Thermal Boundary Layer Research Articles

Numerical Analysis Study of Chemically Radiative MHD Williamson Nanofluid Flow over an Inclined Surface with Heat Source

The design and optimization of systems such as nuclear reactors, solar collectors, and thermal power plants may benefit from an understanding of the behaviour of nanofluids with chemical processes, thermal radiation, and magnetic fields over inclined surfaces with heat sources.This review looks at the magnetohydrodynamic (MHD) flow of a Williamson nanofluid over an inclinable stretched sheet and the impact of thermal radiation, heat source, and chemical processes. The outcomes of the generation of heat or absorption, as well as thermal radiation, are all factored into account in the energy equation. On the other hand, the mass transport equation also takes into account chemical interactions.The similarity substitution serves to turn the governed partial differential equations for velocity, temperature, and concentration into ordinary differential equations, which are then numerically resolved with Mathematica's NDSolve program. Changes in temperature, concentration, and dimensionless velocity as a function of various factors are graphically touched upon. The temperature diminishes while the Prandtl number accelerates as the thermal boundary layer thins and the viscosity enrichment. The temperature contour develops along with the magnetic field strength. When all the parameters were compared for a particular case, a very good association was discovered. Depending on the precise conclusions and understandings drawn from the investigation of chemically radiative MHD nanofluid flow over inclined surfaces with a heat source, the applications may range greatly. It's important to remember that such research often aids in the creation of more effective and environmentally friendly solutions in a variety of sectors.

Numerical study of hybrid binary Al2O3-Cu-H2O nanofluid coating boundary layer flow from an exponentially stretching/shrinking perforated substrate with Cattaneo-Christov heat flux, heat source, suction and multiple slip effects

Modern coating systems are increasingly deploying nanomaterials which offer improved thermal performance. The optimization of these systems can benefit from more elegant fluid dynamic models of the coating process. Inspired by these advancements, the present investigation introduces a novel mathematical model to analyze the boundary layer transport in Al2O3-Cu-H2O hybrid binary nanofluid coating deposition on an exponentially stretching porous substrate (sheet). Lateral mass flux (suction) at the wall is also considered a heat source (generation) for hot spot manufacturing effects. To add further sophistication to the thermal conduction model, a non-Fourier approach is adopted which accurately incorporates thermal relaxation effects i.e. the Cattaneo-Christov heat flux (CCHF) model. The Tiwari-Das volume fraction nanoscale formulation is implemented for different combinations of Alumina (Al2O3) and Copper (Cu) metallic nanoparticles in an aqueous base fluid (H2O). Hydrodynamic wall and thermal slip are also included as they feature in coating processes. The fundamental equations governing mass, momentum, and energy conservation, along with the corresponding conditions at the wall (substrate) and free stream, are made dimensionless through suitable scaling similarity transformations. The resulting nonlinear coupled ordinary differential boundary value problem is subsequently addressed using the efficient MATLAB bvp4c routine. Special cases of the non-Fourier model are validated against published results, and the general model is further confirmed through validation using an Adams-Moulton 2-step predictor-corrector algorithm (AMPC). Furthermore, dual solutions of the generalized model are extracted and visualized. A comprehensive study of the effects of key thermophysical key parameters on momentum and thermal characteristics (velocity, temperature, skin friction and local Nusselt number) is conducted and solutions are visualized graphically. The computations show that higher temperatures are present with intensification in the thermal relaxation parameter (Cattaneo-Christov hyperbolic model parameter), which predicts therefore larger temperatures than the classical Parabolic heat conduction model using Fourier analysis. Effectively, thermal relaxation is responsible for finite heat wave propagation and produces more accurate estimations of heat transfer than the Fourier model. An increase in stretching parameter enhances the skin friction coefficient and elevates the local Nusselt number. As the thermal relaxation parameter increases, the temperature magnitudes corresponding to the first and second solutions are both enhanced as are thermal boundary layer thicknesses. An increase in wall suction induces an escalation in the first solution for velocity whereas it reduces the second solution velocity. Stronger wall suction suppresses temperatures. With increasing thermal slip, the boundary layer is cooled i.e. temperature plummets and thermal boundary layer thickness is decreased. Strong deceleration is induced with greater hydrodynamic (velocity) slip. Both first and second solutions for skin friction are elevated with shrinking whereas they are depressed with stretching. With greater velocity slip both the first and second solutions for skin friction are depleted with greater velocity slip for the shrinking case, whereas they are generally enhanced for the very strong stretching case. The computations offer some new insights into multi-physical thermal fluid dynamics of nanofluid-based coating systems.

