Grashof Number Research Articles

Entropy production in unsteady MHD double diffusive and chemically reactive nanofluid flow past a rotating permeable plate using overlapping grid spectral collocation technique

The entropy production phenomenon due to the applied external magnetic fields, thermal dissipation, chemical reaction and the impact of rotating pervious plate on heat transfer, nanofluid friction and mass transfer has been numerically explored. The nanofluid flow is presumed to be unsteady, smooth, hydro-dynamically and electrically conducting. The well known Navier–Stokes time-dependent equations in cartesian coordinates for velocity, temperature and concentration are modelled and scaled down to a system of ODEs by applying suitable similarity transformations with unsteady dimensionless parameters. A new numerical scheme known as the overlapping grids spectral collocation method (OGSCM) is applied in finding the approximate solutions to the highly nonlinear ODEs. The results obtained are then used for solving the entropy equation and the rate of irreversibility is represented graphically. Several engineering variables, such as the coefficient of heat transfer, Nusselt number and Sherwood number, are also thoroughly examined. The OGSCM proved to be accurate, computationally efficient, time efficient and converges fast. We discovered that increased applied magnetic field, chemical reaction parameter, rotation parameter, and Schmidt parameter insert more energy into the system which reduces the thermal boundary layer and hence reducing the rate of entropy generation. Furthermore, the entropy generation rate is increased by increasing the Grashof number, Brinkman number, permeability, Prandtl number, and thermal radiation parameter.

Experimental study on evolution of longitudinal vortex rolls subject to the duct tilted in the spanwise direction

An experiment was performed in this study to investigate the effect of duct spanwise inclinations on the longitudinal vortex pattern in an air mixed convective flow. Key parameters, including Reynolds (Re) numbers from 20 to 30 and Grashof (Gr) numbers from 4071 to 10,855, are investigated. The spatial and temporal attributes of longitudinal vortex rolls (LVRs) are examined via flow field visualization and transient temperature measurement in details. Compared with the corresponding non-sloping case, the duct inclination significantly influences the LVR evolution. Due to the non-zero spanwise buoyancy, the vortex roll tends to be asymmetrical across the span and causes the delayed onset of lower LVRs. The temperature fluctuates significantly with time adjacent to the upper sidewall at the larger tilt angle. In an inclined duct, lower LVRs will stretch spanwise to squeeze upper vortex rolls with a decrease in Re number. Increasing the Gr number is beneficial to LVR formation for a smaller spanwise-inclined angle. However, the increase in either Gr number or tilt angle makes the vortex flow relatively unstable. We also provide an empirical expression to determine the vortex onset as a function of Re, Pr, Gr numbers, and the tilted angle.

Theoretical Examination of the Volume Concentration and Nanoparticles Density Influence on the Convective Heat Transfer Enhancement of Nanofluid in 2D Cavity Including the Square Heater

Nanofluid is one of the solutions of heat transfer, which can apply in devices fields as nuclear power, Nano-electronics systems, and solar fluid heating. In this work, the natural convection of Cuwater nanofluid is examined using the Lattice Boltzmann Method (LBM) as a mesoscopic approach. The main objectives of this work are to study the performance and pattern of Cu-water nanofluid and to demonstrate that the nanofluids behave differently while improving their energy transfer compared to pure fluids. The set goal was achieved by solving the tasks: based on the streamlines and isotherms profiles to demonstrate how the convection process and temperature gradients improve. Also, conducting study on heat transfer of nanofluid by calculate the Nusselt number. Depending on the nanoparticle volume percentage, the Grashof number Gr , and the hot obstacle have a significant impact on the convection flow and rate of heat transfer. The most important result is the enhancement of heat transfer with the increasing of volume fraction for a particular Grashof number, also it improves with the rising of Grashof number for a particular nanoparticles volume fraction. Therefore, the aspect ratios of the enclosure have played a significant part in Nusselt number variation. In addition, we found that the Nusselt number avg Nu is higher in the case of cavity without hot obstacle more than for cavity with hot obstacle, so the heat transfer improves in the case of cavity without hot obstacle. The significance of the obtained results consists that the nanofluid is one of the ways to improve heat transfer due to its specific characteristics and properties.

