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The significance of the Soret effect on the boundary-layer stagnation-point flow past a stretching/shrinking sheet in a nanofluid-saturated non-Darcy porous medium is investigated in this study. The nanofluid-saturated porous medium is considered by incorporating the Brownian motion and thermophoresis effects. A similarity transformation is used to reduce the governing fluid flow equations into a set of differential equations and then solved numerically by an accurate implicit finite-difference method. The flow; temperature; concentration and nanoparticle concentration fields; skin friction coefficient; and heat, mass, and nanoparticle mass transfer rates are affected by the complex interactions among the various physical parameters involved in the analysis. These profiles are illustrated graphically in order to reveal interesting phenomena. [ABSTRACT FROM AUTHOR]

There is growing interest in application of inclined fins to a cavity wall. As such, this paper focuses on the numerical investigation of laminar free convection flow and heat transfer in an enclosure with an inclined thin local thermal non-equilibrium porous fin and saturated by a nanofluid. The porous medium is assumed to be isotropic and homogenous, the cavity walls are assumed to be impermeable to the nanoparticles, and there is a no-slip boundary condition on the enclosure boundaries. The vertical walls are isothermal and the horizontal ones are adiabatic. Moreover, the influence of indispensable parameters regarding heat and mass transfer, such as Rayleigh number, Darcy number, Prandtl number, porosity, thermophoresis and Brownian parameters, fin length, fin position, and the fin angle on the average Nusselt number, are taken into account. Generally, it is found that the average Nusselt number is an increasing function ofRa, Pr, Da, and porosity (ε). Furthermore, increasing either fin position (Sp) or thermal conductivity ratio (η) produces corresponding decreases in average Nusselt number. Finally, heat transfer shows a different behavior for different values of fin angles and lengths. [ABSTRACT FROM AUTHOR]

All studies regarding the double passages channel use a rigid baffle to separate the two passages. In the current paper, we use a flexible separator and inspected its role in enhancing the performance of the heat transfer. The cold fluid is forced upward in the channel which is heated isothermally by different temperatures on its walls. A flexible sheet is fixed from its two ends and equally separate the channel to two passages. The problem is investigated numerically using the finite element method coupled with the arbitrary Lagrangian-Eulerian approach. The problem is casted in dimensionless form and several pertained parameters have been inspected, like Reynolds number in each passage, elasticity of the separating sheet and the temperature ratio of the channel walls. Results are promising where it is found that the enhancement of heat transfer is possible passively in either passage with the aid of using a flexible separator rather than rigid separator. A 6% enhancement in the Nusselt number of the left passage, which comprises the higher temperature, is obtained by making the separator flexible. The flexible sheet is found to increase the pressure drop to 200% in some cases which leading to decline the thermal performance criterion to lower than unity. However, the thermal performance criterion TEC was feasible in the right passage which subjects to lower temperature. • A monolithic finite element approach using high-order schemes in space and time is utilized. • Heat transfer enhancement is possible passively in a passage with the aid flexible separator rather than rigid separator. • A 6% enhancement in the Nusselt number of the left passage is obtained by making the separator flexible. • The flexible sheet increases the pressure drop to 200% in some cases leading to decline the thermal performance criterion. • Thermal performance criterion TEC was feasible in the right passage which subjects to lower temperature. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to investigate hydromagnetic two dimensional boundary layer flow with heat transfer of a viscous, incompressible, electrically conducting, heat absorbing and optically thick heat radiating fluid over a permeable exponentially stretching sheet considering the effects of viscous and Joule dissipations in the presence of velocity and thermal slip. Design/methodology/approach – Using similarity transform, governing differential equations representing mathematical model of the problem are solved with the help of fourth-order Runge-Kutta method along with shooting technique. Numerical solutions of fluid velocity and fluid temperature are depicted graphically for various values of pertinent flow parameters whereas numerical values of wall velocity gradient and wall temperature gradient are displayed graphically for various values of pertinent flow parameters. Findings – Numerical results obtained in this paper are compared with earlier published results and are found to be in excellent agreement. Magnetic field and suction tend to enhance the wall velocity gradient whereas dimensionless co-ordinate, injection and velocity slip factor have reverse effect on it. Suction and heat absorption tend to enhance wall temperature gradient whereas magnetic field, velocity slip factor, injection, thermal radiation, thermal slip factor and viscous dissipation have reverse effect on it. Originality/value – The investigation of this problem may have bearing in several engineering processes such as extrusion of plastic sheet, annealing and tinning of copper wire, paper production, crystal growing and glass blowing, continuous casting of metals and spinning of fibers. [ABSTRACT FROM AUTHOR]