Nonlinear heat radiation and mass transfer characteristics on MHD Walters’ B fluid flow through a porous medium over a stretching sheet

To handle the continuous thermal power supply is very important in thermal systems and industries, so magnetized heat transport with non-Newtonian fluid is an appropriate platform for thermal power energy. In view of this usefulness, this paper provides a numerical assessment of electrically conducting Walter's B fluid flow through nonlinear permeable stretching sheet subject to mixed convective, porous medium, and Newtonian heating phenomena. Thermophoresis and Brownian motion effects have been included in energy and species diffusion equations to account for the impacts of nonlinear thermal radiation, joule heating, heat source and chemical reaction. The system of governing equations has been reduced to dimensionless nonlinear coupled equations using similarity transformations. The bvp4c technique has been used to obtain the solution for velocity, temperature, and concentration distributions. We consider both regions of assisting and opposing flow and provide various tables and graphs to examine the impact of varying values of emerging factors. Heat source and thermal radiation characteristics are found to enhance the thermal boundary layer thickness, which may be used to dissipate heat. The magnetic parameter augmented the fluid temperature and decelerated the velocity field. The chemical reaction parameter accelerated the concentration distribution. Further, the Sherwood number, Nusselt number, and skin friction coefficient have been determined and compared well to prior research that has been published.

Direct Numerical Simulation of single bubble dynamics in nucleate pool boiling with micro-region modeling and thermal coupling to a solid wall

In this study, we conduct two-dimensional, axisymmetric simulations to investigate the growth and departure of a single bubble, with a particular focus on the conjugate heat transfer between the fluid and the heating wall. A multiscale modeling approach is employed to account for nanoscale effects near the liquid-vapor-solid triple contact line (CL). At the macro (bubble size) scale, the interface dynamics is captured with the front-tracking method by using the open-source code TRUST/TrioCFD. The macro scale algorithm is coupled with a sub-grid micro-region model. It is driven by the wall superheating at the CL as input, and predicts the macroscopic apparent contact angle and heat fluxes. To validate our modeling approach, we first conduct quantitative comparisons using the data on the bubble growth experiment RUBI and its simulations. Next, an investigation of the case of water under atmospheric pressure and gravity is performed. Notably, we observe a significant spatial variation in temperature near the nucleation site during the expansion and contraction of the bubble base. This variation greatly affects the thermal boundary layers in the fluid and solid domains and the bubble growth, demonstrating the need to resolve the conjugate heat transfer in the considered cases.

Thermodynamic effects in cavitating flow

Cavitation is a phenomenon characterized by vapor generation and condensation in liquid flows, at approximately constant temperature. Cavitation is usually triggered by a local pressure drop in the vicinity of a cavitation nucleus. As the bubble grows, latent heat is supplied from the surrounding liquid to the interface, creating a thermal boundary layer. This creates a thermal boundary layer. The result is a local drop in the liquid temperature, which leads to a drop in vapor pressure. This delays the further development of the bubble, as a greater pressure drop is required to maintain the process. This phenomenon is known as thermal delay or thermodynamic effect and plays a moderating role in the development of cavitation. Thermodynamic effects can usually be neglected for liquids whose critical temperature is much higher than the operating temperature. However, this is not the case for liquids whose operating temperature is close to the critical temperature, such as in cryogenics.The understanding of the thermodynamic effects of cavitating flow is crucial for applications like turbopumps for liquid hydrogen LH2 and oxygen LOx in space launcher engines. Experimental studies of this phenomenon are rare as most of them were performed in the 1960s and 1970s. Due to the extreme difficulties of experimental investigation, predicting of thermodynamic effects in cavitation often bases on data in liquids other than cryogenics. Most often used surrogate liquids are hot water or certain refrigerants, which are selected by a single fluid property, most commonly by the thermodynamic parameter ∑.

