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This study aims to investigate the flow and heat transfer characteristics of a Bingham viscoplastic fluid subjected to the combined effects of axial rotation and radial stretching of a circular disk. Building upon existing models for Bingham fluids on stationary walls, we extend the formulation to incorporate the effects of a linearly stretching disk using von Kármán similarity transformations.

The resulting system of nonlinear ordinary differential equations is solved to characterize the flow and thermal fields. Three dimensionless parameters govern the momentum layer: a swirling number capturing the balance between rotation and stretching, a Bingham number characterizing the fluid’s yield stress and a modified Reynolds number incorporating the disk stretching. The Prandtl number controls the thermal response.

For purely stretching flows, a two-dimensional flow structure emerges. However, the introduction of rotation induces three-dimensional flow behavior. Unlike previous studies suggesting that moderate Bingham numbers are sufficient for non-Newtonian effects on purely revolving disks, the findings indicate that significantly higher yield stresses are required to observe non-Newtonian characteristics under radial stretching conditions. This difference can be attributed to the enhancing influence of wall movement on the fluid dynamics. At high Bingham numbers, a two-layer flow structure develops, comprising an unyielded plug region above the disk and a yielded shear layer adjacent to the wall. The von Kármán viscous pump mechanism drives the Bingham flow within this regime.

Physical quantities such as drag force due to wall shear stress, torque resulting from tangential shear stress and Nusselt number are extracted from the quantitative data.

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.

This study aims to explore the hydrodynamic and thermal behavior of an incompressible fluid flowing between uniformly corotating disks with finite radii. The narrow gap between the disks necessitates accounting for slip flow in the radial direction, departing from the classic no-slip model.

The author uses a perturbation approach and derives full analytical approximations to the Navier–Stokes and energy equations up to the second order. Higher-order truncations require significant numerical effort due to the complexity of the resulting expressions.

For the no-slip case, the momentum solutions perfectly match those found in the literature. The author then demonstrates the convergence of the series solutions with slip for selected specific parameter sets. Finally, the author investigates the impact of both slip and Reynolds number on the velocity field, pressure and temperature field between the inlet and outlet positions.

The key finding is that both factors lead to thinner momentum and thermal boundary layers within the corotating finite disk setup, resulting in cooler disk surfaces.

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.