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The passive feature of natural convection encourages continuous investigation on this field. This research work studies the natural convection inside a cavity of wavy vertical surfaces, including a heat source block standing on the base of cavity. The employed liquid is a hybrid water–Cu–Al 2 O 3 nanofluid. The vertical wavy surfaces are fixed at low temperature, while the heat source remains constant at a higher temperature. The Galerkin finite element method is applied to obtain the numerical solutions. Besides the common visualization tools, the heatlines tool is used in this paper as well. It is found from the outcomes that the Nusselt number is purely proportional to the length of the heat source. In addition, the hybrid water–Cu–Al 2 O 3 nanofluid exhibits a higher Nusselt number than that corresponding to a pure water and as well as other regular nanofluids. The percentages of the average heat transfer gained by the hybrid nanofluid at ϕ = 0.02 are 13.7% and 5% higher than those for pure water and other nanofluids. [ABSTRACT FROM AUTHOR]

A numerical study is conducted to analyze the effects of a flexible fin on unsteady convective flow in a square enclosure composed of a vertical fluid layer and a porous layer. The fin is attached to the heated left wall of the enclosure. The Brinkman-Forchheimer-extended Darcy flow model is assumed in the porous layer. The governing equations are written in the Arbitrary Lagrangian–Eulerian (ALE) formulation in the fluid and structure domains and then solved using the FEM. The result shows that the fin oscillation impacts the area below the fin rather than the area above the fin or the area in the center. The overall rate of heat transfer is improved as the Darcy number, the fluid layer thickness, and the fin elasticity increase. The overall rate of heat transfer increases exponentially with the rise of the oscillation amplitude. An oscillation amplitude of 0.1 could result in 3.4 percent improvement in the heat transfer rate. [ABSTRACT FROM AUTHOR]

A numerical study is made on the entropy generation and magnetohydrodynamics natural convection of Al 2 O 3 -water non-homogeneous nanofluid inside a square enclosure equipped with a heated trapezoidal body. The Galerkin weighted residual finite element method is applied to solve the dimensionless governing equations within the utilized computational domain along with the algorithm of Newton–Raphson iteration that is used for simplifying the nonlinear terms in the equations. The characteristics of fluid flow fields, temperature distributions and entropy generation are studied for an enormous range of the Rayleigh number (10 3 ≤ R a ≤ 10 6) , volume fraction of nanoparticles ( 0 ≤ ϕ ≤ 0.04 ), Hartmann number (0 ≤ H a ≤ 50) , thermal conductivity of the trapezoidal solid body ( k w = 0.5 , 0.76, 1.95, 7 and 16) and the height of the trapezoidal solid body ( 0.15 ≤ D ≤ 0.45 ). It is shown that the streamlines pattern is more sensitive to the increase in the Hartmann number in comparison with the augmentation of the volume fraction of nanoparticles. Also, for a more thermodynamically optimized system, the higher Hartmann number at a higher solid volume fraction of nanofluid is recommended as they show less entropy generation. [ABSTRACT FROM AUTHOR]