A computational modeling on two-dimensional laminar flow and thermal characteristics through a strongly bent square channel

In order to have a precise knowledge on how pressure gradients and buoyancy force affect fluid flow and energy distribution in a bending channel, it is important to perform a comprehensive study on flow characteristics and heat transfer mechanisms that trigger out the transition of fluids into a turbulent state, subject to a sustained pressure gradient. The present paper explores a computational modeling on two-dimensional fluid flow and thermal characteristics in a bent square channel of strong curvature. The Newton–Raphson (N-R) iteration method is applied to obtain a bifurcation structure depending on the pressure-driven force, the Dean number (De), covering 0 < De ≤ 5000. As a consequence, four branches of asymmetric steady solutions are identified for each of the cases of the Grashof number, Gn (=1000, 1500, and 2000), where only the first branch is found to exhibit asymmetric two-vortex solutions while the remaining branches encompass two- to four-vortex solutions. The similarity and disparity in the branching structure are also demonstrated. Then, adopting the Adam–Bashforth (A-B) method together with Crank–Nicholson (C-N) formula, the unsteady solutions (US) have been explored, validated by power spectrum density (PSD) and phase space Within the realm of US, two- and three-vortex solutions are found and these solutions exhibit transitions from steady to chaotic behavior profoundly. Effects of the Grashof number with convective heat transfer (CHT) are also compared. By analyzing the Nusselt number (Nu), it is observed that in case of highly chaotic flow, CHT experiences substantial enhancement. This intensified CHT arises from increased turbulence and mixing, facilitating more efficient thermal energy exchange under such chaotic flow conditions.

Numerical study of solution structure and nonlinear behavior of Dean flow with vortex structure in a bending square duct

Fluid flow and heat transfer in bending channels are topics of much research interest because of increasing demand in various fields, particularly in the medical and industrial arenas. This paper presents a numerical study of fluid flow and heat transfer in a bending channel with a square cross section. Numerical calculations using spectral methods were performed for a curvature of 0.001 and a Dean number (Dn) in the range of 0<Dn≤5000. A temperature difference was maintained between the horizontal walls for a Grashof number of Gr = 1000, with the bottom wall heated and the outer and inner walls thermally insulated. Applying Newton–Raphson iteration and path continuation, two branching structures of steady solutions with two to eight vortices were obtained. The first branch comprises multi-vortex up to eight and it occurs at Dn≥3500 while the second branch comprises to multi-vortex up to a maximum of four. The first branch forms symmetric solution while the second branch for its complexity forms asymmetric solutions. For unsteady solutions, time-evolution calculations were performed to investigate the nonlinear behavior, and it was found that with increasing Dn, the unsteady flow experienced various flow instabilities. The time evolution was plotted in phase space to clarify the unsteady flow characteristics. Distinctive contours of the secondary flow patterns, streamwise velocity distributions, and isotherms were also obtained, and the unsteady flow was found to comprise two to six vortices. Finally, convective heat transfer was explored by obtaining temperature contours, and the secondary flow was found to magnify the convective heat transfer significantly. Because of the increase of several secondary vortices in the chaotic solutions, heat transfer occurred markedly in the flow.

