRACE) distribution function, which was defined as the sum of the exponential distribution and the gamma distribution. A comparison of the volume ratio of the exponential and gamma components of the GRACE distribution revealed that the exponential component of the DSD was larger than the gamma component in the bimodal DSD. These results suggest that the DSD became bimodal during the period when stratiform rainfall predominated because of the weakening of convective rainfall. The GRACE distribution is useful for understanding cloud‐microphysical processes in mixed stratiform and convective precipitation conditions.

An experimental and numerical comparison study on a heat sink thermal performance with new fin configuration under mixed convective conditions

The heat sinks thermal performance with four aluminum fin configurations set under mixed convection settings at three voltage values 100, 150, and 200 V, was examined. Six fins are part of a heat sink. The flat fin is the first type (case1), the corrugated fin was the second (case2), the third one was a corrugated fin with rectangular perforations with its rib (case3), and the last one was corrugated with triangle perforations with its rib (case 4). The surface area of all studied cases is equal. The third and fourth studied cases are new proposed configurations by this work. The air velocity was 1.5 m/s. The temperature distribution along the fin surface was measured for each case study. The theoretical study was held on each studied case using a fluent package (ANSYS18 software). The absolute deviation between the experimental and numerical study for each studied case temperature distribution is 2.95% for case 1, 3.37% for case 2, 1.41% for case3 and, and 1.2% for case 4 at 160 W supplied power heater. Cases (3 and 4) will enhance the heat transfer coefficient compared to the flat fin case 11) which was 4.16% and 4.27% respectively. The fin perforations with its ribs case (3 and 4) decrease the material cost and heat sink weight to 7.7% and 8.3% respectively. Also, the required space to locate the heat sink is minimized

Numerical investigation of turbulent mixed convection flow and heat transfer characteristics of 2 × 2 subchannels with spacer grids

AbstractIn turbulent mixed convection conditions, flow and heat transfer can deteriorate under specific conditions, thus affecting the performance of the safety of the system, which could imperil the safety of the nuclear reactor. In this paper, by analyzing the velocity, temperature distributions, and other thermal‐hydraulic parameters, the steady‐state computational fluid dynamics approach with the SST k–ω turbulence model used in this study was verified. Then, flow and heat transfer characteristics in turbulent mixed convection inside 2 × 2 subchannels with and without spacer grids were investigated. The results showed that the velocity profiles were distorted and the heat transfer capacity was impaired due to the influence of buoyancy. The Nusselt number ratio (Nu/Nuf) between turbulent mixed convection and forced convection increased with the increase of Reynolds number (Re) until unity but decreased with the increases of Grashof number (Gr) and Buoyancy parameter (Bo*).

Upward flame spread over discrete thick fuels under mixed convection flow

In this paper, flame spread over a vertically oriented discrete fuel array is investigated experimentally under mixed-convective flow conditions, using polymethyl methacrylate (PMMA) as the solid fuel. It is found that under mixed convective conditions, the flame propagation over a discrete fuel array can be categorized into three regimes with decreasing fuel coverage. The flame spread rate is observed to exhibit a positive relationship with fuel coverage and fuel length. The limiting fuel coverage ratio that supports the flame spread reduces with the length of fuel blocks. Meanwhile, a peak value of mass flux is observed at a fuel coverage value below unity due to a delayed thickening of the thermal boundary layer with the inert insulation board effects. This indicates that the distribution of discrete fuel array in addition to fuel properties and fuel loading significantly affects the flame spread rate and the risks associated with it. Additionally, the flame spread model can accurately predict the flame spread rate and the onset of limiting conditions for the flame spread over a discrete fuel array under mixed-convective conditions. The results of this paper may be crucial for developing effective mitigation strategies for fire safety in façades, wildland, and urban environments.

Analysis of entropy generation and nonlinear convection on unsteady flow of MHD Prandtl fluid with Soret and Dufour effects

Here the assessment of entropy generation with Soret and Dufour impact in flow of MHD Prandtl fluid along an unsteady stretching surface has been measured. Nonlinear mixed convection and convective conditions for heat/mass transfer are imposed at the surface. The outcome of viscous dissipation and radiation is considered in heat transfer features. The obtained system of nonlinear PDEs is converted to ODEs by consuming dimensionless variables. Resulting systems are solved for the convergent solutions. Impacts of Prandtl fluid parameters, unsteadiness parameter, Soret and Dufour numbers, magnetic parameter, nonlinear thermal and concentration parameter, Prandtl number, radiation parameter, thermal and concentration Biot numbers, ratio of concentration to thermal buoyancy, Eckert number and Schmidt number are addressed. Skin friction coefficient, local Nusselt and Sherwood numbers are analyzed graphically. Unsteady parameter { epsilon } has reverse behavior on the velocity and temperature profiles, velocity declines while temperature raises. Prandtl fluid parameter { alpha } and { beta } boost the velocity field. Mixed convection parameter le and N* (ratio of concentration and buoyancy force) enhance the velocity field and resultant boundary layer thickness. Magnetic parameter change its behavior on f(eta )theta (eta ) and . Soret/Dufour number enhances the energy flux due to mass transfer rate and mass flux which radically increases the temperature. Far away from the wall entropy generation grows rapidly for greater values of a and b. Magnetic and radiation parameter increase the entropy generation while radiation parameter decreases.

