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This paper aims to working out exact solutions for the boundary layer flow of some nanofluids over porous stretching/shrinking surfaces with different configurations. To serve to this aim, five types of nanoparticles together with the water as base fluid are under consideration, namely, Ag, Cu, CuO, Al₂O₃ and TiO₂.

The physical flow is affected by the presence of velocity slip as well as temperature jump conditions.

The knowledge on the influences of nanoparticle volume fraction on the practically significant parameters, such as the skin friction and the rate of heat transfer, for the above considered nanofluids, is easy to gain from the extracted explicit formulas.

Particularly, formulas clearly point that the heat transfer rate is not only dependent on the thermal conductivity of the material but it also highly relies on the heat capacitance as well as the density of the nanofluid under consideration.

This paper aims to seek purely analytical results relying on the physical parameters including the temperature jump parameter.

The exponential fin profiles and heat transfer enhancement influenced by a temperature jump at the base are the main targets of this paper.

The introduced temperature slip at the base penetrates through the surface of the fin and reorganizes the distribution of temperature all over the surface. The overall impact of the temperature jump on the fin efficiency is such that it acts to lower the fin efficiency. However, the efficiency of the exponential fin is increasing for growing shape exponential fins as compared to the rectangular and decaying ones. Hence, exponential fins amenable to certain temperature jump has significance in technological cooling processes. Finally, the optimum dimensions regarding the base fin thickness and the fin length of the exponential profiles are assessed by means of optimizing the base heat transfer rate given a cross-sectional area.

Exact solutions are provided for optimum exponential type fins subjected to a temperature jump. The optimum dimensions regarding the base fin thickness and the fin length of the exponential profiles are assessed.

This study aims to numerically simulate the flow induced by a radially expanding/contracting and rotating sphere with suction. In the absence of rotation, one-dimensional flow motion occurs as expected. Otherwise, centrifugal force slows down the induced flow motion, in addition to the radial movement of the surface.

The present work is devoted to the analysis of a rotating permeable sphere. The sphere, because it is elastic, is allowed to expand or contract uniformly in the radial direction while rotating.

Numerical simulations of the governing equation in spherical coordinates are supported by a perturbation approach. It is found that the equatorial region is effectively smoothen out by the wall suction in non-expanding, expanding and contracting wall deformation cases. The radial inward flow in the vicinity of the equator is no longer valid in the case of sphere expansion, and strong suction causes nearly constant radial suction velocities. More fluid is sucked radially inward near the pole region when wall contraction is active.

The problem is set up for the first time in the literature. It is determined physically, the wall expansion mechanism requires more torque with less drag.

The purpose of the present study is to explore a three-dimensional rotating flow of water-based nanofluids caused by an infinite rotating disk.

Mathematical formulation is performed using the well-known Buongiorno model which accounts for the combined influence of Brownian motion and thermophoresis. The recently suggested condition of passively controlled wall nanoparticle volume fraction has been adopted.

The results reveal that temperature decreases with an increase in thermophoresis parameter, whereas it is negligibly affected with a variation in the Brownian motion parameter. Axial velocity is negative because of the downward flow in the vertical direction.

Two- and three-dimensional streamlines are also sketched and discussed. The computations are found to be in very good agreement with the those of existing studies in the literature for pure fluid.

The fluid flow and heat transfer between a rotating cone above a stretching disk is the prime purpose of the current work. Making use of suitable similarity transformations, it is shown that the physical phenomenon is represented by a system of similarity equations, which is compatible with that of literature in the absence of wall expansion.

Numerical simulation of the system enables us to seize the physical character of fluid filling the conical section as well as of the heat transfer, from small to adequately large gap sizes. How the surface expansion will contribute to the momentum and thermal layers; moreover, to the swirl angle from the disk wall, and heat transports from the cone and disk surfaces is studied in detail.

The results are clear evidences that the wall stretching completely changes the flow and heat behaviors within the conical gap. For instance, the centripetal/centrifugal flow properties of disk/cone are completely altered and the flow swirling angles are increased by means of the wall deformation.

The original value is that at small gap angles faster expansion of the wall overall leads to near-disk surface cooling, while causing the heated region near the cone surface, which has physical implications in practical applications.

The purpose of this study is to target the solution of nonlinear porous fin problem. In contrast to the various complicated numerical or analytical approximate procedures existing in the literature used to approximate the temperature field over a porous fin, this study outlines a direct method based on series expansion of the temperature in the vicinity of the mounted surface, eventually requiring no numerical treatment at all to resolve the temperature field.

