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This paper focuses on applying the Corcione model to the microchannel. The Corcione model is highly relevant because it provides accurate empirical relationships for forecasting the dynamic viscosity and effective thermal conductivity of nanofluids. These qualities are crucial for building and improving different thermal systems. The model presents and discusses two simple empirical correlating equations for forecasting the dynamic viscosity and effective thermal conductivity of nanofluids. Hence the aim of this work is to use Corcione’s model to demonstrate the fully developed laminar flow of an electrically conducting nanoliquid through an inclined microchannel. The energy equation takes into account the physical impacts of the heat source/sink, temperature jamp, and viscous dissipation. TiO₂ nanoparticles in water are taken into consideration in this work for enhanced cooling. Using the numerical program Maple, Runge–Kutta–Fehlberg 4th–5th-order method is utilized to solve the present research. Making use of graphs, all of the flow parameters are shown, and the physical consequences on the flow and temperature profiles are thoroughly examined. It is noted that a higher inclined angle enhances the velocity profile whereas a larger temperature jump declines the temperature profile. Furthermore, Corcione’s model often has greater velocities, temperatures, and reduced surface drag forces than the Tiwari–Das model.

In this paper, axisymmetric magnetohydrodynamic (MHD) Homann flow is studied normally over a stretching and spiraling disk in the stagnation region. Homann’s problem is modified with simultaneous effects of the radial linear stretching and uniform rotation of the disk. The magnetic field is applied perpendicular to the motion of the flow. The energy and mass distribution phenomena are analyzed by using Cattaneo–Christov (CC) double diffusion model, heat sink/source and chemical reaction effects. The main purpose of this study is to highlight the significance of CC theory on Homann problem along with asymptotic behavior. Similarly, ansatzes are utilized to transform the partial differential equations into ordinary differential equations. The solutions are computed numerically by a built-in scheme, namely, bvp4c in MATLAB. Moreover, it is concluded that the surface velocity is produced in the form of a spiral logarithm because of the continual activity of radial stretching and uniform rotation of the disk. The outcomes of magnetic field, rotation and stretching parameters are discussed graphically for coefficients of skin friction. The coefficient of skin friction along the $x$-axis is enhanced, whereas along $y$-axis, it is decreased by varying stretching and rotating parameters. The impact of thermal and solutal relaxation time coefficients reveals that they reduce the heat and mass transfer rates, respectively.

This research paper shows the insight into the study of magnetohydrodynamics (MHD) reactive nanomaterial flow of Newtonian fluid with Silver (Ag), Ferric Oxide (Fe₃O₄) and Copper (Cu) towards a stretchable surface. The flow is generated subject to stretchable surface with porosity effect. Mixed convection, which is a combination of both free and forced convections, is accounted. The heat source/sink, chemical reaction, Joule heating and activation energy effects are considered in the development of energy and concentration equations. The system of considered problem is solved numerically via shooting method (boundary value problem fourth convergence (bvp4c)) and outcomes are sketched graphically. The engineering impact i.e., skin friction coefficient and Nusselt number is discussed via different parameters and results are displayed in tabular form. The important and main points are listed in the final remarks of the paper. The used nanoparticles have numerous applications in medical industry, applications in sustainability of natural resources and applied mathematics and physics. Also, these nanoparticles can be utilized in engineering sciences, biophysics, high-temperature and cooling process, space technology, biosensors, medicines, cosmetics, paints, medical devices and conductive coatings.

This research paper investigates the heat and mass transport characteristics in an unsteady flow of Maxwell nanofluid (NF). While examining heat transfer properties, thermal radiation is taken into account. Further, copper oxide with water-based NF is considered. The mass transfer and effective thermal conductivity of nanofluid flow are scrutinized by Koo and Kleinstreuer–Li (KKL) NF model. Through apt transformations, relevant flow expressions are converted to ordinary differential equations (ODEs). The numerical approach Runge–Kutta–fourth–fifth Fehlberg’s order process (RKF-45) algorithm with shooting technique is utilized to solve the generated ODEs. Results reveal that, the rise in values of unsteadiness parameter has a positive impact on both concentration and thermal profiles. The Deborah number has constructive impact on heat transport and reverse influence on velocity field. The improved heat transport is seen for augmented values of radiation and heat source/sink parameters. The Brownian motion parameter has positive influence on heat transport and reverse effect on mass transport.