Charging characteristics of finned thermal energy storage tube under variable rotation

Solar photovoltaic-thermal (PVT) systems effectively offset the drawbacks of intermittent solar and low photovoltaic conversion efficiency. Thermal energy storage (TES) tanks of PVT systems with high charging efficiency and consistent thermal safety might achieve efficient utilization of solar energy for building. A new variable rotational strategy has been proposed to optimize the charging characteristics for TES tubes, taking into consideration the non-uniformity of melting. A series of simulations based on the volume-averaged model are conducted to investigate the thermal energy storage property of TES tubes under variable rotary mechanism. Qualitative and quantitative comparisons are made between variable rotation (ω = 1.5–0.5, 1.5–1.0, 1.5–2.0 rad·s−1), constant rotation (ω = 1.5 rad·s−1), and stationary systems. The focus of the comparison is melting efficiency, temperature distribution, and natural convection. The results indicate that rotation effectively shortens charging time, with a 57.62% and 15.73% reduction with variable rotary mechanisms of 1.5–1.0 rad·s−1 when compared with stationary and constant rotating tubes. Meanwhile, in the final moment, the greatest medium-temperature (55–65 °C) proportion of 90.58% and less low-temperature (25–55 °C) and high-temperature (65–70 °C) paraffin occupation of 4.67% and 4.75% could be obtained, reflecting the completed latent heat storage and stable thermal safety. The optimal variable rotation achieves improvements of 47.84% and 106.73% in time-integral Grashof number (Gr) and heat storage rate, compared with traditional stationary tubes.

CFD investigation of fluid and heat transfer in a single-phase natural circulation toroidal loop

Natural circulation occurs due to a temperature-induced density gradient, typically observed within closed loops where the fluid is heated in the upper section and cooled in the lower section. This phenomenon finds numerous engineering applications, particularly as a passive heat removal mechanism in nuclear reactors, significantly enhancing their safety. However, the computational modeling of natural circulation poses challenges due to its complex, multidimensional, and nonlinear characteristics. Furthermore, in such systems, fluid dynamics and thermal aspects are intricately intertwined. Hence, the objective of this study is to evaluate the fluid and thermal behavior of a toroidal loop under natural circulation using the Computational Fluid Dynamics (CFD) ANSYS CFX package. A 2D model is employed, along with the Boussinesq approximations, as they are well-suited for toroidal systems. Turbulence is calculated using the k−ϵ. Various modified Grashof Numbers (Gr) normalized by the geometric parameter (NG) are utilized, ranging from 5.4×103 to 4.7×105, for two different Prandtl numbers. The lowest Grm/NG value in each simulation represents the convection lower limit (flow initiation), while the highest value indicates the convergence limit, beyond which a steady state cannot be achieved. Temperature and velocity profiles are presented, and their variations with the power level are discussed. The resulting Reynolds of Steady State (Ress) are plotted against Grm/NG values, demonstrating good agreement with experimental data. As the Prandtl Number increases, the system is observed to enter an unstable zone at an earlier stage. Finally, it is observed that multiple steady states exist for Pr=0.7, and their implications are discussed.

Numerical investigation of heat source induced thermal slip effect on trihybrid nanofluid flow over a stretching surface

The fluid flow model is evaluated with the mass and energy transfer through the trihybrid nanofluid (Thnf) past a stretching permeable sheet. The proficiency of the nanofluid could be more effective, improved and stable by introducing nanoparticles with various thermal and rheological properties. The trihybrid nanoliquid has been prepared by the dispersion of silver (Ag), cobalt ferrite (CoFe2O4), and magnesium oxide (MgO) nanocomposites in water. The consequences of Darcy-Forchheimer are engaged in the momentum equation, to evaluate the permeability effect. The fluid flow is expressed in the form system of PDEs with effect of natural convection, magnetic field and heat source. Which are converted into a non-dimensional set of ODE by using similarity variables substitutions. Moreover, the numerical approach PCM (parametric continuation method) is used to deal the derived set of ODEs. The results are relatively compared to the existing study for accuracy purposes. It has been noted that the Thnf has higher thermal conductivity than ordinary and hybrid nanoliquid. The velocity field rises with the mounting values of the thermal Grashof number. The velocity curve drops with the effect of a power law, Forchheimer's, and porosity parameters.