The present numerical work is performed to analyze the heat transfer and fluid flow due to free convection in a porous equilateral triangular enclosure with a heated square body in the presence of magnetic field and heat generation. The left inclined wall of the enclosure is adiabatic while the horizontal wall is heated at a uniform temperature: the lower portion of the right inclined wall is considered to be nonisothermal and the upper portion of the wall is cold. The square body is maintained at a constant temperature. The governing equations are solved numerically subject to appropriate boundary conditions by the finite element method using Galerkin's weighted residuals scheme. Results are presented by streamlines, isotherms, mean Nusselt numbers for the different parameters such as Hartmann number (Ha), heat generation (λ), and size of the square body (lb). The Prandtl number (Pr) and Rayleigh number (Ra) are considered fixed. It is observed that the size of the body plays an important role with regard to the heat and fluid flow inside the cavity. [ABSTRACT FROM AUTHOR]

The present study considers transient buoyancy-opposed double diffusive free convection of a micropolar fluid consisting of rigid and non-deformable particles suspension with its own rotation in a square enclosure. The governing equations are written in terms of the primitive variables and a numerical solution of the complete set of nonlinear equations has been done without any scaling to the flow terms. The modified Marker and Cell (MAC) method is used for the solution of the variables in the primitive form with the help of the Alternating Direction Implicit (ADI) scheme. In order to handle effectively the advection terms, the gradient dependent consistent hybrid upwind scheme of second order (GDCHUSSO) and the operator-splitting algorithm have been employed. A parametric study is conducted to illustrate the effects of the Rayleigh number, Prandtl number, buoyancy ratio and the vortex viscosity parameter. Interesting features of stability at critical buoyancy ratios with the inclusion of the vortex viscosity parameter is reported. Detailed distributions of isotherms, isoconcentrations, flow lines and microrotation lines are provided to reveal the concealed physics of the complex phenomenon. A power spectrum analysis and phase plane maps are provided to bring clarity about the instability involved in the phenomenon. Correlations have been developed for the average Nusselt and Sherwood numbers based on the computed results. [ABSTRACT FROM AUTHOR]

One of the challenging points in the simulation of a nanofluid flowing through a porous medium is modeling the surface heat flux in the presence of nanoparticles and internal solid matrix. The question is how much energy is absorbed by the solid phase, fluid phase, and particles at the surface of imposing heat flux? To reach a suitable answer, a local thermal nonequilibrium approach (including three energy equations) is presented in this paper and three heat flux models are proposed for the first time. The proposed models are compared and analyzed. The effects of interstitial heat transfer coefficients on the heat transfer in a porous channel are completely studied. The fluid temperature distributions and heat transfer rate obtained by homogenous and nonhomogenous approaches (for the proposed models) are completely studied and compared. The results show that the nonhomogeneous approach experiences larger Nusselt number than the homogeneous one for all the recommended heat flux models. [ABSTRACT FROM AUTHOR]

The present work deals with magnetoconvection of molten gallium in a cuboid rotating about a vertical axis passing through its center. The governing equations are derived in a non-inertial frame of reference considering both centrifugal and Coriolis forces. A vertical magnetic field is applied through the center opposite to the direction of gravity. The cuboid is heated from below and cooled at top, while the remaining walls of the cuboid are thermally insulated. The modified Marker and Cell method is adopted for the numerical solution of the governing equations. The gradient dependent consistent hybrid upwinding scheme of second order is adopted for the discretization of the convective terms in the momentum equations. The operator splitting algorithm is used for the numerical treatment of the energy equation. The effects of cavity rotation and applied magnetic field on heat and momentum transport processes have been investigated. The uniform thorough mixing of fluids by rotation and regularization of flow by magnetic field are observed. The governing flow field and temperature distribution are shown graphically to elucidate the intricate physics of the phenomenon. [ABSTRACT FROM AUTHOR]