This research reports the thermo-solutal mixed convective non-Newtonian (tangent-hyperbolic) fluid flow from a stretchable surface under the effect of viscous dissipation. Impermeable surface with stratifications (thermal and solutal) creates the flow. The Buongiorno nanoliquid model capturing Brownian diffusion and thermophoresis is opted for analysis. Energy expression modeling is based on heat source/sink and thermal radiation. Consideration of chemical reaction accounts for species concentration. Via relevant transformations, the flow model of nonlinear governing partial differential conservation equations and free-stream boundary conditions are extracted into coupled nonlinear ordinary differential equations which are solved analytically using homotopy technique. Comparative results ensuring the soundness of the employed technique are included. Analytical results are presented graphically for the influence of pertinent parameters on velocity, temperature, skin-friction coefficient, local Nusselt and Sherwood numbers. The obtained outcomes witness that the concentration of nanoparticles is increased with stronger values of thermophoresis and concentration Biot number while it declines with increasing values of solutal stratification variable, Brownian motion and Schmidt number.

In this paper, magnetohydrodynamics of a Casson fluid flow is inspected with the presence of thermal radiation and chemical reaction. Employing the perturbation procedure, the modeling equations are tenacious; the graphs are acquired to illustrate the results. The Casson fluid velocity increases as the perturbation parameter increases. Grashof values for heat and mass transport enhanced Casson fluid velocity. Increasing Casson, magnetic, heat source, and radiation parameters reduce the flow velocity. Prandtl number, heat source, and radiation parameter all reduced the temperature profiles. Chemical reaction parameters lowered the concentration profiles. The skin friction enhances with Casson parameter impact. However, the skin-friction coefficient, Sherwood and Nusselt numbers reduce with an increment in the perturbation parameter. In certain cases, this study’s answers agreed well with the previous literature. Casson liquid with a magnetic region using mixed convection by an exponential vertical boundary layer is the novelty of the work.

In the presence of a constant heat source/sink in both layers of the porous–fluid system, the Darcy–Bènard Triple-Diffusive Convection (DBTDC) problem is investigated for two types of Thermal Boundary Combinations (TBCs). For type (i) adiabatic–adiabatic and type (ii) adiabatic–isothermal TBCs, the system of ordinary differential equations derived from normal mode analysis is solved in closed form for the eigenvalue, Thermal Marangoni Number (TMN). The depth ratio thoroughly explains the influence of several parameters on the eigenvalue, hence on DBTDMC. It is noticed that the parameters in the study have a larger influence on the porous layer dominant composite layer systems than that on the fluid layer dominant composite systems.

This study provides an insight into the effects of various nanoparticle shape factors on magnetohydrodynamic boundary layer flow and heat transfer over a stretching sheet. Choosing appropriate nanoparticles can control velocity and heat transfer. A magnetic field is part of the momentum equation, and the effects of radiation and heat source/sink are part of the energy equation. Equations governing the problem are converted into nonlinear ODEs by similarity transformation. Afterwards, Runge–Kutta fourth-order scheme combined with shooting technique is employed. A magnetic field and porosity decrease the velocity. Radiation and a heat source/sink both escalate temperature. The Eckert number and porosity also improve the temperature. As nanoparticle volume fraction increases, the Nusselt number decreases and skin friction increases. Among the nanoparticle shapes considered in this study, platelet-shaped nanoparticles have the best flow and heat transfer performance. According to the studies we examined, the results obtained are consistent with those previously published.

This paper signifies the consequence of the thermal diffusion (Soret) and diffusion-Thermo (Dufour) effect on MHD stagnation point flow and transportation of thermal energy near a stretching plate. However, the inclusion of thermal radiation, heat generation/absorption, and chemical reaction enriches the profiles significantly. By using similarity transformation, the set of leading equations is altered into a set of dimensionless ordinary differential equations. After that, the aim is to convert boundary layer equations into dimensionless ones so that the set of converting equations is computed by using bvp4c solver on MATLAB software. The governing nonlinear equations were resolved with Runge–Kutta fourth-order technique numerically. The significance of radiation, magnetic field, suction, Schmidt number, velocity ratio parameter, heat absorption coefficient, permeability, thermo-diffusion number, diffusion-thermo number on momentum gradient, energy gradient and concentration gradient distribution is analyzed. The parameters, diffusion-thermo number Du and thermo-diffusion number Sr have opposite behaviors on both temperature and concentration fields. Here, also, it is observed that the heat sink parameter has a noticeable influence on the fluid temperature distribution profile.