In this study, the conjugate natural convection in a square cavity filled with Al 2 O 3 –water nanofluid with an inner conducting solid block is studied numerically using nonhomogeneous Buongiorno's two-phase model. The left wall of the cavity is partially heated and the remaining parts of the wall are adiabatic, while the right wall is fully cooled. The top and bottom horizontal walls are adiabatic. The numerical simulations are based on the finite difference method. The results are simulated for various values of the nanoparticle volume fraction (0 ≤ ϕ ≤ 0.04) , Rayleigh number (10 2 ≤ R a ≤ 10 6) , thermal conductivity of the conjugate square (k w = 0.28 , 0.76 , 1.95 , 7.0) and 16.0 (epoxy: 0.28, brickwork: 0.76, granite: 1.95, solid rock: 7, stainless steel: 16), the size of the inner solid (0 ≤ D ≤ 0.7) , and the length of the heater ( 0.1 ≤ H ≤ 1.0 ). The numerical results for the average and local Nusselt numbers, isotherms, distribution of nanoparticles, and streamlines are presented graphically. The findings indicate that increasing the average solid volume fraction and the size of the solid block as well as the thermal conductivity will enhance the rate of the heat transfer at low values of Rayleigh number R a = 10 3 . On the other hand, increasing these parameters at high values of Rayleigh number ( R a > 10 5 ) decreases the average Nusselt number. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • FEM was employed to solve the governing equations subject to the boundary conditions. • Two-phase nanofluid model in a wavy cavity with conductive inner block is considered. • Comparisons with previously experimental and numerical published results are provided. • A selection of optimal number of oscillations can enhance the heat transfer inside the cavity. Abstract By employing the finite element method, thermophoresis and Brownian diffusion are studied numerically relating to the natural convection in a wavy cavity that is filled with an Al 2 O 3 -water nanofluid possessing a central heat-conducting solid block that is influenced by the local heater located on the bottom wall. An isothermal condition is established in the two wavy vertical walls, while adiabatic condition is for the top horizontal wall. Partial heating is applied to the bottom of the horizontal wall, while the remaining part remains in the adiabatic condition. Empirical correlations are employed for the thermal conductivity and dynamic viscosity of the nanofluid. The number of oscillations (1 ⩽ N ≤ 4), Rayleigh number ( 10 3 ⩽ Ra ≤ 10 6 ), nanoparticles volume fraction (0 ⩽ ϕ ≤ 0.04) and dimensionless length of the bottom heater (0.2 ⩽ H ⩽ 0.8) govern the parameters in this study. The grid independency test, as well as experimental and numerical data from other published works, was employed to validate the developed computational code comprehensively. Based on the obtained results, it was found that the heat transfer inside the cavity is enhanced by introducing nanoparticles as well as a selection of optimal number of oscillations. [ABSTRACT FROM AUTHOR]

The present study investigates the conjugate heat transfer in a square cavity heated by a triangular solid and saturated with Al2O3-water nanofluid. Two-phase Buongiorno's model is used for modeling the nanofluid heat transfer. The finite element method is used for numerical solution of the dimensionless governing equations subject to the boundary conditions. Comparisons of the proposed method with previously published experimental and numerical works show a good agreement. The effects of some parameters such as the Rayleigh number, thermal conductivity ratio, dimensionless triangular wall thickness and nanofluid volume fraction on heat transfer and nanoparticle distributions are completely studied and discussed. The results show clockwise rotations for streamlines and nanoparticle migration. Also the Nusselt number increases with the nanofluid volume fraction. A continuous reduction is seen for the mean Nusselt number by increasing the dimensionless triangular wall thickness for all the considered values of the Rayleigh number. [ABSTRACT FROM AUTHOR]

In the present paper, an unsteady motion of fluid flow in a pulsating pipe is studied to determine the effect of non-sinusoidal waveforms on the heat transfer performance. Three non-sinusoidal waveforms, namely sawtooth, square and triangular waveforms have been considered. Explicit analytical expressions for a periodic laminar flow describing the flow and heat transfer at small and large times with sawtooth and square pressure waveforms have been derived using Bessel transform technique. The heat transfer performance of periodic flow at sawtooth and square pressure waveforms has been compared with the published result for triangular waveform [1] . The temperature performance for a triangular waveform pressure is very different from the sawtooth and square pressure waveforms. [ABSTRACT FROM AUTHOR]

In this paper, we present an approximate solution method for the problem of magnetohydrodynamic (MHD) flow and heat transfer of a second grade fluid in a channel with a porous wall. The method is based on the Bernstein polynomials with their operational matrices and collocation method. Under some regularity conditions, upper bounds of the absolute errors are given. We apply the residual correction procedure which may estimate the absolute error to the problem. We may estimate the absolute error by using a procedure depends on the sequence of the approximate solutions. For some certain cases, we apply the method to the problem in the numerical examples. Moreover, we test the impact of changing the flow parameters numerically. The results are consistent with the results of Runge-Kutta fourth order method and homotopy analysis method. [ABSTRACT FROM AUTHOR]