Finite element analysis of MHD naturally convective flow past an exponentially accelerated plate with viscous dissipation

The MHD finite element analysis naturally convective flow across an exponentially accelerating plate with viscous dissipation is investigated numerically. In this process dimensional partial differential equations are changed to dimensional less form. The Galerkin finite element method is emerged to solve non-dimensional partial differential equations. Obtained results are effectively depicted through the utilization of graphs, allowing for a comprehensive understanding of the impact that different physical parameters on primary velocity, transverse velocity, temperature, and concentration profiles. The study effectively differentiated between the present and prior findings, ultimately demonstrating a strong consensus of excellent agreement between the results. The key findings of this study are: The primary velocity increases on growing the values of Thermal Grashof number, Solutal Grashof number, Eckert number, and Dufour number and decreases on climb up the values of Magnetic parameter, Prandtl number, Schmidt number, and Hall parameter. The secondary velocity increases on raising the values of Thermal Grashof number and Solutal Grashof number and diminishes on enhancing the value of Hall parameter. The temperature increases on increasing the values Eckert number and Dufour number and decreases on improving the value of Prandtl number. The concentration decreases on increasing the value of Schmidt number.

Heat transfer analysis of Maxwell tri-hybridized nanofluid through Riga wedge with fuzzy volume fraction

This contribution aims to optimize nonlinear thermal flow for Darcy-Forchheimer Maxwell fuzzy left( {{text{Al}}_{{2}} {text{O}}_{{3}} + {text{Cu }} + {text{TiO}}_{{2}} {text{/EO}}} right) tri-hybrid nanofluid flow across a Riga wedge in the context of boundary slip. Three types of nanomaterials, {text{Al}}_{{2}} {text{O}}_{{3}} , Cu and {text{TiO}}_{2} have been mixed into the basic fluid known as engine oil. Thermal properties with the effects of porous surface and nonlinear convection have been established for the particular combination left( {{text{Al}}_{{2}} {text{O}}_{{3}} + {text{Cu}} + {text{TiO}}_{{2}} {text{/EO}}} right){.} Applying a set of appropriate variables, the set of equations that evaluated the energy and flow equations was transferred to the dimensionless form. For numerical computing, the MATLAB software's bvp4c function is used. The graphical display is used to demonstrate the influence of several influential parameters. It has been observed that flow rate decay with expansion in porosity parameter and nanoparticles volumetric fractions. In contrast, it rises with wedge angle, Grashof numbers, Darcy-Forchheimer, nonlinear Grashof numbers, and Maxwell fluid parameter. Thermal profiles increase with progress in the heat source, nanoparticles volumetric fractions, viscous dissipation, and nonlinear thermal radiation. The percentage increases in drag force for ternary hybrid nanofluid are 13.2 and 8.44 when the Modified Hartmann number takes input in the range 0.1 le {text{Mh}} le 0.3 and wedge angle parameters 0.1 le m le 0.3. For fuzzy analysis, dimensionless ODEs transformed into fuzzy differential equations and employed symmetrical triangular fuzzy numbers (TFNs). The TFN makes a triangular membership function (M.F.) that describes the fuzziness and comparison. This study compared nanofluids, hybrid nanofluids, and ternary nanofluids through triangular M.F. The boundary layer flow caused by a wedge surface plays a crucial role in heat exchanger systems and geothermal.

Vapor Cloud Behavior of Heavier-Than-Air Hydrocarbon Liquid Evaporating From a Microliter Volume Heated Well Cavity

Abstract Detailed characterization of the vapor cloud above a well or reservoir is not available in literature irrespective of its several practical importance. This study aims to understand the vapor cloud characteristics and vapor phase transport of a heavier-than-air vapor cloud evaporating from a heated microliter circular reservoir. Evaporation of a heavy hydrocarbon (cyclohexane) and a comparatively lighter fluid (ethanol) is studied. Digital holographic interferometry has been used for the characterization of vapor cloud. Gravimetric analysis is used for measurement of evaporation rate from the reservoir. A flat disk-shaped vapor cloud is observed in both heated and nonheated reservoir cases. This is attributed to the presence of radial outward natural convection. The evaporation rate is underpredicted by the diffusion model at a higher Grashof number, i.e., for well heating. Solutal convection dominates near the interface region and thermal convection effect increases in the region away from the liquid–vapor interface. The mole fraction profile depends on the relative strength of the thermal and solutal Grashof number. Thermal convection effect is stronger in lighter vapor of ethanol compared to that of cyclohexane. Overall, this study shows dominance of solutal convection on the vapor cloud characteristics above both heated and unheated reservoir.

