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The purpose of this study is to conduct a numerical computation to analyse the thermal attribute and heat transfer phenomenon of a fully wetted porous fin of a longitudinal profile. The fin considered is that of a functionally graded material (FGM). Based on the spatial dependency of thermal conductivity, three cases such as linear, quadratic and exponential FGMs are analysed.

The governing equations are nondimensionalised and solved by applying Runge-Kutta-Fehlberg fourth-fifth order technique.

The parametric investigation is executed to access the significance of the pertinent parameters on the thermal feature of the fin and heat transmit rate. The outcomes are portrayed in a graphical form.

No such study has yet been published in the literature.

In heat transfer, fluids and nanoparticles can provide new innovative technologies with potential to adapt the heat transfer fluid’s thermal properties through control over particle size, shape and others. This paper aims to examine the effects of spherical and non-spherical (cylinder, disk, platelets, etc.) shapes of silver (Ag) nanoparticles on heat transfer enhancement and inherent irreversibility in hydromagnetic water base nanoliquid flow over a convectively heated stretching sheet with heat generation/absorption.

Applying suitable similarity constraints, the model partial differential equations are transformed into a set of nonlinear ordinary differential equations. Solutions are obtained analytically via optimal homotopy asymptotic method (OHAM) and numerically via shooting technique coupled with the Runge-Kutta-Fehlberg (RK-F) method.

The impact of Ag nanoparticle’s shape along with other germane factors, such as Biot number, magnetic field, solid volume fraction and heat source/sink on velocity and thermal profiles, Nusselt number, skin friction coefficient, heat transfer enhancement, rate of entropy generation and irreversibility ratio, are scrutinized via graphical simulations and discussed. This study revealed that cylindrical shape Ag nanoparticles generate high entropy and fluid friction irreversibility, whereas disk shape Ag nanoparticles exhibit high transfer enhancement rate. Moreover, a boost in magnetic field intensity, volume-fraction parameter and Biot number enhances the thermal boundary layer thickness.

The main objective of this work is to examine the different Ag nanoparticles shape effects on the heat transfer enhancement and inherent irreversibility owing to hydromagnetic nanoliquid flow past a convectively heated stretching sheet with heat source/sink, which has not been yet studied. It is hope that this study will bridge the gap in the present literature and serve as impetus to scholars, engineers and industries for more exploration in this direction. The intrinsic nonlinearity of the model equations precludes its exact solution; hence, OHAM and shooting technique coupled with the RK-F method have been used to numerically tackle the problem. Pertinent results are discussed quantitatively and displayed graphically and in tabular form.

This report offers the detailed investigation of Couette–Poiseuille flow of nanoliquid with varying viscosity. The analysis is carried out by considering flow between two parallel plates in a rotating permeable channel with the aid of nonlinear thermal radiation and Hall effect. The predominant equations governing the physical phenomenon are demonstrated using the Buongiorno model.

Numerical computation for the demonstrated physical problem is achieved through the implementation of the Runge–Kutta–Fehlberg fourth–fifth-order method along with shooting technique.

The theoretical view of Brownian motion, nonlinear radiation, Hall effect and thermophoresis parameter is presented graphically.

It is revealed that flow velocity increases with the upper wall motion parameter and magnetic field. Also, it is established that an increase in the Nusselt number is achieved for increasing values of nonlinear radiation parameter.

This paper aims to study the temperature performance with natural convection and radiation effect on a porous fin in fully wet condition.

The finite element method (FEM) is applied to generate numerical solution of the obtained non-dimensional ordinary differential equation containing highly nonlinear terms. The parameters which impact on the heat transfer of fin have been scrutinized by means of plotted graphs.

The porous fin is taken for the analysis in radial profile moving with constant velocity. Here, the thermal conductivity is considered to be temperature dependent. The Darcy’s model has been implemented to study the heat transfer analysis.

The paper is genuine in its type, and there are hardly any works on fins as per the authors’ knowledge.

The influence of radiation on nanoliquid flow through a vertical microchannel in the presence of heat source is examined. This study aims to investigate the efficiency of multi-walled carbon nanotube (MWCNT) considering water and engine oil as base fluid.

Nondimensional variables are used to obtain the dimensionless physical model. The solutions are computed numerically via Runge–Kutta–Fehlberg integration scheme.

It is established that (k_nf/k_f)_Lamina > (k_nf/k_f)_Column > (k_nf/k_f)_Tetrahedron > (k_nf/k_f)_Hexahedron > (k_nf/k_f)_Sphere.

Thermal conductivity of MWCNT is analyzed using different models. Also, it is remarked that Xue model exhibits higher thermal conductivity for MWCNT compared to Maxwell model, Yu-Choi model and Hamilton-Crosser model.

The purpose of this paper is to study the thermal behaviour of a fully wet porous fin of longitudinal profile. The significance of radiative and convective heat transfer has been scrutinised along with the simultaneous variation of surface emissivity, heat transfer coefficient and thermal conductivity with temperature. The emissivity of the surface and the thermal conductivity are considered as linear functions of the local temperature between fin and the ambient. Darcy’s model was considered to formulate the heat transfer equation. According to this, the porous fin permits the flow to penetrate through it and solid–fluid interaction occurs.

Runge–Kutta–Fehlberg fourth–fifth-order method has been used to solve the reduced non-dimensionalized ordinary differential equation involving highly nonlinear terms.

The impact of pertinent parameters, such as convective parameter, radiative parameter, conductivity parameter, emissivity parameter, wet porous parameter, etc., on the temperature profiles were elaborated mathematically with the plotted graphs. The heat transfer from the fin enhances with the rise in convective parameter.