The aim of the present numerical study to analyze the conjugate natural convection heat transfer in a rotating enclosure with finite wall thickness. The enclosure executes a steady counterclockwise an- gular velocity about its longitudinal axis. The staggered grid arrangement together with the Marker and Cell (MAC) method was employed to solve the governing equations. The governing parameters considered are the wall thickness, 0.05 ≤ D ≤ 0.2, the conductivity ratio, 0.5 ≤ Kr ≤ 10 and the Taylor number, 8.9 104 ≤ Ta ≤ 1.1 106, and the centrifugal force is assumed weaker than the Coriolis force. It is found that decreasing the conductivity ratio or/and rotational speed stabilize of the convective flow and heat transfer oscillation. The global quantity of the heat transfer rate increases by increasing the conductivity ratio and it decreases about 12% by increasing 20% wall thickness for the considered rotational speeds. [ABSTRACT FROM AUTHOR]

The buoyant Marangoni convection heat transfer in a differentially heated cavity is numerically studied. The cavity is filled with water-Ag, water-Cu, water-AlO, and water-TiO nanofluids. The governing equations are based on the equations involving the stream function, vorticity, and temperature. The dimensionless forms of the governing equations are solved by the finite difference (FD) scheme consisting of the alternating direction implicit (ADI) method and the tri-diagonal matrix algorithm (TDMA). It is found that the increase in the nanoparticle concentration leads to the decrease in the flow rates in the secondary cells when the convective thermocapillary and the buoyancy force have similar strength. A critical Marangoni number exists, below which increasing the Marangoni number decreases the average Nusselt number, and above which increasing the Marangoni number increases the average Nusselt number. The nanoparticles play a crucial role in the critical Marangoni number. [ABSTRACT FROM AUTHOR]

Natural convection heat transfer in a rotating, differentially heated enclosure is studied numerically in this paper. The rotating enclosure is filled with water-Ag, water-Cu, water-Al2O3, or water-TiO2 nanofluids. The governing equations are in velocity, pressure, and temperature formulation and solved using the staggered grid arrangement together with MAC method. The governing parameters considered are the solid volume fraction, 0.0 = ɸ = 0.05, and the rotational speeds, 3.5 = Ω = 17.5 rpm, and the centrifugal force is smaller than the Coriolis force and both forces were kept below the buoyancy force. It is found that the angular locations of the local maximums heat transfer were sensitive to rotational speeds and nanoparticles concentration. The global quantity of heat transfer rate increases about 1.5%, 1.1%, 0.8%, and 0.6% by increasing 1% ɸ of the nanoparticles Ag, Cu, Al2O3, and TiO2, respectively, for the considered rotational speeds. [ABSTRACT FROM AUTHOR]

Conjugate natural convection in a square porous enclosure sandwiched by finite walls under the influence of non-uniform heat generation and radiation is studied numerically in the present article. The horizontal heating is considered, where the vertical walls heated isothermally at different temperatures, while the horizontal walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and finite difference method is applied to solve the dimensionless governing equations. The governing parameters considered are the ratio of wall thickness to its width $$(0.02 \le D \le 0.3)$$ , the wall to porous thermal conductivity ratio $$(0.1 \le k_\mathrm{r} \le 10.0)$$ , the internal heating $$(0 \le \gamma \le 5)$$ , and the local heating exponent parameters $$(1 \le \lambda \le 20)$$ . It is found that the average Nusselt number on the hot and cold interfaces increases with increasing the radiation intensity. Very high non-uniformity heating does not affect the average Nusselt number at very thick walls. [ABSTRACT FROM AUTHOR]

Effect of rotation on linear and nonlinear instability of cross-diffusive convection in an anisotropic porous medium saturated with Newtonian fluid has been investigated. Normal mode technique has been used for linear stability analysis, however nonlinear analysis is done using spectral method, involving only two terms. The Darcy model with Coriolis terms, has been employed in the momentum equation. Nonlinear analysis is used to find the thermal and concentration Nusselt numbers. The effects of various parameters, including Soret and Dufour parameters, on stationary and oscillatory convection, have been obtained, and shown graphically. [ABSTRACT FROM AUTHOR]

The effects of time-periodic boundary temperatures and internal heating on Nusselt number in the Bénard-Darcy convective problem has been considered. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small. By performing a weakly non-linear stability analysis, the Nusselt number is obtained in terms of the amplitude of convection, which is governed by the non-autonomous Ginzburg-Landau equation, derived for the stationary mode of convection. The effects of internal Rayleigh number, amplitude and frequency of modulation, thermo-mechanical anisotropies, and Vadasz number on heat transport have been analyzed and depicted graphically. Increasing values of internal Rayleigh number results in the enhancement of heat transport in the system. Further, the study establishes that the heat transport can be controlled effectively by a mechanism that is external to the system. [ABSTRACT FROM AUTHOR]