Thermal behavior and dynamics of flow boiling in a pin-fin microchannel

As the need for effective heat dissipation in specialized systems intensifies, the study of flow boiling in microchannels has gained prominence due to its high efficiency and cost benefits. Utilizing a three-dimensional computational model incorporating the Volume of Fluid (VOF) and Saturated Interfacial Volume (SIV) methodologies, this research scrutinizes the behavior of saturated flow boiling in a microchannel featuring a centrally positioned, heated square cylinder. The analysis focuses on variations in bubble morphology, fluidic behavior, and thermal profiles, revealing that the evaporation of a thin liquid film contributes significantly to heat transfer efficacy. A systematic assessment of temperature gradients, heat transfer coefficients, and liquid film metrics uncovers the critical drivers behind effective heat transfer across different surfaces. Additionally, the study elucidates the role of Reynolds number and initial bubble size, indicating that higher Reynolds numbers thicken the liquid film, reducing heat transfer efficiency, while larger initial bubble diameters thin the liquid film, thereby boosting efficiency. Factors such as thermal boundary layer disruption and superheated fluid absorption further contribute to heat transfer optimization. This investigation enriches the current understanding of phase-change heat transfer dynamics and bubble interactions in microchannel environments equipped with a heated square cylinder.

A hybrid atomistic-continuum framework for multiscale simulations of boiling

Boiling is a multiscale physics process where the nucleation of vapour bubbles occurs due to molecular-scale interactions between the fluid and a heated wall, but it also depends on the larger-scale hydrodynamics and thermal boundary layers determined by the outer system boundary conditions. Modelling boiling from the nanometre up to the millimetre scales at which bubble departure occurs is not possible via state-of-the-art simulation methods: Molecular Dynamics (MD) simulations can capture nucleation from first principles but are limited to nanometre scales due to their computational cost, whereas computational fluid dynamics (CFD) simulations based on the continuum Navier-Stokes equations cannot capture nucleation. Here, we present a novel multiscale simulation method which merges MD and CFD descriptions into a single modelling framework, where MD resolves the near-wall region where molecular interactions are important, and a CFD solver resolves the bulk flow. We model the progressive heating of a Lennard-Jones fluid via contact with a solid wall until a vapour bubble nucleates in the MD region of the domain and grows by entering in the CFD domain. Our results show that an incompressible CFD flow model based on the Volume Of Fluid method with interphase mass transfer calculated via the Hertz-Knudsen-Schrage equation is sufficient to obtain seamless coupling of phase fraction, velocity and temperature fields, with the hybrid MD-CFD framework yielding bubble dynamics closely matching those of MD alone.

A combined experimental and numerical approach for heat transfer enhancement in a minichannel using half rectified pulsating flows

The miniaturization of electronic packages and their associated high-power density circuits requires more innovative cooling solutions. Single phase pulsating flows offer a promising solution due to their disruption of the thermal boundary layer. This study aims to bridge the knowledge gap by using experimental and computational methods to investigate the complex flow characteristics of laminar pulsating flows in a heated rectangular minichannel and couple that analysis with an investigation of thermal-hydraulic performance. Experimental analysis involves a uniformly heated thin foil approximating a constant heat flux bottom wall. Wall temperature measurements are recorded using an infrared thermography system. Analogous to the experimental conditions, a three-dimensional conjugate heat transfer computational model is developed with a volumetric heat generation source. Positive and negative half rectified sinusoidal pulsating flow waveforms are studied for dimensionless pulsation frequencies or Womersley numbers of Wo = 2.5 and 5.1 at a fixed flow rate amplitude A 0 = 3. For the positive half rectified waveform, a marginal enhancement in heat transfer of 2.2% for Wo = 2.5, A 0 = 3 was obtained. Whereas the negative half rectified case leads to a heat transfer enhancement of 9% and 6% for Wo = 2.5 and Wo = 5.1 respectively, with a high thermal performance of η = 2.4 over corresponding steady flow.