The aim of this study is to present forced convective nanofluid flow over a moving plate embedded in an absorbent medium. Following Darcy law’s for porous medium, the flow analysis is explored in attendance of warmth basis/drop. The main objective of this study is to explore the effects of Brownian motion and thermophoresis. The plate is considered to move in both directions: in the way of movement of fluid and in the opposite route of fluid movement. Similarity alterations have been applied to alter the leading partial differential equations (PDEs) to ordinary differential equations (ODEs). Numerical solutions have been obtained with the help of MATHEMATICA software. Dual solutions have been obtained when the plate and liquid go in reverse ways. Wall shear stress, Nusselt and Sherwood numbers all are found to rise with the rising permeability parameter of absorbent medium. For Nusselt and Sherwood numbers, ranges of dual solutions diminish by the mounting values of permeability parameter K. The critical values for porosity parameter $K=0.01$, 0.02, 0.03 are $R_{c_1}=1.872909$, $R_{c_2}=1.927211$, $R_{c_3}=1.9824284$, respectively. For decreasing values of s, range of dual solutions decreases. For $s=-0.45$, dual solutions exist in the range $(1.19,1.20)$.

Presently, due to its extraordinary mechanical, thermal, electrical and biomedical facets nanofluids deliver several prospects to exaggerate the propensity of isothermal systems by augmenting the conductivity features of the host fluids. In various areas of the energy partition, nanoparticles show a remarkable measure in energy storage, energy variation, and energy convertible, i.e. thermoelectric plans, petroleum cells, supercapacitors, stellar cells, rechargeable batteries, light-radiating diode and carbon-based light-radiating diode, smart coatings. In this current conversation, we anticipated an unsteady 3D flow of the Sutterby nanofluid consequence of a bidirectional extended surface. To envision the thermophoresis and Brownian motion properties in Sutterby’s nanofluid, the Buongiorno association is utilized in an additional refined technique. Variable thermal conductivity with heat source/sink property occurred deliberated considering heat transmission techniques. The appropriate transformation is applied for transposing the PDEs into nonlinear ODEs. For numerical results, the bvp4c programmed is prerequisite for elucidating the subsequent Ordinary differential equations. The distinct performance of the Sutterby nanofluid temperature and the concentration field are designated and discussed in the physical parameter’s aspect. It is clear that the temperature of the Sutterby fluid decreases with respect to the ratio of stretching rates parameter and similar developments are observed for the thermophoresis and Brownian motion parameters. Furthermore, the concentration profile declines for sophisticated estimates of the Lewis number and thermophoresis parameters.

The analysis brings out the investigation of the impact of thermal buoyancy on conducting the flow of an unsteady nanofluid within parallel moving walls embedded with a porous matrix. However, the medium is also embedded with permeable materials. Additionally, the impact of a uniform heat source is assumed to affect the designed model. The special attraction of the model is the variation of differently shaped nanoparticles using Hamilton–Crosser conductivity in which the base fluid is concatenated with the gold nanoparticles. The simulation is carried out for the governing equations numerically followed by requisite similarity rules used for the conversion of nonlinear problems of PDEs to ODEs. Further, shooting-based Runge–Kutta fourth-order scheme is imposed for the set of first-order ODEs. The behavior of several characterizing components within their range is presented for both the flow profiles via graphs and numerical results of the rate constants are deployed through the tabular form. Finally, the important outcomes are the particle concentration shows its greater impact in enhancing the fluid velocity neat the plate region and smooth retardation occurs at the central region further, the heat transfer rate retards significantly.