Darcy-Bénard convection in a square porous enclosure with a localized heating from below and lateral cooling is studied numerically in the present paper. A finite-thickness bottom wall is locally heated, the top wall is kept at a lower temperature than the bottom wall temperature, and the lateral walls are cooled. The finite difference method has been used to solve the dimensionless governing equations. The analysis in the undergoing numerical investigation is performed in the following ranges of the associated dimensionless groups: the heat source length- $${0.2\leq H \leq 0.9}$$, the wall thickness- $${0.05\leq D \leq 0.4}$$, the thermal conductivity ratio- $${0.8\leq K_{\rm r} \leq 9.8}$$, and the Biot number- $${0.1\leq Bi \leq 1.1}$$. It is observed that the heat transfer rate could increase with increasing heat source lengths, thermal conductivity ratio, and cooling intensity. There exists a critical wall thickness for a high wall conductivity below which the increasing wall thickness increases the heat transfer rate and above which the increasing wall thickness decreases the heat transfer rate. [ABSTRACT FROM AUTHOR]

An analysis has been carried out to study the flow and heat transfer in a liquid film over a permeable stretching sheet. Using similarity transformations, the time-dependent boundary layer equations are reduced to a set of nonlinear ordinary differential equations. The resulting parameter problem and velocity as well as temperature fields are solved using the homotopy analysis method (HAM). Analytic series solutions are given, and numerical results for velocity and the temperature profiles are presented through graphs of different values for pertinent parameter. The effects of unsteadiness parameter and permeability parameter on the velocity and temperature profiles are explored for different values of blowing or suction parameter. [ABSTRACT FROM AUTHOR]

In this article we study the combined effect of internal heating and time-periodic gravity modulation on thermal instability in a closely packed anisotropic porous medium, heated from below and cooled from above. The time-periodic gravity modulation, considered in this problem can be realized by vertically oscillating the porous medium. A weak non-linear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number has been obtained in terms of the amplitude of convection which is governed by the non-autonomous Ginzburg-Landau equation derived for the stationary mode of convection. The effects of various parameters such as; internal Rayleigh number, amplitude and frequency of gravity modulation, thermo-mechanical anisotropies, and Vadász number on heat transport has been analyzed. It is found that the response of the convective system to the internal Rayleigh number is destabilizing. Further it is found that the heat transport can also be controlled by suitably adjusting the external parameters of the system. [ABSTRACT FROM AUTHOR]

Effects of a conductive wall on natural convection in a square porous enclosure having internal heating at a rate proportional to a power of temperature difference is studied numerically in this article. The horizontal heating is considered, where the vertical walls heated isothermally at different temperatures while the horizontal walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and finite difference method is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (0 ≤ Ra ≤ 1000), the internal heating and the local exponent parameters (0 ≤ γ ≤ 5), (1 ≤ λ ≤ 3), the wall to porous thermal conductivity ratio (0.44 ≤ Kr ≤ 9.9) and the ratio of wall thickness to its width (0.02 ≤ D ≤ 0.5). The results are presented to show the effect of these parameters on the fluid flow and heat transfer characteristics. It is found a strong internal heating can generate significant maximum fluid temperature more than the conductive solid wall. Increasing value thermal conductivity ratio and/or decreasing the thickness of solid wall can increase the maximum fluid temperature. It is also found that at very low Rayleigh number, the heat transfer across the porous enclosure remain stable for any values of the thermal conductivity ratio. [ABSTRACT FROM AUTHOR]

In this paper, a non-standard finite difference scheme is proposed for solving a steady finite Rayleigh number convection in a porous cavity with an inclined magnetic field and non-uniform internal heating. Numerical results are compared with the classical finite difference scheme. [ABSTRACT FROM AUTHOR]