• The present work addresses the impact of partially active magnetic fields on the enhanced thermal performance of hybrid nanofluid (Cu–Al 2 O 3 –H 2 O) filled a porous oblique-wavy enclosure heated partially. • A partially active magnetic field can be used as an effective means to control local flow-fields and heat transfer that is found ∼13.97% less compared to that of the whole-domain magnetic field case. • The variations in the width of the partial magnetic field, heater length are also analyzed exhaustively. • The magnetic field's intensity, porosity, permeability, and the nanoparticles' volume fraction are used to analyze thermo-fluid flow aspects extensively. • The use of a wavy wall enhances heat transfer up to ∼22.16% compared to a plain vertical wall. Improved controllability along with enhanced thermal performance in modern thermal devices could be achieved using the combination of partial magnetic fields and hybrid nanofluid flow. The present attempt demonstrates the impact of partially active magnetic fields on the enhanced thermal performance of hybrid nanofluid (Cu–Al 2 O 3 –H 2 O) flow in an oblique wavy porous enclosure. The enclosure is partially heated from the bottom and cooled through its wavy sides and suffers from a partially active magnetic field normal to the sidewalls. The transport equations involving complex wavy walls, localized thermal gradient, porous substance, hybrid nanofluid, partial magnetic fields are solved by the finite volume approach numerically using a written FORTRAN code. The effectiveness of the novel implementation of a partial magnetic field is examined rigorously for wide ranges of variations of active heating length (L h), active width of the partial magnetic field (W b) and its positions, magnetic field strength (Ha), the inclination of the cavity (γ), Darcy-Rayleigh number (Ra m), Darcy number (Da), and hybrid nanoparticles concentration (ζ) additionally applying no and whole-domain magnetic field. The correlation for the average Nusselt number is derived. Finally, the results conclude that the presence of complex wavy walls enhances the heat transfer of ∼22.16% compared to a plain vertical wall; however, the strength of circulation drops. A partially active magnetic field can be utilized as an effective means to control field variables with a lesser reduction in heat transfer (∼13.97%) compared to the whole domain magnetic field. The middle-centered partial magnetic field offers a significant impact on the overall thermal behavior depending on the active width and intensity of the magnetic field, active heating length, and all other involved parameters. Tilting of the cavity reduces the heat transfer rate. [Display omitted] [ABSTRACT FROM AUTHOR]

Boundary-layer forced convection flow of a Casson fluid past a symmetric wedge is investigated. Similarity transformations are used to convert the governing partial differential equations to ordinary ones and the reduced equations are then solved numerically with the help of the shooting method. Comparisons with various previously published works on special cases are performed and the results are found to be in excellent agreement. A representative set of graphical results is obtained and illustrated graphically. The velocity is found to increase with an increasing Falkner-Skan exponent whereas the temperature decreases. With the rise of the Casson fluid parameter, the fluid velocity increases but the temperature is found to decrease in this case. The skin friction decreases with increasing values of the Casson fluid parameter. It is found that the temperature decreases as the Prandtl number increases and thermal boundary layer thickness decreases with increasing values of the Prandtl number. A significant finding of this investigation is that flow separation can be controlled by increasing the value of the Casson fluid parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(8): 665-675, 2013; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21065 [ABSTRACT FROM AUTHOR]