Entropy generation analysis of non-miscible couple stress and Newtonian fluid in an inclined porous channel with variable flow properties: HAM Analysis

The aim of this study is to investigate the entropy production characteristics of two non-miscible fluids in an inclined porous channel with temperature-dependent thermal conductivity and viscosity. The porous region of the channel is divided in two regions. In region-1 and region-2, the Couple stress and Newtonian fluid take place due to constant pressure gradient, respectively, under the influence of a uniform magnetic field. Here, the Darcy–Brinkman model is used for the flow of immiscible fluid through the porous media. In this work, we used a semi-analytical method named as homotopy analysis method (HAM) to solve the coupled nonlinear ordinary differential equations. The goal of the considered problem is to examine the consequences of a variety of thermophysical parameters, including Hartmann number, varying viscosity parameter, varying thermal conductivity parameters, and Grashof number on the characteristics of entropy generation, Bejan number distribution, thermal behavior and flow characteristics of non-miscible couple stress and Newtonian fluid passing through a porous channel. The novel aspect of this study is the formation of entropy and Bejan number as a result of non-miscible Newtonian and couple stress fluids with varying thermal conductivity and viscosity in porous media. In terms of rheological investigation, a semi-analytical simulation for changeable thermal and flow properties in an immiscible Newtonian and couple stress fluid via an inclined porous channel is a brand-new concept, and the behaviors of such flows have not been examined yet. From this study, it is concluded that on raising the variable thermal conductivity, Hartmann number and the permeability of the porous medium, the flow velocity, thermal characteristics and entropy generation number decrease. The authors also come to the significant conclusion that non-miscible Newtonian and couple stress fluids have larger entropy production numbers, flow velocities, and temperature profiles for higher values of Grashof number, variable viscosity parameter, and couple stress parameter. The findings of this work have also been graphically validated through the previously established work. The results of the present analysis can be used in petroleum industry, lubrication theory, etc.

Experimental Investigation of Transient Flow Phenomena in Rotating Compressor Cavities

Abstract The clearance of compressor blade tips during aero-engine accelerations is an important design issue for next-generation engine architectures. The transient clearance depends on the radial expansion of the compressor discs, which is directly coupled to conjugate heat transfer in co-rotating discs governed by unsteady and unstable buoyancy-induced flow. This paper discusses an experimental and modeling study using the Bath Compressor Cavity Rig, which simulates a generic axial compressor at fluid-dynamically scaled conditions. The rig was specifically designed to generate heat transfer of practical interest to the engine designer and validate computational codes. This work presents the first study of the fundamental fluid dynamic and heat transfer phenomena under transient conditions. The rotating flow structure was seen to be characterized by coherent pairs of cyclonic/anticyclonic vortex pairs; the strength, rotational frequency, stability, and number of these unsteady structures changed with changing rotational Reynolds and Grashof numbers during the transients. These structures, measured by unsteady pressure transducers in the rotating frame of reference, were only present when the flow in the rotating cavity was dominated by buoyancy. Experimental correlations of both Nusselt number and radial mass flowrate in the rotating core were correlated against Grashof number. Remarkably, the experiments revealed a consistent correlation for both steady-state and transient conditions over a wide range of Gr. The results have a practical application to thermo-mechanical models for engine design.