This paper examines the effects of thermocapillarity and thermal radiation on the boundary layer flow and heat transfer in a thin film on an unsteady stretching sheet with nonuniform heat source/ sink. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation and then are solved by using the homotopy analysis method (HAM). The effects of the radiation parameter, the thermocapillarity number, and the temperature-dependent parameter in this study are discussed and presented graphically via velocity and temperature profiles. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to study the flow of nanofluid and heat transfer characteristics between two horizontal plates in a rotating system. The lower plate is a stretching sheet and the upper one is a solid porous plate. Copper (Cu0 as nanoparticle and water as its base fluid have been considered. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similarity transformation, which is then solved analytically using the homotopy analysis method (HAM). Comparison between HAM and numerical solutions results showed an excellent agreement. The results for the flow and heat transfer characteristics are obtained for various values of the nanoparticle volume fraction, suction/injection parameter, rotation parameter, and Reynolds number. It is shown that the inclusion of a nanoparticle into the base fluid of this problem is capable of causing change in the flow pattern. It is found that for both suction and injection, the heat transfer rate at the surface increaseswith increasing the nanoparticle volume fraction, Reynolds number, and injection/suction parameter and it decreases with power of rotation parameter. [ABSTRACT FROM AUTHOR]

Heat transfer performance utilizing nanofluids in a trapezoidal enclosure is investigated taking into account variable thermal conductivity and viscosity. Transport equations are modelled by a stream-vorticity formulation, and are solved numerically by the finite difference method. The effects of the Rayleigh number, base angle, volume fraction, and size of nanoparticles on flow and temperature patterns as well as the heat transfer rate are presented. We found that the effect of the viscosity was more dominant than the thermal conductivity, and there is almost no improvement in heat transfer performance utilizing nanofluids. [ABSTRACT FROM PUBLISHER]

Abstract: Using the theory of dynamical systems, this study investigated the effects of a uniform internal heat generation on chaotic behaviour in thermal convection in a fluid-saturated porous layer subject to gravity and heated from below for low Prandtl number. A low-dimensional, Lorenz-like model was obtained using Galerkin truncated approximation. The fourth-order Runge–Kutta method was employed to solve the nonlinear system. We found that there is an inverse proportional relation between the level of internal heat G and the scaled Rayleigh number R, and consequently the porous media gravity-related Rayleigh number Ra. [Copyright &y& Elsevier]

Abstract: In this paper, the effects of thermocapillarity and a magnetic field on the flow and heat transfer in a liquid film over an unsteady elastic stretching surface is analyzed. Similarity transformations are used to transform the governing equations to a set of coupled ordinary differential equations. The differential equations are solved analytically by the homotopy analysis method (HAM). The effects of various parameters in this study are discussed and presented graphically. [Copyright &y& Elsevier]

Abstract: The Marangoni instability in a temperature-dependent-viscosity fluid layer with deformable free surface under the influence of a linear feedback control strategy is investigated. The exact analytical solution for the stationary modes is developed and the effects of the interaction between variable viscosity, controller gains, free surface deformation, gravity waves and heat transfer mechanism on the onset of Marangoni convection are determined. The destabilizing effect of exponential viscosity variation can be effectively suppressed through small controlled perturbations in the thermal boundary data. [Copyright &y& Elsevier]

Abstract: The effect of feedback control on the onset of steady and oscillatory surface-tension-driven (Marangoni) convection in a rotating horizontal fluid layer with a flat free upper surface and heated from below is considered theoretically using linear stability theory. The role of the controller gain parameter on the Ta–Pr parameter space, dividing stability domains into which either steady or oscillatory convection is preferred, is determined. [Copyright &y& Elsevier]

Abstract: The onset of stationary Marangoni instabilities in a horizontal fluid layer with free surface deformation and heated from below with a uniform heat flux is considered theoretically using linear stability theory. The explicit solution is obtained and the influences of temperature-dependent viscosity, surface deformability, gravity waves and heat transfer mechanism at the free surface on the stability thresholds are investigated. Small stabilizing effect is observed in fluids with a small viscosity variation while large viscosity variation strongly destabilizes the fluid layer. The stability thresholds are critically dependent on viscosity variation, surface deformation and heat transfer mechanism. [Copyright &y& Elsevier]