The two-phase flow and heat transfer of a Cu–Al 2 O 3 water hybrid nanofluid in a wavy enclosure partially filled with a porous medium is investigated. The concentration gradient of the composite nanoparticles is modeled considering the thermophoresis and Brownian motion nanoscale forces. The porous medium is also modeled using the local thermal non-equilibrium model. The governing equations are converted into a non-dimensional form and then solved using the finite element technique. The impact of the Darcy number, convection interface, and the wave amplitude on the concentration distribution of nanoparticle flow and heat transfer is addressed. The outcomes show that the convective heat transfer in the liquid and solid phases could be increased by 4.5 and 2.7 folds by increasing the Darcy number from 1 0 − 5 to 1 0 − 2 . The growth of the concentration of the nanoparticles from 0 to 0.04 improves the liquid Nusselt number by 17%. The hybrid nanofluid shows a better heat transfer enhancement compared to simple nanofluids. [Display omitted] • Natural convection within nanofluid superposed wavy porous layers is investigated. • LTNE model and Forchheimer–Brinkman-extended Darcy approach are employed. • The impacts of amplitude on the three composite layers are examined. • As the porosity rises, both heat transfer phases declines for low D a and increases for high D a. [ABSTRACT FROM AUTHOR]

• The work presents impact of surface undulation on mixed MHD nano-bioconvective heat and mass transfer due to swimming of oxytactic bacteria in a porous enclosure. • Bioconvection from oxytactic organisms produces a secondary circulation on the left heated wavywall. The shape and strength of this circulation are markedly influenced by the involved flow controlling parameters n, Rb, Ha, Da, Le, Pe and Gr. • The curved surface enhances the heat transfer up to certain optimum undulations (n), whereas mass transfer increases with the increasing undulations (n). • The average value of Sh magnitude increases with undulations, bioconvection raises further the Sh value. Transport phenomena involving thermo-bioconvection have become an interesting field of research due to their novel application in various fields of engineering, bio-energy systems, fuel cells, medical science, etc. Design as well as proper control of such a system involving multiphysical transport in a complex geometry is a very difficult task. On such a system, the present study is conducted aiming to examine the magnetohydrodynamic (MHD) mixed bioconvection with oxytactic microorganisms suspended in copper-water nanofluid. The flow takes place through porous media in a top-wall-translating enclosure with a complex wavy sidewall heated uniformly. The right vertical wall is isothermally cooled; other walls are adiabatic. A magnetic field is imposed along the horizontal direction. Evolved flow physics are analyzed by modeling this complex problem involving an undulating heated wall and many coupled transport equations (due to the presence of motile bacteria or organisms) are numerically solved through a finite volume-based code. The thermo-fluid behaviors are studied extensively to explore the controllability of different involved parameters that could help the system's design and operation. The important parameters influencing the complex physics in the enclosure are the number of undulations (n), bioconvection Rayleigh number (R b), Darcy number (Da), Hartmann number (Ha), Peclet number (Pe), Lewis number (Le), oxygen diffusion ratio (χ), Grashof number (Gr). The study reveals that the undulating curved surface enhances the heat transfer up to certain optimal magnitudes of undulations at the different operating conditions. The mass transfer rate increases with all undulations and bioconvection supports this trend. Bioconvection always favors heat transfer. In general, it is found that by adjusting the involved flow parameters and number of undulations, the local as well as global transport mechanisms, can be controlled effectively. The concept of this investigation could be found in the designing of microbial fuel cells and different nanotechnology-based bioconvection. [Display omitted]. [ABSTRACT FROM AUTHOR]

The study is aimed to understand the heat transfer coefficient and thermal entropy generation analyses of plate heat exchanger by using water-based nanodiamond nanofluids. The experiments were conducted in the volume concentration range: 0 ≤ ϕ ≤ 1.0%, the Reynolds number range: 140 ≤ Re ≤ 610, the mass flow rate range: 0.05 ≤ m ̇ ≤ 0.183 kg / s , and the Peclet number range from 895.78 ≤ Pe ≤ 3882.72, respectively. The effect of Reynolds number, Peclet number and particle volume loadings of nanodiamond nanofluids on heat transfer characteristics and entropy generation has been investigated. Water and nanodiamond nanofluids were considered as hot and cold medium in the plate heat exchanger, respectively, for the experimental study. The study reveals considerable augmentation in heat transfer coefficient and Nusselt number with an increase of nanofluid particle loadings. The study showed 32.50%, 55.47%, 35.11%, 22.80%, and 18.93% enhancements in overall heat transfer coefficient, heat transfer coefficient, Nusselt number, pressure drop and pumping power compared to base fluid at a Reynolds number of 526.37 at ϕ = 1.0%. Improved effectiveness, number of transfer units and exergy efficiency of 14.41%, 32.81% and 19.72% was observed at ϕ = 1.0% and at a Reynolds number of 526.37 against base fluid data. The thermal entropy and friction entropy generation was showed decreasing and increasing trends respectively, in the measured particle volume loadings. The Bejan number and entropy generation number demonstrated the roles of heat transfer and friction factor in the entropy generation. From the experimental results a new Nusselt number and friction factor correlations were proposed. [Display omitted] • The heat transfer, entropy generation and exergy efficiency of ND/water nanofluids flow in a PHE has been estimated. • The heat transfer coefficient and Nusselt number is increased to 55.47% and 35.11% at ϕ = 1.0%. • The thermal entropy generation is decreased to 20.66% to that of water at ϕ = 1.0%. • The exergy efficiency is enhanced to 19.74% at ϕ = 1.0% and at Re of 526.37. [ABSTRACT FROM AUTHOR]

