Non-similar Solutions Research Articles

Thermal analysis of hybrid nano-fluids: Modeling and non-similar solutions

The thermal analysis of hybrid nano-fluids is a significant research area with diverse applications in industries such as paint, electronics, and mechanical engineering. Existing literature provides limited solutions to the governing equations for the flow of these fluids. Modeling and deriving non-similar solutions for these equations pose interesting and challenging mathematical problems. This study focuses on investigating heat transfer in the flow of two types of nano-fluids, specifically Al2O3/H2O micropolar nano-fluid and Al2O3 + Ag/H2O hybrid nano-fluid, near an isothermal sphere. Conservation laws are employed to formulate the mathematical problem, and by normalizing the variables, the governing equations are converted into a set of dimensionless partial differential equations. Non-similar solutions are then obtained using numerical methods. A comparative analysis is carried out to assess the influence of various parameters on different profiles and engineering quantities for both types of nano-fluids. Both linear and rotational velocities fall down near the surface of sphere with rising microstructure in hybrid nanofluid. The micro-rotation parameter rises the temperature profile while reduces the Nusselt number of both traditional Al2O3/water based nanofluid as well as hybrid nanofluid.

Non-similar solution of Casson fluid flow over a curved stretching surface with viscous dissipation; Artificial neural network analysis

PurposeThe main focus is to provide a non-similar solution for the magnetohydrodynamic (MHD) flow of Casson fluid over a curved stretching surface through the novel technique of the artificial intelligence (AI)-based Lavenberg–Marquardt scheme of an artificial neural network (ANN). The effects of joule heating, viscous dissipation and non-linear thermal radiation are discussed in relation to the thermal behavior of Casson fluid.Design/methodology/approachThe non-linear coupled boundary layer equations are transformed into a non-linear dimensionless Partial Differential Equation (PDE) by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ordinary differential equations (ODEs). The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.FindingsThe results indicate that the non-linear radiation parameter increases the fluid temperature. The Casson parameter reduces the fluid velocity as well as the temperature. The mean squared error (MSE), regression plot, error histogram, error analysis of skin friction, and local Nusselt number are presented. Furthermore, the regression values of skin friction and local Nusselt number are obtained as 0.99993 and 0.99997, respectively. The ANN predicted values of skin friction and the local Nusselt number show stability and convergence with high accuracy.Originality/valueAI-based ANNs have not been applied to non-similar solutions of curved stretching surfaces with Casson fluid model, with viscous dissipation. Moreover, the authors of this study employed Levenberg–Marquardt supervised learning to investigate the non-similar solution of the MHD Casson fluid model over a curved stretching surface with non-linear thermal radiation and joule heating. The governing boundary layer equations are transformed into a non-linear, dimensionless PDE by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ODEs. The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

Comparative analysis of varied thermal conductivity and viscosity models in a hybrid nanofluid flow - a non-similar solution

ABSTRACT We aim to investigate the flow of an ethylene glycol-based hybrid nanofluid over a horizontal surface with a free stream velocity. To assess the viscosity and thermal conductivity of nanoparticles with various shapes, we employed the Brinkman, Timofeeva, and Yamada Ota unit cell models. The study explores heat transfer in the flow system considering the effects of viscous and ohmic dissipations, linear radiative heat flux, and heat generation under convective boundary conditions. A non-similar system is developed using appropriate non-similarity transformations up to the third-level truncation and numerically solved using the bvp4c algorithm. The novelty of the proposed model lies in obtaining the non-similar solution and incorporating the Brinkman, Timofeeva, and Yamada Ota unit cell models. The results indicated that the Brinkman viscosity model resulted in an increase in the wall heat transfer rate with a rise in particle volume fraction. It is also inferred that platelet-shaped nanoparticles exhibit a significantly higher heat transfer rate compared to spherical-shaped nanoparticles.