Abstract: In this Letter, the problem of determining the temperature distribution of a straight rectangular fin with power-law temperature-dependent surface heat flux is revisited. The solution of the corresponding nonlinear boundary-value problem (BVP) based on the homotopy-perturbation method (HPM) presented earlier is corrected and extended. [Copyright &y& Elsevier]

The aim of the present study is to analyze the convective flow and heat transfer of nanofluid in an inclined cavity filled with heat generating porous medium using the local thermal non-equilibrium model. The horizontal bottom wall of the cavity is maintained at a constant higher temperature while the left and right vertical walls are maintained at a constant lower temperature. The top wall is to be kept as adiabatic. The Darcy model is adopted for flow through the porous medium and the Boussinesq approximation is taken into account. The pores are saturated by a water-based nanofluid consisting of Cu nanoparticles. The governing equations are solved iteratively by finite difference based Alternating Direction Implicit (ADI) method. The results are discussed by various combinations of parameters involved in the study. The average heat transfer rate decreases when increasing the values of nanoparticle volume fraction for the case of high Rayleigh numbers. The heat transfer rate is enhanced by increasing values of the modified conductivity ratio and the porosity of the media. The results have possible applications in the heat-storage nanofluid-saturated porous systems. [ABSTRACT FROM AUTHOR]

The effects of nonuniform heating and a finite wall thickness on natural convection in a square porous cavity based on the local thermal nonequilibrium (LTNE) model are studied numerically using the finite difference method (FDM). The finite-thickness horizontal wall of the cavity is heated either uniformly or nonuniformly, and the vertical walls are maintained at constant cold temperatures. The top horizontal insulated wall allows no heat transfer to the surrounding. The Darcy law is used along with the Boussinesq approximation for the flow. The results of this study are obtained for various parametric values of the Rayleigh number, thermal conductivity ratio, ratio of the wall thickness to its height, and the modified conductivity ratio. Comparisons with previously published work verify good agreement with the proposed method. The effects of the various parameters on the streamlines, isotherms, and the weighted-average heat transfer are shown graphically. It is shown that a thicker bottom solid wall clearly inhibits the temperature gradient which then leads to the thermal equilibrium case. Further, the overall heat transfer is highly affected by the presence of the solid wall. The results have possible applications in the heat-storage fluid-saturated porous systems and the applications of the high power heat transfer. [ABSTRACT FROM AUTHOR]

Abstract: The problem of unsteady natural convection induced by a temperature difference between a cold outer square enclosure and a hot inner circular cylinder is studied in this paper. The cylinder temperature is assumed to vary sinusoidally with time about a fixed mean temperature. The coupled momentum and energy equations have been solved numerically over a wide range of values of the amplitude and the frequency of the source temperature signal, as well as the source radius. It is found that the heat transfer rate tends to increase by oscillating the source temperature signal. The maximum heat transfer augmentation was obtained for frequency between 25π and 30π for a high amplitude and a moderate source radius. [Copyright &y& Elsevier]

Abstract: Double-diffusive convection in an anisotropic porous layer heated and salted from below with an internal heat source and Soret effect is studied analytically using both linear and nonlinear stability analyses. The generalized Darcy model including the time derivative term is employed for the momentum equation. The critical Rayleigh number and wavenumber for stationary and oscillatory modes and frequency of oscillations are obtained analytically using linear theory. The effects of the anisotropy parameters, concentration Rayleigh number, internal heat source, Soret parameter, Vadasz number and Lewis number on the stationary, oscillatory, and heat and mass transfer are shown graphically. Heat and mass transfer have been obtained in terms of the Nusselt number and Sherwood number. [Copyright &y& Elsevier]

Abstract: Convective heat transfer in a differentially heated square enclosure with an inner rotating cylinder is studied theoretically. The free space between the cylinder and the enclosure walls is filled with water–Ag, water–Cu, water–Al2O3 or water–TiO2 nanofluids. The governing equations are formulated for velocity, pressure and temperature formulation and are modeled in COMSOL, a partial differential equation (PDE) solver based on the Galerkin finite element method (GFEM). The governing parameters considered are the solid volume fraction, 0.0⩽ ϕ ⩽0.05, the cylinder radius, 0⩽ R ⩽0.3 and the angular rotational velocity, −1000⩽Ω⩽1000. The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. It is found that the strength of the flow circulation is much stronger for a higher nanoparticle concentration, a better thermal conductivity value and a smaller cylinder with a faster, negative rotation. The maximum heat transfer are obtained at a high nanoparticle concentration with a good conductivity value, a slow positive rotation and a moderate cylinder size located in the center of the enclosure. [Copyright &y& Elsevier]