• Nanofluid pool boiling on a horizontal cylinder with and without various numbers of fins has numerically studied. • The correlations for nucleate site density and bubble diameter were implemented according to nanoparticles. • Discrete phase modelling was used to track the location of nanoparticles on the cylinder. • The aspect ratios of the fins played a major role in heat transfer compared to the number of fins. • Heat transfer was improved for nanofluids with volume fractions less than 1%. Flow and thermal features of nanofluid pool boiling on a circular heat sink with mirco-fins attached were numerically investigated. The initial geometry consisted of a horizontal cylinder with an outside diameter of 20 mm submerged in a saturated water/nanofluid for validation cases. Physical micro-fins with various configurations were added to the outside surface of the cylinder for the purpose of this study. Due to the presence of nanoparticles, three phases were considered in modelling as liquid, vapour and particles. Unsteady Eulerian- Eulerian from multiphase two-phase flow approach was combined with wall boiling model to identify the heat and mass transfer at the hot surface, as well as interaction forces between the liquid and vapour phases. For the case of nanofluid, thermo-physical properties were modified based on particles concentration. To track the fate of nanoparticles, discrete phase modelling was employed from the Lagrangian frame. To solve the boiling heat transfer at the hot surface and fins, nucleate site density and bubbles diameter were modified and implemented to account for the presence of nanoparticles and corrected roughness. All the equations were discretised and solved by CFD commercial software, ANSYS-Fluent v19.5. The results showed that the impacts of fin aspect ratio on heat transfer are higher compared to the number of fins. However, the role of these geometrical parameters decreased as the nanofluid concentration increased. In addition, it was found that the best enhancement in heat transfer was obtained for nanofluid volume fraction around 1% vol. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamic conjugate heat transfer characteristics of a ferrofluid-filled porous inclined enclosure heated differentially have been investigated numerically in the present work. Two-conducting fins are attached to the hot wall of the cavity and the horizontal walls are insulated. The ranges of dimensionless flow controlling parameters are taken as: modified Rayleigh number (10 ≤ Ra ⁎ ≤ 104), length of the fins (a = 0.3, 0.5, 0.7), gap between the two fins (b = 0.3, 0.5, 0.7), and Darcy number (10−5 ≤ Da ≤ 10−2), volume fractions of nanoparticles (0 ≤ ϕ ≤ 0.06), Hartmann number (0 ≤ Ha ≤ 50), and the cavity inclination angles (0 ≤ γ ≤ 90o). The finite element method has been used to solve the governing equations and the present code have been validated with previously published work. The results show that the average Nusselt number increases by increasing the modified Rayleigh number, Darcy number, fins length while it decreases by increasing the Hartmann number. For any range of modified Rayleigh numbers, the highest fin length and the widest gap between the fins can be a superior heating strategy. At a fixed fin length, the lower gap between the fins is of a better choice to boost heat transfer when the cavity inclination angle increases up to 30o. [ABSTRACT FROM AUTHOR]