Effects of surface roughness in multiple microchannels on mixed convective heat transfer

• Effect of process-induced surface roughness on mixed convection was investigated. • Height, width and average roughness parameters were studied on multiple microchannels. • Surface roughness is an important geometric parameter and affects heat transfer. • Mixed convection increases with decreasing cross-section and increasing roughness. The most widely used type of heat transfer in applications is convection heat transfer, and both natural and forced convection modes have an effect in total heat transfer to a certain extent, whether any of these modes is neglected or not. In this study, the contribution of natural and forced convection effects to total heat transfer in rectangular microchannels was investigated experimentally for determining the effect of manufacturing process-induced surface roughness in multiple microchannels fabricated using stainless steel material. The experiments were conducted with microchannel heat sinks having three different surface roughness values of 1.1 µm, 1.8 µm, and 3.0 µm, three microchannel widths of 300 µm, 500 µm and 700 µm and two heights of 300 µm and 450 µm. During the manufacturing process, surface roughness values were controlled by changing electro-erosion fabrication parameters, and detailed surface maps were generated for the microchannel heat sinks. In the experiments using pure water as the working fluid, constant heat flux was applied to the bottom surface of the microchannel heat sink. The experiments were conducted in the range of 10–80 Reynolds numbers to ensure mixed convection conditions. In conclusion, it was determined that surface roughness had a significant effect on mixed convective heat transfer. An increase in surface roughness from 1.1 µm to 1.8 µm in microchannel heat sinks with cross-sections of 300 µm × 300 µm, 700 µm × 300 µm, 300 µm × 450 µm, and 700 µm × 450 µm s led to an increase of about 24 %, 19 %, 17 %, and 13 %, respectively, in the Nusselt number. Likewise, the increase in surface roughness from 1.8 µm to 3.0 µm resulted in an increase of 17 %, 15 %, 14 %, and 10 %, respectively, in the Nusselt number in the same channel cross-sections. In general, an increase in hydraulic diameter led to a reduction in the effect of surface roughness on overall heat transfer. For a constant microchannel width and height, the effect of surface roughness on mixed convection could be observed only with the increase in the Grashof number. Among the eighteen microchannel heat sinks with different geometric parameters, the best heat transfer results were obtained for the smallest microchannel cross-section of 300 µm × 300 µm and the highest roughness value of 3.0 µm.

The effect of spanwise heterogeneous surfaces on mixed convection in turbulent channels

Turbulent mixed convection in channel flows with heterogeneous surfaces is studied using direct numerical simulations. The relative importance of buoyancy and shear effects, characterised by the bulk Richardson number $Ri_b$ , is varied in order to cover the flow regimes of forced, mixed and natural convection, which are associated with different large-scale flow organisations. The heterogeneous surface consists of streamwise-aligned ridges, which are known to induce secondary motion in the case of forced convection. The large-scale streamwise rolls emerging under smooth-wall mixed convection conditions are significantly affected by the heterogeneous surfaces and their appearance is considerably reduced for dense ridge spacings. It is found that the formation of these rolls requires larger buoyancy forces than over smooth walls due to the additional drag induced by the ridges. Therefore, the transition from forced convection structures to rolls is delayed towards larger $Ri_b$ for spanwise heterogeneous surfaces. The influence of the heterogeneous surface on the flow organisation of mixed convection is particularly pronounced in the roll-to-cell transition range, where ridges favour the transition to convective cells at significantly lower $Ri_b$ . In addition, the convective cells are observed to align perpendicular to the ridges with decreasing ridge spacing. We attribute this reorganisation to the fact that flow parallel to the ridges experience less drag than flow across the ridges, which is energetically more beneficial. Furthermore, we find that streamwise rolls exhibit a very slow dynamics for $Ri_b=1$ and $Ri_b=3.2$ when the ridge spacing is of the order of the rolls’ width. For these cases the up- and downdrafts of the rolls move slowly across the entire channel instead of being fixed in space, as observed for the smooth-wall cases.

Rheology of Variable Viscosity-Based Mixed Convective Inclined Magnetized Cross Nanofluid with Varying Thermal Conductivity

Cross nanofluid possesses an extraordinary quality among the various fluidic models to explore the key characteristics of flowing fluid during very low and very high shear rates and its viscosity models depend upon shear rate. The current study establishes the numerical treatment regarding variable viscosity-based mixed convective inclined magnetized Cross nanofluid with varying thermal conductivities over the moving permeable surface. Along with variable thermal conductivities, we considered thermal radiation, thermophoresis, and the Brownian motion effect. An inclined magnetic field was launched for velocity scrutiny and the heat transfer fact was numerically seen by mixed convective conditions. Similarity variables were actioned on generated PDEs of the physical model and conversion was performed into ODEs. Numerical results showed that the frictional force and Nusselt quantity considerably influence the skinning heat transfer processes over the geometry of a moving permeable surface. Furthermore, less velocity was noticed for the greater suction parameter and the Brownian motion parameter corresponds to lower mass transport.