Peristaltic flow of bioconvective Ree–Eyring nanofluid through an inclined elastic channel with partial slip effects

Pharmaceutical fluid processing is a procedure of medication manufacturing, utilizing a particular kind of heat transfer in a biofluid designed to maintain the desired temperature for extended periods. Choosing a suitable fluid can have a positive effect on the operating efficacy of the system and lengthen the fluid’s and system’s life spans. As an outcome of this development, we investigate the influence of the partial slip and gyrotactic microorganisms on the peristaltic transport of a magnetohydrodynamic Ree–Eyring nanofluid via an aligned porous conduit with thermal radiation, energy generation, along with cross and double diffusion effects. By invoking suitable nondimensional parameters, the proposed dimensional governing equations are transformed into a system of dimensionless partial differential equations. The analytical solutions for the system of partial differential equations are obtained by incorporating the homotopy perturbation method. Further, tabular and graphical presentations are used to examine the characteristics of the various sundry parameters on the temperature, concentration, motile microorganism density, axial velocity, trapping, and other relevant flow quantities. The observations of this study indicate that the Darcy number and thermal Grashof number have the capability to enhance the velocity distribution of the Ree–Eyring nanofluid in the presence of bioconvection. The trapped bolus size and the skin friction coefficient increase noticeably because of an enhancement in the Ree–Eyring fluid parameter. Also, the Darcy number and the Hall current parameter increase the skin friction coefficient. Furthermore, validation of the results is carried out to examine the consistency between the current and the previous findings for some special cases and excellent agreements are found.

Natural convective loops heat transfer scaling analysis

Heat transfer arising in natural convective loops is analyzed numerically and theoretically. Combining 3D direct numerical simulations, unidirectional heat-transfer semi-analytical computations, scaling arguments and asymptotic analysis new universal scaling laws are proposed to account for dimensionless heat transfer behavior of natural convective loops. It is found that the Reynolds number Re resulting from the buoyancy driven rotating convection (as well as the Péclet number) scales as Grashof number Gr as Re∼Gr3/4 for imposed temperature boundary conditions and Re∼Gr3/5 for mixed imposed temperature/flux heating conditions. These scaling laws are successfully confronted with experimental measurements in both heating configurations. It is shown that these scaling result from boundary layers dominated transfers without noticeable influence of possibly complex 3D flow patterns found in the fluid flow. These simple scaling laws constitute a progress over previously existing correlations which have disregarded the effect of boundary layers, heating configurations as well as fluid to solid variable diffusivity/conductivity.

Investigation of dissipative heat transfer and peristaltic pumping on MHD Casson fluid flow in an inclined channel filled with porous medium

A theoretical investigation is performed for free convective peristaltic pumping of a Casson fluid through an inclined porous wavy channel. The flow is subjected to uniform magnetic field in the transverse direction. In addition, the energy equation contains porous and viscous dissipation effects. The governing flow problem is modeled for Casson fluid with the help of conservation laws of mass, momentum, and energy under the long wavelength assumption. Using a regular perturbation method, we obtained the analytical expressions for the axial velocity, temperature, pressure rise per one wavelength, and heat transfer rate. The consequences of various effects on the flow quantities are demonstrated in the form of graphical representations and discussed in detail. The findings reveal that the rise in the thermal Grashof number and permeability parameter leads to an increment in the velocity and thermal fields. The heat transfer rate strengthened when the Casson parameter and magnetic parameter were increased. The pressure rise exhibits an enhancing trend for the Brinkmann number and permeability parameter. Further, we observed a decreasing behavior on streamlines for increasing magnetic field strength. Moreover, the obtained findings are applicable to a variety of fields in the bioengineering and medical sciences, such as targeted drug delivery, heart-lung machines, MRI, cancer therapy, power conversion devices, and micromanufacturing processes.