A numerical study is presented for the thermo-free convection inside a cavity with vertical corrugated walls consisting of a solid part of fixed thickness, a part of porous media filled with a nanofluid, and a third part filled with a nanofluid. Alumina nanoparticle water-based nanofluid is used as a working fluid. The cavity's wavy vertical surfaces are subjected to various temperature values, hot to the left and cold to the right. In order to generate a free-convective flow, the horizontal walls are kept adiabatic. For the porous medium, the Local Thermal Non-Equilibrium (LTNE) model is used. The method of solving the problem's governing equations is the Galerkin weighted residual finite elements method. The results report the impact of the active parameters on the thermo-free convective flow and heat transfer features. The obtained results show that the high Darcy number and the porous media's low modified thermal conductivity ratio have important roles for the local thermal non-equilibrium effects. The heat transfer rates through the nanofluid and solid phases are found to be better for high values of the undulation amplitude, the Darcy number, and the volume fraction of the nanofluid, while a limit in the increase of heat transfer rate through the solid phase with the modified thermal ratio is found, particularly for high values of porosity. Furthermore, as the porosity rises, the nanofluid and solid phases' heat transfer rates decline for low Darcy numbers and increase for high Darcy numbers. [ABSTRACT FROM AUTHOR]

• Impact of heat source on mixed convection of nanofluids in wavy-walled cavity does reported via heatline concept. • Finite element method is applied to solve the dimensionless governing equations with dimensionless BCs. • Validations with the experimental/numerical data are accomplished regarding the validity of the existing code. • Outcomes of length and location of the heat source, number of oscillations as well as Reynolds number are established. The appearance of a heat source at the bottom of a cavity against the cold part at the top wavy surface is examined in this work. The heat transportation, velocity of the fluid, and the temperature behaviour toward the mixed convection of nanofluids are obtained from the simulation of the Galerkin finite element technique and the Navier-Stokes equations. The other surfaces are considered adiabatic as well as both sides of the lid-driven cavity. It should be noted that the Grashof number, the volume fraction of alumina-nanoparticles, and the differentially-moving vertical walls are fixed at 10 5 , 0.02, the upward (right) and downward (left), respectively. To verify the computational code of derivation, the experimental and theoretical data from other researchers are compared. The results of the non-primitive variables, including the Richardson number, Reynolds number, number of undulations, dimensionless length, and the location of the heat source are compared. The numerical results indicate that larger values of the Richardson number and the Reynolds number enhance the rate of heat transfer. Not only two waves appear at the upper surface, but the heat source located at the centre with optimum height causes the entire cavity to have maximum heat transfer performance. The current problem is solved to benefit the installation of microelectronic cooling of a water-to-air heat exchanger or a pin-fin MHS heat transfer media. [ABSTRACT FROM AUTHOR]

In recent times, a different kind of nanofluid, namely hybrid nanofluid, has been taken to enrich the rate of heat transfer in base fluid additionally. In the present study, a novel type of hybrid nanofluid having H2O as a base with aluminum oxide (Al2O3) and copper (Cu) nano‐sized particles has been numerically demonstrated to improve the flow at nodal/saddle stagnation point. Radiative heat transfer and the magnetic field are included in this analysis. Depending on Tiwari‐Das nanofluid technique, an innovative direct mathematical idea has been framed and introduced. The rate of flow is measured through partial differential equation (PDE). These equations are complex nonlinear, so a set of appropriate transformations is used to decrease the order of these equations. The reduced system is evaluated by applying a fifth‐order R.K. Fehlberg technique together with the shooting process. The obtained outcomes are exhibited in graphs and tables. The concluding remark is that the rate of heat transfer is increased by 20.51% and 49.81% in hybrid nanofluid when compared with hybrid nanofluid and all kinds of other fluids (i.e., regular and nano), respectively. [ABSTRACT FROM AUTHOR]