Heat transport issues of wedge-shaped flow on hybrid nanofluids are of special significance by reason of their importance in manufacturing uses including heat exchangers solar panels, electronic equipment cooling, drying processes, and air heaters. Consequently, the current investigation investigates the behavior of dissipative Single-walled Carbone nanotubes (SWCNT) — Multi-walled Carbon nanotubes (MWCNT) hybrid nanofluid in the buoyant flow towards a radiative vertical permeable wedge subjected to variable wall temperature considering heat source/sink. By selecting appropriate similarity conversions, the resultant flow regulating nonlinear boundary layer PDEs are subsequently transformed into coupled nonlinear ODEs. After that, the boundary layer Boussinesq approximations are numerically resolved. The significant outcome of the current investigation is the heat transport which is higher for linear radiation, volume fraction, and uniform heat source parameters. The momentum is controlled with wedge angle and volume fraction of nanotube particles. The momentum boundary layer is upsurged with mixed convection parameters for an assisting flow. Changes to the Nusselt number and fluid flow rate are measured for flow-controlling parameters. Furthermore, the results are compared and effectively validated with previously reported literature results.

Nanofluids are a relatively new class of materials that have gained attention in recent years due to their unique physical and thermal properties. They are used as contrast agents in biomedicine, including for magnetic resonance imaging (MRI) and computed tomography (CT). Keeping the above applications in mind, this theoretical study intended to explore the consequence of transient magnetized Casson nanoliquid driven by a permeable bi-direction time-dependent stretching platform positioned inclined subject to nonlinear heat source/sink. The Brownian movement, thermophoretic force, chemical reaction, and variable internal heating impacts are incorporated into the proposed flow problem. The leading constitutive PDEs are diminished into coupled nonlinear self-similar dimensionless ODEs through pertinent non-dimensional quantities. The resulting problems are addressed utilizing “Particle Swarm Optimization (PSO)” and a hybrid shooting methodology inspired by the Runge–Kutta four (RK4) method. The novelty of this work is the investigation of the numerical solution of magnetized Casson nanoliquid enclosing thermal radiation and chemical reaction via PSO along with hybrid shooting technique over time-dependent stretching sheet, which has not been elaborated on to date. The physical appearance of relevant physical factors on different flow phenomena are evaluated via graphs. For the stability purpose of the numerical method Average Square Residue Error (ASRE) and Total Average Square Residue Error (TASRE) are computed. For the validation purpose the present work is associated with the available work and great correlation is found.

In order to reduce friction between moving elements in automobiles’ heat exchange systems, SAE50 is a vital lubricant. Additionally, by preventing corrosion and abrasion of moving parts, it increases durability, reduces fuel consumption, and improves efficiency. SAE50 has a low thermal conductivity, despite this. The current inquiry is concentrated on how Zinc Oxide-Society of Automotive Engineers 50 nanolubricant flow (ZnO-SAE50 nanolubricant) through a permeable rotating disk is affected by a uniform horizontal magnetic field (UHMF) and thermal radiation. By employing the appropriate transformations, the governing modeled equations are changed into ordinary differential equations (ODEs). Then the ODEs are solved numerically by combining the Runge–Kutta-fourth-and-fifth Fehlberg’s (RKF-45) order and shooting tactic. The findings show that radiation is crucial in enhancing heat transfer for the flow of ZnO-SAE50 nanolubricant over the disk surface. With higher heat source/sink parameter values, it is discovered that the temperature boundary layer produces energy, causing thermal profiles to rise. Further in this scenario, it is found that the increase in magnetic field decreases the fluid flow gradually at rate of 5–10%.

The heat transfer characteristics of nanofluid play an important role in several industries to optimize their performance with the interaction of dissipative heat. However, in energy harvesting its application is vital. Therefore, the current heat transfer analysis was carried out based on the consequence of viscous and Joule dissipation in favour of the hybrid nanofluid flow over an elongating permeable curved convective thermal surface. Additionally, the external heat source and linear thermal radiation influence the flow phenomena whenever the velocity slip and nanoparticle shape effects associated with Hamilton–Crosser thermal conductivity model are significant. The designed equations relating to the flow phenomena are solved numerically using shooting-based Runge–Kutta fourth techniques followed by the similarity transformations used for the nondimensional form of the system of equations. The role of characterizing factors is deployed via graphs and described briefly. The correlation with the earlier investigation for the numerical outcomes of the rate of energy transport is also reported. The major outcomes of the study reveal that the enhanced curvature parameter along with the particle concentrations within their limit overshoots the velocity profiles further, the external heat source combined with thermal radiation also favors in enhancing fluid temperature.