Effect of heat and mass transfer on magneto-hydrodynamic flow with chemical reaction and viscous energy dissipation past an inclined porous plate

In this paper, a mathematical model describing heat and mass transfer of magneto-hydrodynamic flow with chemical reaction and viscous energy dissipation past an inclined porous plate is presented. The governing partial differential equations which describe the phenomenon were nondimensionalized with the aid of some dimensionless quantities. The dimensionless coupled non-linear partial differential equations were solved using the harmonic solution technique. The results obtained were discussed graphically. Findings from the results obtained reveal that increase in Peclet number; Heat source parameter and Grashof number enhance the velocity profiles. Similarly, an increase in the Peclet energy number, Eckert number, Heat source parameter, angle of inclination, permeability parameter and Stuart number leads to an increase in the temperature profile.

Heat transfer analysis of generalized second-grade fluid with exponential heating and thermal heat flux

The aim of present work is to apply the Caputo–Fabrizio fractional derivative in the constitutive equations of heat transfer. Natural convection flow of an unsteady second grade fluid over a vertical plate with exponential heating is discussed. The generalized Fourier law is substituted in temperature profile. A portion of the dimensionless factors are utilized to make the governing equations into dimensionless structures. The solutions for temperature and velocity profiles of Caputo–Fabrizio model are acquired through the Laplace transform method. These solutions are greatly affected through the variation of different dimensionless variables like Prandtl number, Grashof number, and second-grade fluid parameter. Finally, the influence of embedded parameters is shown by plotting graphs through Mathcad. From the graphical results it is concluded that, the temperature of the fluid decreases with the increasing values of the Prandtl number and Second grade fluid parameter and increases with the passage of time. The velocity of the fluid increases with increasing values of the Grashof number, second grade parameter and time while decreases with increasing values of fractional parameter and Prandtl number.

Radiating and electromagnetic nanofluids flow over an exponentially accelerated Riga plate with heat sink

In current history, there has been a significant interest in contemporary nanostructures for nanoelectronic systems. These systems progressively employ dynamic media to boost efficiency. Inspired by its applications in engineering, The effect of radiation and heat sink on electromagnetic nanofluids flow past an exponentially accelerated Riga surface is studied analytically using the Laplace transform technique. The base fluid is water, and three selected nanoparticles are used: Copper, Titanium dioxide, and Aluminium oxide. The porous medium is taken into account, as well as the validity of the Boussinesq approximation. The influence of modified Hartmann number, heat absorption, Grashof number, and thermal radiation parameter on nanofluid velocity and temperature profiles is depicted graphically and discussed. The shear stress and Nusselt number are determined, and outcomes are presented via plots and a table. The exact solution shows that the modified Hartmann number, nanofluid volume fraction and heat sink tend to improve as the values of Shear stress (skin friction) for Cu – water nanofluid shows a comparative increase over Al2O3 and TiO2 nanofluids. Whereas the Radiation effect tends to decrease as the shear stress values for Cu–water nanofluids show a higher decline over Al2O3 and TiO2 nanofluids.

Heat transfer and entropy generation on mixed convection hydromagnetic slip-flow in a channel filled with porous medium: Adomian decomposition approach

This study analyses the heat transfer and entropy generation on mixed convection hydromagnetic fluid flow in a permeable parallel wall vertical channel; filled with an optically thick and electrically conducting liquid permeated by a uniform transverse magnetic field. The study considers the nonlinearity in thermal radiation, the irregular thermal heat produced/consumed, and the slipperiness and mass flux at the walls. The nonlinear coupled governing partial differential equations are reduced to ordinary dimensionless types. The Adomian Decomposition Method (ADM) is applied to solve the emerging boundary value problem. Comparisons are made for some basic emergent scientific parameters using the evaluated values of the velocity and temperature profiles for ADM and numerical algorithm (RKF 4-5) in the Maple, and the results are impressive. Entropy generation numbers are computed through the Bejan formulation. The results are presented for the velocity, temperature and entropy generation profiles and discussed quantitatively. Amongst others, it is perceived that velocity increases with heat generation and suction-based parameters while entropy generation surges consequentially to the improved Grashof and Darcy numbers in the entirety of the flow regime. This study finds applications in modern engineering systems for energy loss control, frequently encountered in the manufacturing, nuclear energy and processing industries.