Large-eddy simulation of axial, radial and mixed centrifugal convection in a closed rotating cavity

Large-eddy simulations (LES) of centrifugal convection in a closed rotating cavity with different thermal boundary conditions are presented for Rayleigh numbers (Ra) 107∼109. Previous results for radial convection with a positive radial temperature gradient and for axial convection with low Ra are confirmed. For axial convection, turbulence develops in the core flow at Ra=109, but is considerably weaker than the turbulence for the radial and mixed convection. In mixed convection, the mean core temperature shows little radial variation as in radial convection, but has a significant axial temperature gradient as in axial convection. Compared to the radial and axial convection cases, both shroud and disc heat transfer are increased in mixed convection. Changes in disc heat transfer from the axial convection case are particularly strong. In all the conditions, laminar kinematic Ekman layers occur on the discs, but the disc thermal boundary layers for axial and mixed convection are considerably thicker.

A generalized differential quadrature approach to the modelling of heat transfer in non-similar flow with nonlinear convection

This study aims to investigate heat transfer and entropy production in the non-similar flow of an incompressible fluid, with nonlinear convection and viscous dissipation. To obtain precise solutions, the Sparrow-Quack-Boerner local non-similarity method is implemented. The non-similarity arises from the nonlinear convection term present in the momentum equation. The non-similarity arises from the nonlinear convection term present in the momentum equation. Consequently, the inclusion of non-similarity terms into the energy equation is achieved through the interconnection of momentum and energy equations. Entropy generation is explored by employing the second law of thermodynamics. Numerical results from several truncation levels are presented in tabular form, and equations for both first and second-level truncations are generated. The one- and two-equation models are solved by implementing the Generalized Differential Quadrature Method (GDQM). Comparison with a second level of truncation reveals significantly greater inaccuracies in numerical results obtained from the first level. This discrepancy arose due to the omission of non-similar terms in the primary governing equations at the first truncation stage. The validity and accuracy of the derived numerical solutions are further demonstrated by the application of the GDQM and the midpoint method with Richardson extrapolation. Additionally, a plot of the numerical data produced from the second level of truncations is presented together with a discussion of the various physical factors. Increasing the mixed convection parameter accelerates fluid velocity, also when the viscous dissipation parameter increases, temperature and the Bejan number increase. The Prandtl number and the thickness of the thermal boundary layer are observed to be inversely related. Moreover, the quantity of entropy generated at the stretching surface and inside the boundary layer rises in proportion to the increases in the Prandtl and Eckert numbers.

Soret and Dufour effects on an unsteady MHD flow about a permeable rotating vertical cone with variable fluid properties

The objective of the present work is to examine the characteristics of unsteady incompressible magnetohydrodynamic fluid flow around a permeable rotating vertical cone. The effects of thermal radiation, viscous dissipation, and the Soret and Dufour effects are investigated in the analysis of heat and mass transfer. The viscosity of the fluid is considered inversely proportional to the temperature, and the thermal conductivity of the fluid is considered directly proportional to the temper-ature. The governing equations are converted into ordinary differential equations using suitable similarity transformations, which are then solved numerically using bvp4c from MATLAB. Results obtained in this study are in excellent correlation with previously conducted studies. The results demonstrate that the Dufour and Soret effects subsequently reduce the heat transit rate (by –3.3%) and mass transit rate (by –1.2%) of the system. It is also detected that fluids with higher viscosity tend to increase tangential skin friction (+8.9%) and azimuthal skin friction (+8.3%). The heat transit rate of the system is found to be more efficient for fluids with higher viscosity and lower thermal conductivity and Eckert numbers. Further-more, the thickness of the momentum, thermal, and concentration boundary layers significantly reduces while the heat and mass transit rates (+17.8% and +18.3%, respectively) of the system become more efficient for greater values of the un-steadiness parameter.