The unsteady thermal flow and heat transfer adjacent to the sidewall of a differentially heated cavity with single and multiple nonconductive fins are investigated utilizing the finite element method. The transition to the unsteady flow, as well as flow oscillations, is described for the water-filled cavity and Rayleigh numbers ranging from 1 × 10 7 to 1 × 10 10 , including the critical Rayleigh number. Characteristics of unsteady flows are investigated for early, transitional, and quasi-steady stages. For all cases, heat transfer from the finned sidewall to the interior fluid is quantified and compared with the cavity without the fin. Results show that the volumetric flow rate along the vertical axis in the middle of the cavity rises by increasing the number of fins (up to 13.41% for the cavity with two fins for Ra = 1.84 × 10 9 ) in transitional and quasi-steady stages. Moreover, the increment of fin number and Ra leads to a higher enhancement factor (ε) that shows the heat transfer enhancement or depression. For Ra = 1.84 × 10 9 , the maximum ε for the cavity with one and three fins is calculated about 17.5% and 34% respectively. • The unsteady flow within a differentially heated cavity is investigated. • Multiple nonconductive fins are installed on the heated sidewall of the cavity. • Volumetric flow rate in the middle of the cavity rises by the number of fins. • Increment of fin number and Ra leads to a higher enhancement factor. [ABSTRACT FROM AUTHOR]

This article addresses the Cattaneo–Christov heat flux, radiation and joule heating model as applied to a Blasius–Rayleigh–Stokes flow through a transitive magnetic field. The mathematical models are converted into a pair of self-similarity equations by applying appropriate transformations. The reduced similarity equivalences are then solved numerically by the Runge–Kutta–Fehlberg 45th-order method. To better perceive the problem, the flow and energy transfer characteristics are explored for distinct values of different factors. From this analysis we found that Higher values of Q increase the f ′ η field and its interrelated thickness of the boundary layer. The temperature of the fluid and its interrelated layer thickness enhances for boost up values of γ. Also found that the streamline graphs are dominant for Q=2 when compared with Q=0.5. The presence of Q has more impact on the results when compared to the case where Q is absent. The local R e x C f x and N u x R e x − 1 2 scale back for increasing values of ω. • The streamline graphs are dominant for Q = 2 when compared with Q = 0. 5. • θ (η) field rises of enhanced values of R. • An intensification in the f ′ (η) field is seen with the increment of ω and Q. • Interrelated thickness of the thermal boundary layer decays for higher values of P r. • The heat transfer rate is greater in the presence of R than in the absence of R. • The presence of Q has more impact on the results when compared to the case where Q is absent. [ABSTRACT FROM AUTHOR]

The current study investigates the 2D entropy production and the mixed convection inside a wavy-walled chamber containing a rotating cylinder and a heat source. The heat source of finite-length h is placed in the middle of the left vertical surface in which its temperature is fixed at T h . The temperature of the right vertical surface, however, is maintained at lower temperature T c . The remaining parts of the left surface and the wavy horizontal surfaces are perfectly insulated. The governing equations and the complex boundary conditions are non-dimensionalized and solved using the weighted residual finite element method, in particular, the Galerkin method. Various active parameters are considered, i.e., Rayleigh number R a = 10 3 and 10 5 , number of oscillations: 1 ≤ N ≤ 4 , angular rotational velocity: − 1000 ≤ Ω ≤ 1000 , and heat source length: 0. 2 ≤ H ≤ 0. 8 . A mesh independence test is carried out and the result is validated against the benchmark solution. Results such as stream function, isotherms and entropy lines are plotted and we found that fluid flow can be controlled by manipulating the rotating velocity of the circular cylinder. For all the considered oscillation numbers, the Bejan number is the highest for the case involving a nearly stationary inner cylinder. [ABSTRACT FROM AUTHOR]

Reiner–Philippoff fluid flow over a heated surface through theory of Cattaneo–Christov for heat diffusion is executed in this work. The impacts of Cattaneo–Christov heat flux, Ohmic heating and transverse magnetic field are also considered. The Transformations are used to reduce system of partial differential equations into ordinary ones and are solved numerically by using RKF-45 method. The dimensionless numbers on velocity and temperature are elaborated. Further engineering curiosity of local Nusselt are tabulated, depicted and interpreted. • Reiner–Philippoff fluid flow over a heated surface is modeled. • Theory of Cattaneo–Christov for heat diffusion is executed for energy expression. • The impacts of ohmic heating and transverse magnetic field are considered. • The dimensionless numbers on velocity and temperature are elaborated. [ABSTRACT FROM AUTHOR]