Local nonsimilar solution and heat analysis of mixed convective flow across whole spherical shape with nonisothermal surface temperature

This study investigates the behavior of a mixed convective boundary layer flowing around a rigid spherical shape with non-isothermal wall temperature. The fluid assumed in this examination exhibits both incompressibility and viscosity. The major purpose is to examine the impact of the non-uniform surface temperature on the flow patterns, including velocity outlines and temperature outlines. An examination is conducted on the modified conservation equations of the boundary layer flow utilizing the local non-similarity method. The MATLAB built-in code bvp4c is used to find computational solutions. The outcomes are then shown for both air and water, specifically at a temperature of 21°C. The influence of several factors, such as the mixed convective variable [Formula: see text] and the exponent [Formula: see text] in the wall temperature function [Formula: see text]), is shown in velocity and temperature profiles. In addition, the study computes the local frictional force factor and local wall heat transport factor and compares these values with results from earlier research. Significantly, the study expands upon data made around the lower stagnating point to include other sites within the sphere, thereby offering a thorough comprehension of the whole flowing field.

Two Models on the Unsteady Heat and Fluid Flow Induced by Stretching or Shrinking Sheets and Novel Time-Dependent Solutions

Abstract This study sheds light on unsteady heat and fluid flow problems over stretching and shrinking surfaces, enriching our understanding of these complex phenomena. We derive two mathematical models using a rigorous approach. The first model aligns with the model commonly employed by researchers in this field, but its steady-state solution remains trivial. The second model, introduced in this work, demonstrably captures the physically relevant steady-state solutions well-studied in the literature. Notably, we introduce new similarity solutions for the temperature field specifically within the first model. We further demonstrate that a uniform wall temperature condition leads to the optimal heat transfer rate. While similarity solutions can be derived for specific cases with the second model, nonsimilar solutions may be necessary for more general scenarios. We discuss the implications of our analysis for stagnation-point flow and non-Newtonian viscoelastic fluid flow problems, illuminating future research directions in the open literature.

Boundary layer flow and heat transfer enhancement by utilizing Casson ternary nanofluid past a horizontal cylinder in a non-Darcy porous medium with thermal radiation effects – Non-similar solutions

The aim of this study is to examine the results of MHD, radiation and Casson ternary fluid over a horizontal cylinder with a saturated porous medium. The nanofluids used in this study are trihybrid, consisting of Cu, Al2O3 and Tio2 particles suspended in blood as the base fluid. The dimensional form of governing equations is transformed into dimensionless form by manipulating non-similar solutions. The conservation equations are solved using the Keller Box Method (KBM). The presence of several emerging dimensionless parameters, namely the Casson fluid parameter (β), Darcy number (Da), Forchheimer parameter (∧), radiation parameter (Rd) and magnetic field (M) on fluid momentum and energy changes in the boundary layer regime are investigated in detail. The Prandtl value (Pr) for blood is determined to be 21. The application of porous medium models spans across various fields, including engineering, environmental science, biology, and materials science.

Local non-similar solutions for EMHD nanofluid flow with radiation and variable heat flux along slandering stretching sheet

Nanofluids are the next-generation energy-transfer substrate due to their exceptional thermodynamic properties. The study of heat transfer on stretched surfaces is important due to its applications in industry, manufacturing, and medicine. The flow across a nonlinear stretched surface with different thicknesses is examined in this study to analyze the impacts of magnetic and electrical field, joule heating, viscous dissipation, and thermal radiation by considering Cu/water as nanofluid. To explore the physical characteristics, initially the mathematical model of the problem is evaluated and cataloged all of its features. Basic flow equations and fundamental rules were used to formulate the considered problem. The flow-controlling “partial differential equations” (PDEs) are transformed into a set of non-dimensional ordinary differential equations” (ODEs) via appropriate non-similar transformations. By utilizing the local non-similarity procedure operating bvp4c, the mathematical model is reconstructed. Physical representations of temperature as well as velocity profiles show how various emerging parameters interact with the flow. It is perceived that when the strength of the magnetic field grows, the velocity of nanoparticles decreases. However, as the electric field’s strength progresses and the velocity distribution does as well, the temperature profile for the nanomaterials rises. The radiation factor enhances the temperature field. The presence of time- and space-dependent characteristics for radiation, heat production increases as the fluid temperature rises. The authors investigate the procedure for replicating the dimensionless non-similar framework adopting the local non-similarity procedure. As per the author’s observations, there is currently no comparable study available in the literature for the flow model under consideration. This research holds significant potential for researchers engaged in the exploration of industrial applications of nanofluids, particularly within geophysical and geothermic domains, solar water heating technologies, biomedical applications, and other interdisciplinary fields.