The wet nature of the fin enhances heat transfer and in many practical applications the parameters, such as thermal conductivity, heat transfer coefficient as well as surface emissivity, vary with temperature. Hence, the main objective of the current study is to depict the significance of simultaneous variation in surface emissivity, heat transfer coefficient and thermal conductivity with respect to temperature under natural convection and radiation condition in a totally wetted longitudinal porous fin.

The purpose of this paper is to study the thermal behaviour of radial porous fin wetted with nanofluid containing different shaped nanoparticles in the presence of natural convection and radiation. Here, the nanofluid suspended with molybdenum disulfide nanoparticle with base fluid as water is considered. The influence of non-spherical nanoparticles such as platelet, cylinder, brick and blade shapes is also investigated.

The modeled equations are non-dimensionalized and solved numerically via Runge–Kutta–Fehlberg method combined with shooting scheme.

The flow natures of the pertinent parameter are represented graphically and discussed their physical significance. From the validation of obtained outcome, it is found that the use nanofluid has significant influence on heat transfer rate. Among platelet, cylinder, brick and blade shapes, brick-shaped nanoparticle shows better heat transfer rate.

The present paper deals with an analysis of the flow of molybdenum disulfide nanoparticles suspended in water over a porous fin of a radial profile. The effect of differently shaped nanoparticles on the heat transfer enhancement through the radial porous fin is investigated for the first time. The natural convection and radiation effects are also considered. The modeled equations are non-dimensionalized and solved numerically via Runge–Kutta–Fehlberg method combined with shooting scheme. The effect of pertinent parameters on temperature field is examined. From the validation of obtained outcome it is found that the use nanofluid has significant influence on heat transfer rate. Among platelet, cylinder, brick and blade shapes, brick-shaped nanoparticle shows better heat transfer rate.

This study aims to portray the systematic study of hybrid nanofluid with particle shape effect on significant heat transfer enhancement. The steady flow of hybrid nanoliquid in a microchannel with the aid of porous medium has been considered. The dispersion of copper and Al₂O₃ in water is taken as hybrid mixture. The impact of thermal radiation, slip length and convective conditions on flow and thermal features are examined numerically.

The modelled equations are made dimensionless by means of nondimensional entities. The solutions are computed numerically by the implementation of Runge–Kutta-based shooting technique. The results depict that the shape of hybrid mixtures plays a significant role in convective heat transfer. Relevant results on flow velocity, temperature, Nusselt number and friction factor for various physical constraints have been perused. The obtained outcomes are displayed graphically.

The acquired results depict that Nusselt number augments with Eckert number and solid volume fraction of hybrid nanoparticles, which has a vibrant role in enriching the heat transfer coefficient. Also, it is emphasized that the Nusselt number is larger for blade-shaped nanoparticle compared to other shapes.

The analysis of individual effect of thermal radiation, Joule heating, viscous dissipation and magnetic field on the flow of Cu and Al₂O₃ hybrid nanofluid through microchannel has vivacious role in augmenting heat transmission. Along with this, the impact of porous medium, shape factor, slip and convective peripheral conditions are also emphasized.

The purpose of this paper is to study the thermal behavior of radial porous fin surrounded by water-base copper nanoparticles under the influence of radiation.

In order to optimize the response variable, the authors perform sensitivity analysis with the aid of response surface methodology (RSM). Moreover, this study enlightens the applications of artificial neural networks (ANN) for predicting the temperature gradient. The governing modeled equations are firstly non-dimensionalized and then solved with the aid of Runge–Kutta fourth order together with the shooting method in order to guess the initial conditions.

Numerical results are analyzed and presented in the form of tables and graphs. This study reveals that the temperature of the fin is decreasing as the wet porous parameter increases (m₂) and the temperature for 10% concentration of nanoparticles are higher than 5 and 1%. Physical parameters involved in the study are analyzed and processed through RSM. It is come to know that sensitivity of temperature gradient to radiative parameter (Nr) and convective parameter (Nc) is positive and negative to dimensionless ambient temperature (θ_a). Furthermore, after ANN training it can be argued that the established model can efficiently be used to predict the temperature gradient over a radial porous fin for the copper-water nanofluid flow.

To the best of our knowledge, only a few attempts have been made to analyze the thermal behavior of radial porous fin surrounded by copper-based nanofluid under the influence of radiation and convection.

The present study aims to encompass the bidirectional magnetized flowing of a hybrid-nanofluid over an unsteady stretching device with the inclusion of thermal radiation and entropy generation. Brick-shaped nanoparticles (zinc-oxide and ceria) are suspended in water, serving as the base-fluid to observe the performance of the hybrid mixture. The Maxwell thermal conductivity relation is employed to link the thermophysical attributes of the hybrid mixture with the host liquid. Additionally, a heat source/sink term is incorporated in the energy balance to enhance the impact of the investigation. Both prescribed-surface-temperature (PST) and prescribed-heat-flux (PHF) conditions are applied to inspect the thermal performance of the hybrid nanofluid.

The transport equations in Cartesian configuration are transformed into ordinary differential equations (ODEs), and an efficient method, namely the Keller-Box method (KBM), is utilized to solve the transformed system. Postprocessing is conducted to visually represent the velocity profile, thermal distribution, skin-friction coefficients, Bejan number, Nusselt number and entropy generation function against the variations of the involved parameters.

It is observed that more entropy is generated due to the increases in temperature difference and radiation parameters. The Bejan number initially declines but then improves with higher estimations of unsteadiness and Hartmann number. Overall, the thermal performance of the system is developed for the PST scenario than the PHF scenario for different estimations of the involved constraints.

To the best of the authors' knowledge, no investigation has been reported yet that explains the bidirectional flow of a CeO2-ZnO/water hybrid nanofluid with the combined effects of prescribed thermal aspects (PST and PHF) and entropy generation.