Heat transfer performance study of fluid rotating microchannel heat sink

The study presents a novel fluid rotating microchannel heat sink (FR-MC) and reports its heat transfer performance. The FR-MC features two cross ribs positioned in the channel. These cross ribs are inclined in the direction of fluid flow, with each rib inclining in opposite directions. This design enables the fluid to ascend or descend along the ribs, creating rotation after passing through the center to alter the flow direction. Experimental validation confirms the accuracy of the model and numerical simulations. The study investigates the heat transfer capability of FR-MC through comparative analysis, and explores the reasons for the improved performance. The results indicate a 45 % reduction in thermal resistance compared to a rectangular microchannel (R-MC). This improvement is attributed to the rotation of fluid promoting the exchange between the upper and lower parts and the mixing of hot and cold portions, effectively disrupting the thermal boundary layer near the wall. Further exploration into the impact of microchannel dimensions on heat transfer performance indicates that the FR-MC outperforms the R-MC across various heights and widths, achieving thermal resistance reductions ranging from 16 % to 50 %, illustrating the superior heat transfer performance of FR-MC.

A numerical simulation of the hydrothermal characteristics of a microchannel using cavities, ribs, and secondary channels

To tackle the overheating problem in microelectronic devices, microchannel heat sinks (MCHSs) are promising solutions. However, there is a need to improve their thermal performance while maintaining an acceptable pressure drop. This research investigates the effect of integrating multiple passive techniques for heat transfer enhancement, specifically examining the impact of combining triangular cavities, streamlined ribs, and oblique secondary channels (TC-SR-SC) on hydrothermal characteristics across a range of Reynolds numbers 100 to 600. By exploring the influence of each technique and their combining effects on fluid flow and heat transfer, the study aims to strike a balance between high thermal performance and low-pressure drop. Furthermore, the research also explores the thermal resistance, overall performance, entropy generation, and irreversibility of the novel design, comparing it numerically with commensurate geometries using the commercial software, FLUENT. The results reveal that the design of isosceles triangular cavities, streamlined ribs, and secondary channels combination (TC-SR-SC) achieves a maximum overall performance of 1.70 at Re = 400 due to the interruption and redevelopment of the thermal boundary layer. The presence of oblique secondary channels leads to the diversion of mainstream flow, resulting in better flow mixing between main adjacent channels. It also represents the lowest flow and heat transfer irreversibility, ultimately improving thermal performance based on the second law of thermodynamics perspective.

Mixed convection heat transfer in a partial porous layered split lid-driven wavy wall cavity with Cu–H2O nanofluid

This numerical study investigates mixed convection heat transfer in a two-dimensional irregularly-shaped enclosure with a nanofluid-saturated porous medium. The enclosure has wavy vertical walls, a centered triangular block, and a lid split into two regions moving in opposite directions. Transport equations are solved using the finite element method under varied Darcy (10−5 to 10−1), Reynolds (50 to 200), Richardson (0.1 to 10), amplitude (0 to 0.2), and nanoparticle volume fraction (0 to 0.1) numbers. Results demonstrate the combined effects of forced convection from lid motion and natural convection from temperature differences significantly enhance heat transfer. The wavy walls induce secondary flows and periodic disruption of thermal boundary layers. Increasing Darcy number enables deeper penetration into the porous block. Copper nanoparticles incrementally improve conductive heat transfer. Richardson number effects are more prominent at higher Reynolds numbers as buoyancy forces influence vertical convection. This study provides novel insights into synergistically utilizing wavy geometries, nanofluids, porous media, and active pumping for optimizing heat transfer in irregular enclosures for electronics cooling and thermal management.