Abstract: In the present study the magnetohydrodynamic (MHD) liquid flow and heat transfer over non-linear permeable stretching surface has been presented in the presence of chemical reactions and partial slip. By means of proper similarity variables, the fundamental equations of the boundary layer are transformed to ordinary differential equations which for the fixed values of the x-coordinate along the plate local similarity solution would be valid appropriately. The ordinary differential equations are solved numerically using an explicit Runge–Kutta (4,5) formula, the Dormand–Prince pair and shooting method. As a result, the velocity profiles, the concentration profiles, temperature profiles, the wall shear stress, the local Sherwood number and the local Nusselt number for the various values of the involved parameters of the problem are presented and discussed in details. [Copyright &y& Elsevier]

Abstract: Heat transfer enhancement utilizing nanofluids in a trapezoidal enclosure is investigated for various pertinent parameters. Transport equations are modelled by a stream-vorticity formulation and solved numerically by finite difference approach. The inclined sloping boundaries is treated by adopting staircase-like zigzag lines. Based upon the numerical predictions, the effects of Grashof number, inclination angle of the sloping wall, volume fraction of nanoparticles on flow and temperature patterns as well as the heat transfer rate within the enclosure are presented. Water–Cu and water–Al2O3 nanofluids were tested. We found that acute sloping wall and Cu nanoparticles with high concentration are effective to enhance the rate of heat transfer. We also developed a new correlation for the average Nusselt number as a function of the angle of the sloping wall, effective thermal conductivity and viscosity as well as Grashof number. [ABSTRACT FROM AUTHOR]

• FEM and Arbitrary Lagrangian-Eulerian (ALE) procedure are used in the numerical analysis. • Two solid elastic thin fins are attached on the top cold wall. • Elasticity of the flexible fin can highly improve the heat transfer. • The results revealed an essential effect of the fin direction on the flow and heat transfer. The problem of unsteady mixed convection in a square enclosure containing a heated circular cylinder is studied in this paper. Two solid elastic thin fins are attached on the top cold wall. The governing equations for fluid flow and energy in the fluid and structures domains are written in Arbitrary Lagrangian-Eulerian (ALE) formulation. Finite element method was used to obtain the approximate solutions of the governing equation. The governing parameters considered are the oscillating fin direction, fin amplitude and length with various elasticity values and cylinder sizes. The results show that the instantaneous heat transfer characteristics of the contrary oscillation differs greatly from the identical oscillation. The influence of the elasticity value on the heat transfer rate is significant at a sufficiently small amplitude oscillation. [ABSTRACT FROM AUTHOR]

The effects of finite wall thickness and sinusoidal heating on convection in a nanofluid-saturated local thermal non-equilibrium (LTNE) porous cavity are studied numerically using the finite difference method. The finite thickness vertical wall of the cavity is maintained at a constant temperature and the right wall is heated sinusoidally. The horizontal insulated walls allow no heat transfer to the surrounding. The Darcy law is used along with the Boussinesq approximation for the flow. Water-based nanofluids with Cu nanoparticles are chosen for investigation. The results of this study are obtained for various parameters such as the Rayleigh number, periodicity parameter, nanoparticles volume fraction, thermal conductivity ratio, ratio of wall thickness to its height and the modified conductivity ratio. Explanation for the influence of the various above-mentioned parameters on the streamlines, isotherms, local Nusselt number and the weighted average heat transfer is provided with regards to the thermal conductivities of nanoparticles suspended in the pure fluid and the porous medium. It is shown that the overall heat transfer is significantly increased with the relative non-uniform heating. Further, the convection heat transfer is shown to be inhibited by the presence of the solid wall. The results have possible applications in the heat-storage fluid-saturated porous systems and the applications of the high power heat transfer. [ABSTRACT FROM AUTHOR]