This study uses a direct method based on series expansion of the temperature in the vicinity of the mounted surface, eventually requiring no numerical treatment at all to resolve the temperature field.

Explicit closed-form formulae for the fin tip temperature as well as for the heat transfer rate, hence for the fin efficiency, which are functions of the porosity parameter and Biot number, are provided. The thresholds and the convergence regions regarding the physical parameters of the resulting approximations are easy to determine from the residual formula.

The novelty of the method is that the accuracy of the solution is controllable and can be gained up to any significant digit of desire by increasing the number of terms in the series solution.

This paper aims to revisite the traditional Adomian decomposition method frequently used for the solution of highly nonlinear extended surface problems in order to understand the heat transfer enhancement phenomenon. It is modified to include a parameter adjusting and controlling the convergence of the resulting Adomian series.

It is shown that without such a convergence control parameter, some of the published data in the literature concerning the problem are lacking accuracy or the worst is untrustful. With the proposed amendment over the classical Adomian decomposition method, it is easy to gain the range of parameters guaranteeing the convergence of the Adomian series.

With the presented improvement, the reliable behavior of the fin tip temperature and the fin efficiency of the most interested from practical perspective are easily predicted.

The relevant future studies involving the fin problems covering many physical nonlinear properties must be properly treated as guided in this paper, while the Adomian decomposition method is adopted for the solution procedure.

This paper aims to present an elegant exact solution in terms of elementary functions for a special pin fin without the classical length-of-arc approximation.

The temperature distribution along the fin and the surface function, both being the functions of a shape parameter, is inversely proportional to each other. The specialty of the spine is such that its shape and temperature profile are linked for a given Biot number.

Exact formulas for the pin fin tip temperature, pin fin base heat transfer rate, surface area of the spine and thermal fin efficiency are also given.

Without the traditional arc length assumption, the pin fin is shown to be an effective extended surface to remove the excessive heat from the hot surface it is pinned to. Optimum pin fin dimensions leading to the maximum base heat transfer rate are also worked out for a specified fin volume.

The onset of Darcy–Benard convection in a fluid-saturated porous layer within channeled walls can be through either the convectively amplified perturbations or absolutely unstable modes. The convective type route to formation of cellular forms has received much more interest in the literature than the absolute mode. This paper aims to explore the absolute instability mechanism on triggering the Benard convection in the presence of a uniform magnetic field acting perpendicular to the channel walls.

Pursuing a completely theoretical linear stability approach, the locus of wavenumbers and critical Rayleigh numbers with respect to varying Peclet numbers leading to zero complex group velocity, and hence the absolute instability onset, is formulated in closed form. The formulae also incorporate the influence of fluid movement through the porous layer.

Wanenumbers are found to be increasing in magnitude under the effect of the magnetic field. Although the magnetic field expectedly behaves in favor of stabilizing the convection through both convective and absolute instabilities by pushing the threshold value of Rayleigh number to higher values, a peculiarity exists in such a manner that the stabilizing effect of magnetic field can no longer compete against the absolute instability mechanism within the magnetized field after some critical location possessing negative part of the wavenumber.

The significant outcome is attributed to the exchange of instabilities as far as the absolute instability mechanism is concerned. Magnetic field is always stabilizing and no such trend is observed regarding the convective type instability.

The classical integer derivative diffusionmodels for fluid flow within a channel of parallel walls, for heat transfer within a rectangular fin and for impulsive acceleration of a quiescent Newtonian fluid within a circular pipe are initially generalized by introducing fractional derivatives. The purpose of this paper is to represent solutions as steady and transient parts. Afterward, making use of separation of variables, a fractional Sturm–Liouville eigenvalue task is posed whose eigenvalues and eigenfunctions enable us to write down the transient solution in the Fourier series involving also Mittag–Leffler function. An alternative solution based on the Laplace transform method is also provided.

In this work, an analytical formulation is presented concerning the transient and passage to steady state in fluid flow and heat transfer within the diffusion fractional models.

From the closed-form solutions, it is clear to visualize the start-up process of physical diffusion phenomena in fractional order models. In particular, impacts of fractional derivative in different time regimes are clarified, namely, the early time zone of acceleration, the transition zone and the late time regime of deceleration.

With the newly developing field of fractional calculus, the classical heat and mass transfer analysis has been modified to account for the fractional order derivative concept.