Local non-similar solution for MHD mixed convection flow of a power law fluid along a permeable wedge with non-linear radiation

In this study, a novel investigation for the effects of non-linear thermal radiation and magnetic field is conducted on mixed convection flow of non-Newtonian fluid along a permeable wedge. Power-law model is used as a non-Newtonian fluid model that predicts shear thinning/thickening effects. For theoretical analysis, a mathematical model in terms of nonlinear PDEs are transformed into a dimensionless non-similar model which is treated as a non-linear ODE when streamwise coordinate is assumed as a constant. The obtained system is solved numerically using the built-in ‘bvp4c’ technique, and the effects of the pertinent parameters is examined through plots illustrating the velocity profiles, temperature distributions, Nusselt number, and skin friction coefficients. From the results, it is revealed that heat transfer rate accelerates in occurrence of assisting flow as compared to opposing flow and further in the existence of thermal radiation, heat transfer rate becomes higher which is crucial in industry because more enhancement in heat transfer rate is required. Skin friction coefficient reduces in the occurrence of opposing flow as compared to assisting flow and further reduction is noted by taking thermal radiation.

Heat transfer analysis of ternary hybrid nanofluid through variable characteristic porous medium: Non-similar approach

This paper aims at developing non-similar solutions for heat transfer augmentation in ternary hybrid nanofluids. Nanofluid is composed of three distinct (Silver, Copper, Aluminum oxide) nanosize particles while water is considered as a base fluid. Darcy–Forchheimer expression with variable porosity and permeability is adopted. Joule heating and viscous dissipations are also considered. Non-similar approach is utilized. Numerical solutions are computed by bvp4c solver of MATLAB. Graphical illustrations for flow and thermal fields behavior are provided. Comparative results are obtained for ternary hybrid nanofluid and nanoliquid. Physical quantities such as skin drag coefficient and Nusselt number are computed and interpreted. Our results reveal that rate of heat transfer augments substantially for Ag/water nanofluid in comparison to other classes of nanofluid.

Distinctive approach for MHD natural bioconvection flow of Reiner–Rivlin nano-liquid due to an isothermal sphere

The analysis of heat excess through non-Newtonian fluid is noticed proper and promising arena for biomedical technological applications than Newtonian liquid. Herein, a type of non-Newtonian (Reiner–Rivlin) nanomaterial has been scrutinized with gyrotactic microorganisms around an isothermal sphere with surface of zero mass flux. Being mindful of that the model of Buongiorno’s nanofluid is utilized. Non-dimensional formulas for the basic dimensional partial differential equation system are obtained using appropriate non-similarity transformations. MATLAB function bvp4c code is adopted to get the non-similar solutions. The computations disclosed that the velocity of Reiner–Rivlin nanofluid and its gradient accelerate away from the surface of sphere to infinity and reduces in proximity to the sphere surface for higher values of Reiner–Rivlin factor K. The rate of surface density transport, rate of surface heat transport, and gradient of velocity diminish as the stream wise coordinate boosts. As the problem is subjected to special circumstances, there is a remarkable agreement between the acquired and prior numerical calculations resulting from the comparison.

Irreversibility analysis of radiative Williamson nanofluid flow with higher order chemical reaction and quadratic drag force over an extended surface: Non-similar computations