This paper intends to discuss the hybrid nanofluid flow through a cone in a Darcy–Forchheimer porous media, containing base fluid Methanol (CH₃OH), nanoparticles of titanium oxide (TiO₂) and copper (Cu). We have examined the flow under the influences of mixed convection, viscous dissipation, chemical reaction, and nonlinear heat source. In hybrid nanofluid flow, viscous dissipation and mixed convection play a crucial role in heat exchangers. By accounting for both mixed convection and viscous dissipation, the addition of nanoparticles into a base fluid improves the transfer of heat and optimizes the performance of the cooling system. Using the laws of conservation, governing equations have been constructed. The flow model is converted using the appropriate similarity transformations from partial differential equations to ordinary differential equations. The homotopy analysis method is used to solve the updated system of equations. When Forchheimer inertial drag parameter is increased, the velocity profile decreases, but it rises when the Darcy number is increased. As the value of exponential heat source parameter rises, the temperature profile increases as well. The result exposes that with an increment in nanoparticle volume fraction, temperature profile also rises but velocity profile decreases.

This study investigates the convective heat transfer characteristics in the vicinity of a stagnation point for the flow of Maxwell nanofluid over a porous rotating disk. The analysis takes into account the complex inert-active effects arising from nonlinear thermal radiation, activation energy, and the presence of a Darcy–Forchheimer medium. Through numerical simulations, the enhancement of heat transfer due to the addition of nanoparticles is explored, considering their impact on heat transport. The rotational and porous characteristics of the disk, coupled with nonlinear thermal radiation and activation energy effects, are crucial factors in shaping the overall heat transfer behavior. The study aims to provide valuable insights into the complicated interactions of these phenomena, contributing to the understanding of advanced heat transfer processes and their potential applications in various engineering systems. Using suitable variables to convert the system of leading equations to dimensionless form has then been evaluated by employing the bvp4c approach. It has been revealed that Radial flow has retarded with an upsurge in Deborah number, inertial factor, and porous factor while has upsurge with growth in rotational factor. Angular velocity has declined with higher values of Deborah number, and porous factor and has upsurged with escalation in inertial and rotational factors. Azimuthal flow has weakened with an upsurge in porous factor and has augmented with growth in Deborah number, inertial factor, and rotational factor. Thermal profiles have augmented with an upsurge in rotational, porous, inertial, thermophoresis, Brownian, and radiation factors, and Deborah number has declined with growth in the Prandtl number. Concentration distribution has declined with an upsurge in Schmidt number, Brownian motion factor, rotation factor, and porous factor, while has grown with the escalation in chemically reactive, thermophoresis, inertial factors, and Deborah number.

Nanoparticles have the capability to augment the thermal conductivity of nanofluids. For the transmission of heat, the material’s low thermal conductivity is the key problem. Therefore, to increase the thermal conductivity, researchers mixed different nanoparticles in the base fluids. In this field of study, utilizing three different particles is the most recent strategy to form a ternary hybrid nanofluid that gives us better results in terms of heat transfer. The interaction of three different kinds of nanoparticles, i.e. copper, alumina and silver, is considered with water serving as the base fluid to form a ternary hybrid nanofluid. The paper explores the behavior of ternary hybrid nanofluids on heat and mass transportation phenomena of the two-dimensional magnetohydrodynamic (MHD) micropolar flow across a porous extending surface with zero mass flux and convective conditions. The Brownian motion, thermal radiation, heat source and sink, and joule heating are taken into consideration in the temperature equation. The chemical reaction is incorporated into the concentration equation. Appropriate similarity transformations are used to transform the system of partial differential equations (PDEs) to a coupled system of ordinary differential equations (ODEs). The homotopy analysis method (HAM) is used to solve the system of the flow equations. The effects of the nanoparticle’s volume fractions and other different physical parameters on the surface drag force, Nusselt number, velocities, microrotation, temperature and concentration profiles are scrutinized through figures and tables. The outcomes of the present investigation show that the heat transfer rate is augmented with the increasing value of thermophoresis parameter. The magnetic field has augmented temperature while the opposite result is seen in velocity and microrotation profiles. With the escalating values of thermophoresis parameter, the concentration and temperature of ternary hybrid nanofluids are boosted while the increasing Brownian and chemical reaction parameters have decreased the concentration profile. The surface friction coefficient exhibited by the ternary hybrid nanofluid is higher than hybrid and conventional nanofluids.