Experimental investigation of the Reynolds analogy for high Prandtl number fluid with repeated rib roughness

Reynolds analogy describes the relationship between friction (f/2) and heat transfer (St) owing to their superficial resemblance. However, Reynolds analogy is limited to simple geometries with a Prandtl number (Pr) close to unity. To extend Reynolds analogy, we measured the St and f/2 simultaneously using a high Pr fluid in duct flow in vertical duct flow with repeated rib roughness. The experiments were performed at a fixed value of Pr, 2014, Reynolds number (Re) ranging from 9.1 × 103 to 9.6 × 104, and relative roughness (e/D) ranging from 0.01 to 0.04. In the high Pr fluid, the St was much lower than f/2, as most of heat exchange occurred in the conduction sublayer, resulting from a thin thermal boundary layer. On the rough surface, both f/2 and St were higher than on the smooth surface. However, the influence of Re and e/D was different. The differences stem from that the corresponding phenomenon to pressure drag in friction does not exist in heat transfer. The extended Reynolds analogy correlation was developed. In addition, the efficiency factor was defined as the ratio of the enhancement rates of St and f/2 on the rough surface to those on the smooth surface. The efficiency factor decreased with Re and e/D, while it increased with Pr.

CFD approach to analyze entropy generation, heat transfer of perforated conical ring turbulators embedded in heat exchanger with biological ternary hybrid nanofluid

Perforated conical rings greatly enhance heat transfer by causing flow disruption and increasing fluid mixing. With minimal impact on friction loss, it improves heat transfer by breaking the thermal boundary layer. In this work, entropy generation, overall performance of cylindrical pipe heat exchanger equipped with perforated conical rings are numerically calculated. Shape of the holes is oval and the number of hole are 4. Ternary hybrid nanofluid is the working fluid (coolant). The combination of graphene, Cu and Al2O3 nanomaterials are considered with water as a base fluid. A particular range of Reynolds number is taken into account (5000 − 9000). 50% increase in Nusselt number is noted for using higher volume fraction (0.5%) of ternary hybrid nanofluid. Thermal performance of heat exchanger is increased more than 50%. Entropy generation is higher by using the perforated conical rings. Thermal- hydraulic performance evaluation criteria (THPEC), i.e. ration between Nusselt number and friction factor decreases with increasing Reynolds number which is a promising result. The differences in THPEC of cylindrical tube with and without perforated conical ring (PCR) are highlighted.

Experimental and Numerical Investigations on Thermal-Hydraulic Performance of Three-Dimensional Overall Jagged Internal Finned Tubes.

To satisfy the demand for efficient heat transfer, a novel three-dimensional overall jagged internal finned tube (3D-OJIFT) was fabricated, using the rolling-ploughing/extruding method. The thermal performance of the 3D-OJIFT were studied and compared in experiments and three-dimensional numerical simulations. The RNG k-ε turbulence model is well verified with the experimental results. By analyzing the distributions of velocity, temperature, and turbulence kinetic energy, it was found that the 3D-OJIFT destroyed the development of the velocity and thermal boundary layers, increased the turbulence disturbance, and reduced the temperature gradient, thus improving the heat transfer. The influences of the jagged height and jagged spiral angle of the 3D-OJIFT are discussed. The Nu and f increased as the jagged height of the 3D-OJIFT increased. The Nusselt number of the 3D-OJIFT was 1.67-2.04 times the value for the smooth tube. In addition, the comprehensive heat transfer performance of the 3D-OJIFT improved after increasing the jagged spiral angle. Compared with conventional internal helical-finned tubes and other reinforcement structures reported in the literature, the 3D-OJIFT demonstrated better comprehensive heat transfer performance. Finally, empirical correlations of the 3D-OJIFT were obtained.