In this study, we use the finite-difference method to numerically investigate the problem of transient free convective heat transfer in a nanoliquid-saturated porous square cavity with a sinusoidal boundary condition. The left vertical wall of the cavity is maintained at a constant temperature and the right wall is heated sinusoidally. The horizontal insulated walls allow no heat transfer to the surrounding. To regulate the heat transfer, we insert a solid square at the centre of the cavity in such a way that there is symmetry in the flow configuration. We use the Darcy law along with the Boussinesq approximation for the flow, and for the investigation, we employ water-based nanoliquids with Cu, Al 2 O 3 or TiO 2 nanoparticles. We obtain the results of this study for various parameters such as Rayleigh number, periodicity parameter, nanoparticle volume fraction, thermal conductivity ratio, length of the inner solid, modified conductivity ratio, and dimensionless time. We explain the different influences on the parameter contours of streamlines, isotherms, local Nusselt number and weighted-average heat transfer in unsteady and steady regimes based on the thermal conductivities of nanoparticles, water and porous media. The results show that the overall heat transfer is significantly increased with the relatively non-uniform heating. Further, we show that convective heat transfer is inhibited by the presence of the solid insert. The results have the potential for application in heat-removal and heat-storage liquid-saturated porous systems. [ABSTRACT FROM AUTHOR]

The problem of conjugate natural convection in a square cavity filled with a nanofluid with sinusoidal temperature variations on both horizontal walls is visualized by heatlines. Water-based nanofluids with Ag, Cu, Al 2 O 3 , or TiO 2 nanoparticles are chosen for investigation. The governing equations together with the specified boundary conditions are solved numerically using the finite difference method over a wide range of Rayleigh number ( 10 5 ⩽ Ra ⩽ 10 8 ) , nanoparticle volume fractions ( 0 ⩽ ϕ ⩽ 0.2 ), phase deviations ( 0 ⩽ γ ⩽ π ), amplitude ratios ( 0 ⩽ ε ⩽ 1 ), wall to nanofluid thermal conductivity ratios ( 0.44 ⩽ K r ⩽ 23.8 ) and wall thickness to height ratios ( 0 ⩽ S ⩽ 0.7 ). Comparisons with previously published work verify good agreement with the proposed method. Detailed computational results for the influence of the various parameters on streamlines, heatlines, isotherms, and the overall heat transfer are shown graphically. It is found that the heat transfer rate is significantly enhanced by incrementing the solid wall thickness. Different values of the thermal conductivity ratio are shown to depict a variety of enhancements for the heat transfer rate. [ABSTRACT FROM AUTHOR]

Abstract: Convection in a square cavity with a free surface and heated from the side is visualized and analyzed by the heatline concept. The temperature gradient is applied along the top free surface and the heat balance at the surface is assumed to obey Newton’s law of cooling. The finite difference method has been used to solve the dimensionless governing equations. The governing parameters considered are the Marangoni number (0⩽ Ma ⩽1000), the Biot number (0⩽ Bi ⩽6) and the Prandtl number (0.054⩽ Pr ⩽6.2). The flows of heat and fluid are of a similar type except at a strong cooling condition. The heat transfer performance presents a minimum at Marangoni number of roughly 100, 200 and 600 for the cavity filled with liquid metal, mixture of noble gases and air, respectively. [Copyright &y& Elsevier]

Development of modern heat exchangers or solar collectors is related to the analysis of working fluid flow and heat transfer within different channels. The energy transport enhancement can be reached by including nanofluids as working media and irregular channels to intensify the heat removal. The present research is devoted to computational analysis of nanosuspension forced convection in a horizontal wavy channel under the impact of heating from the upper wavy surface. The single-phase nanofluid approach with experimentally-based correlations for viscosity and thermal conductivity holds implemented for an investigation in combination with Newton's second law for the description of the motion of the nanoparticle within the channel. The formulated boundary-value problem has been worked out by the finite element technique. Rules of Reynolds number, number of channel waviness, and dimensionless time on nanoliquid flow, energy transport and nanoparticles motion within the channel as well as average parameters. It has occurred that a rise from Reynolds number characterizes a narrowing of the fluid tube within the channel with an improvement of the average velocity and average Nusselt number. Augmentation of the channel waviness number results in an increment of the average particles velocity and average temperature. [Display omitted] [ABSTRACT FROM AUTHOR]