This study aims to present non-similar solutions for the radiative Williamson nanofluid flow with a quadratic drag force effect over a horizontally extended surface. The sheet is extended along the X-axis, and the magnetic field is applied along the Y-axis, perpendicular to the flow. The Buongiorno nanofluid model is employed to incorporate the random dispersion and thermal characteristics of the nanofluid. The innovation in the proposed model lies in its consideration of the effects of viscous and ohmic dissipation, Robin boundary conditions, and higher-order chemical reactions. The governing equations for the flow are scaled down to the second level using an appropriate transformation combined with a non-similarity technique and computationally assessed using the MATLAB bvp4c algorithm. The significant influences of the dimensionless parameters on the velocity, thermal, and solutal fields are depicted graphically. The findings reveal that the fluid velocity diminishes with increasing Weissenberg and Hartmann numbers. The solutal field experiences a reduction with variations in the chemical reaction parameter, while it rises with an increase in the higher-order chemical reaction parameter. The wall heat transfer rate is augmented with higher Eckert and thermal Biot numbers. The mass transfer rate rises with higher values of the chemical reaction parameter, Schmidt number, and solutal Biot number. A comparison of the results from this study with previous research demonstrates strong agreement, affirming the validity of the proposed model. For the value of the Williamson parameter [Formula: see text], the percentage error of the present analysis with established studies is 0% and 0.096770%.

Convection boundary layers with transpiration: Non-similar solutions and scaling

We present a new formulation and novel scaling relations for natural convection boundary layers on horizontal surfaces with weak transpiration velocities Vi, for intermediate Schmidt numbers (or Prandtl numbers Pr) 1<Sc<20. Using characteristic scales derived from integral boundary layer equations, we define a new similarity variable η=(y/x)(Rex/Grx)1/4/Sc1/5 that has Vi within it, where Rex and Grx are the local Reynolds and Grashof numbers based on Vi and the concentration difference ΔC, respectively. Using η, and the dimensionless transpiration velocity ξ=(Rex/Grx1/5)5/4 as a non-similarity variable, we obtain novel, reduced, non-similar boundary layer equations. Numerical solution of these reduced boundary layer equations using a local non-similarity approach gives us the profiles of horizontal velocity and concentration, boundary layer thicknesses, wall shear stress, and mass flux as functions of Sc, for various ξ in the range ξ<1. Using normalizing functions, we then obtain scaling relations for these parameters; we observe extended similarity where the non-similarity parameter ξ itself appears in the obtained similarity scaling relations.

LOCAL NON-SIMILAR SOLUTIONS OF MAGNETOHYDRODYNAMIC CASSON NANOFLUID FLOW OVER A NON-LINEAR INCLINED SURFACE WITH THERMAL RADIATION AND HEAT GENERATION EFFECTS: A UTILIZATION OF UP TO THIRD TRUNCATION

The current research aims to investigate the influences of thermal radiation, heat generation, and chemical reaction on the magnetohydrodynamic (MHD) Casson fluid flow model over a non-linear inclined surface. The Buongiorno model of the thermal efficiency of fluid flows in the existence of Brownian motion and thermophoresis features served as the foundation of employed non-similar modeling. The present article uses the local non-similarity assumption to solve the problem up to the third degree of truncation. The pseudo similarity parameter, stream function, and modified streamwise coordinate all satisfy the continuity equation in the same way, which transforms the energy, momentum, and mass equations into a non-similar dimensionless boundary layer (BL) problem. Here, the non-similar equations up to third level of truncation are generated in order to compare the numerical results produced by the different iterations. The built-in MATLAB function bvp4c is used to discover numerical values to these equations. In terms of energy, velocity, and mass configuration, the effect of particular physical factors are stated; as the inclination parameter and magnetic parameter increase, the velocity outline decreases. The velocity profile improves when a rise in the Casson fluid factor is observed. As heat generation and absorption increases, the energy profile rises. The growth of the thermophoresis factor and chemical reaction parameter reduces the concentration profile. Mass diffusion portrays increases as the Brownian motion factor rises. Moreover, to compare the answers with various levels of truncation, the relative error was also estimated. The present work is finally validated by comparison with previously published articles for a reduced Nusselt number and Sherwood number.