Insight of Jeffrey flow over a stretching Riga plate with activation energy and viscous dissipation: Melting heat transfer regime

AbstractPresent article highlights the significance of Arrhenius activation energy along with viscous dissipation in Jeffrey fluid over a Riga plate. Riga plate is basically an actuator made up of array of magnets and electrodes scaled on a plane surface to tackle the weaker electrical conductivity during fluid flow. In order to ensure the novelty, a reliable melting heat surface condition has been incorporated on nonlinear stretching Riga plate of variable thickness to reconnoiter features of heat transfer. Moreover, stagnation point has been retained in this study. Adequate transformations are employed in order to attain system of nonlinear ordinary differential equations. A well known semi analytical technique (Homotopy analysis method) is utilized to obtain series solutions of prevailing dimensionless equations. Influence of several apposite parameters on velocity, thermal and concentration distributions is analyzed graphically. Physical evaluation and graphical sketch is presented for drag force coefficient and rate of heat transfer. Analysis of velocity as well as associated boundary layer thickness gives the growing up impact for the strength of modified Hartmann number. Enhancement of dimensionless reaction rate and endothermic/exothermic reaction parameter results in increment for heat flux over stretching Riga plate. Increase in thermal distribution takes place for higher Eckert number while thermal boundary layer thickness depicts opposite trend in this case. Concentration boundary layer thickness enhances while concentration profile declines for higher Schmidt number. Velocity distribution is found to be incremented for intense melting process. Higher dimensionless activation energy parameter is analyzed to be responsible for growing up concentration field.

Further insights into steady three-dimensional MHD Sakiadis flows of radiating-reacting viscoelastic nanofluids via Wakif’s-Buongiorno and Maxwell’s models

AbstractKeeping in mind the stress relaxation tendency of many viscoelastic multi-phase flows (e.g., polymer solution flows and transport phenomena of red cell suspensions within blood media), the present research investigation intends principally to develop a realistic model for revealing properly the aspects of reacting-radiating Maxwell nanofluids during their laminar boundary layer flows in the steady regime over a horizontal impermeable surface under a transversal magnetic influence. For this purpose, the principal leading differential formulation is derived theoretically by linking Wakif’s-Buongiorno approach with Maxwell’s model. By invoking fundamentally the general boundary layer assumptions and the passive control strategy for the nanoparticles, the governing PDEs’ formulation is simplified accordingly and then stated properly for the case of the convective heating condition at the impermeable bi-stretching surface. By executing a feasible non-dimensionalization technique, the monitoring ODEs’ system is achieved successfully, whose solutions are presented precisely in different illustrative scenarios using Richardson’s extrapolation method. After carrying out successfully several validating tests, it is demonstrated that the weakly viscoelastic feature has generally a slight delaying effect on the nanofluid motion. This dynamical weakening can be reinforced more with the generation of thermal energy by intensifying the external magnetic field source. Additionally, these physical factors show an intensifying influence on the surface drag forces. However, a dropping impression is seen for the local heat transfer at the contact surface. Contrary to the broadening impact of the radiative heat transfer as well as the convective heating and thermophoresis mechanisms on the thermal and mass boundary layer regions, it is witnessed that the first-order chemical reaction mechanism and Brownian’s motion exhibit a shrinking impact on the mass boundary layer region.

Generalized vortex flow of nanoparticle shapes over a permeable disc surface with generalized slip conditions

This paper investigates the generalized vortex flow of nanofluid consisting of titanium dioxide (TiO2) with base fluid (H2O) over a permeable disk surface that generates a heat transfer process in the thermal boundary layer of the disk. Four types of non-spherical shapes of nanoparticles (blade, brick, cylinder and platelet) are considered for the research. The motion is produced when the fluid is far from the disk surface and rotates like a solid body with a constant angular velocity [Formula: see text]. The partial differential equations (PDEs) are obtained using boundary layer approximations and then converted into ordinary differential equations (ODEs) using suitable similarity transformations. These nonlinear ODEs are solved using the bvp4c MATLAB solver. The effect of different parameters (n, A, [Formula: see text], [Formula: see text], R and Pr) on the velocity components and temperature profile is shown graphically and in tabular results. This analysis concludes that for all non-spherical shapes, the velocity spectrum of all nanoparticles decreases when the values of factors such as power-law, suction, volume fraction and slip parameter increase. All non-spherical shapes of a nanofluid experience a decrease in fluid temperature due to the Prandtl number, while radiation numbers have the opposite effect.