Non-similar solutions for radiative bioconvective flow with Soret and Dufour impacts

Here two-dimensional electrically conducting bioconvection flow involving Maxwell liquid is explored. Darcy-Forchheimer relation is taken for porous space. Thermal expression comprises nonlinear radiation, heat generation and dissipation. Influences of Arrhenius activation energy and gyrotactic microorganism are discussed. Novel characteristics of diffusion thermo and thermo-diffusion are discussed. Suitable variables are implemented in obtaining required differential system. ND-solve technique is implemented for computations Flow, microorganism field, thermal distribution and concentration are graphically examined. Tabulated values give rise to interest for physical quantities. A decrease in flow is noticed for magnetic variable and Deborah number while reverse behavior holds through mixed convection. An improvement in temperature occurs for higher magnetic field. Dufour number corresponds to upsurge heat transport rate and temperature distribution. Larger radiation results in temperature enhancement. A rise in concentration is observed for Soret number whereas reverse effect seen for Schmidt number. Reduction in microorganism field is noted versus higher Peclet number.

Heat transmission phenomenon in magnetic nanofluid flow across movable flat device with heat source impact: local non-similarity solution with 2nd-stage truncation

Heat transmission phenomenon in magnetic nanofluid flow across movable flat device with heat source impact: local non-similarity solution with 2nd-stage truncation

Blottner finite difference analysis for non-Darcy flow of variable viscosity power-law nanofluids over a truncated cone with Arrhenius activation energy

Examining the behaviors of power-law nanofluid flow and the rate of heat transfer over different surfaces has received great attention due to its numerous industrial applications, such as polymer solutions, molten plastics, pulps, and foods. Also, the investigators focused on the case of constant viscosity, while in several practical situations, the dynamic viscosity of the power-law suspension is variable. So this study aims to examine non-similar solutions for the coupled flow of power-law non-Newtonian nanofluids over a truncated cone. The dynamic viscosity is varied according to the Reynolds viscosity model, and an exponential decaying form is considered for the internal heat generation. The non-Darcy model, where the quadratic drag is significant, is applied to formulate this situation, and the medium's permeability is varied according to the modified Ostwald-de-Waele power law model. Both the Arrhenius activation energy and non-linear thermal radiation impacts are considered. The solution methodology is based on the effective finite differences method with the Blottner scheme. The significant outcomes revealed that the rise in the power-law index n accelerates the flow and boosts the heat transfer rate. The values of the local Nusselt number in the case of the Darcy flow are higher than those of the non-Darcy case. Additionally, considering the case of variable dynamic viscosity, it is recommended to enhance the heat transfer rate. Furthermore, the rate of the heat transfer is enhanced by 29.1% viscosity parameter δ is varied from 0 to 0.5.

Radiative flow of temperature-dependent viscosity power-law nanofluids over a truncated cone saturated heat generating, porous media: Impacts of Arrhenius energy

In this paper, the coupled flow of the pseudo-plastic, dilatant/Newtonian nanofluids along truncated cones is treated using a set of non-similar solutions. The dynamic viscosity is assuming to be a variable and depending on flow region temperature. The non-Darcy model where the quadratic drag is significant is applied to formulate this situation and the medium's permeability is varied according to the modified Ostwald-de-Waele power law model. Both of the Arrhenius activation energy and non-linear radiation flux impacts are assumed. The converted system is treated using the effective finite differences analyses with Blottner scheme. The major outcomes disclosed that the temperature and nanoparticles distributions are higher in case of the pseudo-plastic nanofluids while the dilatant nanofluids types gives the higher rates of the heat and mass transfer. The Darcy flow case causes higher values of the Nusselt number comparing to the non-Darcy case. Further, presence of the activation energy supports the convective situation and enhances the Nusselt and Sherwood coefficient.

Numerical solution for cross nanofluid flow in porous medium over stretching cylinder under MHD and radiation effects

AbstractThe aim of the present study is to analyze heat source in unsteady MHD nanofluid flow subjected to convective boundary conditions past a stretching cylinder incorporated with variable thermal properties. This study is significant in industries involving chemical processing, oil and gas, and manufacturing. The problem possesses a nonsimilar solution when similarity variables are utilized in transforming governing partial differential equations into ordinary differential equations. The numerical solution is found using MATLAB package bvp4c. The velocity, temperature, and concentration curves for various parameters are plotted graphically. The values for the coefficient of skin friction, heat transfer, and mass transfer rate are tabulated for the unsteadiness parameter, Weissenberg number, Prandtl number, Schmidt number, heat source/sink, thermal conductivity parameter, thermal and solutal Biot number, thermophoresis and Brownian parameter, radiation parameter, porosity parameter, and magnetic parameter. It is noted that, rise in porosity (–) and magnetic parameter (–) contributes to the decrease in velocity profile. It is found that, radiation effects help in incrementing rate of heat and mass transfer into fluid when radiation parameter ranges from to . Moreover, present results are in good agreement with the literature published in a limiting context.

Artificial neural network (ANN) analysis of non-similar solution of MHD nanofluid flow past a curved stretching surface

The objective of this study is to predict the non-similar solution of Magnetohydrodynamics (MHD) mixed convection transports of viscous nanofluids over a curved stretching surface by using numerical simulation with an artificial neural network (ANN) algorithm, namely the back-propagation Levenberg–Marquardt scheme. In this article, aluminum oxide and iron oxide are used as nanoparticles to enhance the thermal conductivity of the base fluid. Additionally, aluminum oxide and iron oxide nanoparticles are used in certain biomedical applications, including composite materials, photocatalysis, wastewater treatment, and nanofiltration membranes. The radiation, Joule heating, and viscous dissipation effects are studied along with the convective boundary condition. The flow problem is attained in the form of a system of Partial differential equations (PDEs) and converted into dimensionless PDEs via non-similarity transformation. These dimensionless systems of PDEs are converted into a system of Ordinary differential equations (ODEs) via local, non-similar techniques up to second-order truncations. The Bvp4c technique is used to simulate the numerical results. The data sets are collected using the Bv-p4c technique. These data sets are utilized for the validation, training, and testing phases of the developed Back-propagated Levenberg-Marquardt Scheme- Artificial Neural Network (BLMS-ANN) model to determine the solution of the problem for a variety of physical scenarios. The ANN model is utilized to choose data, construct and train a network, and evaluate the performance of the network through the use of mean square error and regression analysis. The ANN models are used to predict the performance of the Nusselt number for both nanofluids and the results demonstrated that ANN is capable of making accurate predictions of the local Nusselt number for both nanofluids. In the entire study, the ANN model predicts the result of the local Nusselt number of nanofluids with higher accuracy as compared to nanofluids.

Impact of induced magnetic field on ferromagnetic ternary and hybrid nanofluid flows with surface catalyzed reaction and entropy generation assessment

Ternary and hybrid nanofluid flows have a wide range and diverse applications including lubrication, biomedical applications, energy conservation, and heat transfer, and continuous research in this subject is expected to discover new and inventive applications in the future. Aiming the same, the current research is intended to observe the responses of ferromagnetic nanoparticles in a dissipative comparative evaluation of ternary and hybrid nanoliquid flows along an exponentially extended surface under the consequences of an externally induced magnetic field in a porous media. Three distinct forms of ferroparticles—cobalt ferrite (CoFe2O4 ), magnetite (Fe3O4 ), and manganese zinc ferrite (Mn-ZnFe2O4 )—are taken into account using ethylene glycol as the fundamental fluid. The ternary nanofluid is comprised of (CoFe2O4+MnZnFe2O4+Fe3O4 /Ethylene glycol) combination. Whereas (CoFe2O4+MnZnFe2O4 /Ethylene glycol) mixture forms a hybrid nanofluid. A surface-catalyzed reaction is also introduced to regulate the homogeneous and heterogeneous (H-H) reactions and to commence the reaction in a comparatively shorter time. The entropy generation assessment is performed for ferromagnetic ternary and hybrid nanofluid flows. The envisioned mathematical model is transformed into a dimensionless system using a valid non-similarity transformation. The engagement of the non-similar solution eradicates the chance of parameters involving variable terms. The numerical solution for the various distributions is obtained by implementing the bvp4c technique with distinct parameters. Graphical demonstrations and tabular outcomes are given to illustrate the role of emergent parameters. Findings revealed that for surface-catalyzed parameter the concentration profile dwindled more for hybrid nanofluid. Furthermore, hybrid nanofluid flow produces less entropy than ternary nanofluid flow. In addition, it is witnessed that the induced magnetic field is stronger in the case of ternary nanofluid than hybrid nanofluid for increasing magnetic Prandtl number. The corroboration of the presented model is also given.