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The purpose of this paper is to model the boundary layer flow and heat transfer of dusty fluid with suspended nanoparticles over a stretching surface. The effect of multiple slip and nonlinear thermal radiation is taken into the account. Adequate similarity transformations are used to obtain a set of nonlinear ordinary differential equations to govern formulated problem. The resultant non-dimensionalized boundary value problem is solved numerically using the RKF-45 method. The profiles for velocity and temperature, which are controlled by thermophysical parameters, are presented graphically. Based on these plots, the conclusion is given and the obtained numerical results are tabulated. Observed interesting fact is that the SiO₂-water nanoparticles show a thicker thermal boundary layer than TiO₂-water nanoparticles.

The governing partial differential equations are approximated to a system of nonlinear ordinary differential equations by using suitable similarity transformations. An effective fourth–fifth-order Runge–Kutta–Fehlberg integration scheme numerically solves these equations along with a shooting technique. The effects of various pertinent parameters on the flow and heat transfer are examined.

Present results have an excellent agreement with previous published results in the limiting cases. The values of skin friction and wall temperature for different governing parameters are also tabulated. It is demonstrated that the SiO₂-water nanoparticles show a thicker thermal boundary layer than TiO₂-water nanoparticles. It is interesting to note that the dusty nanofluids are found to have higher thermal conductivity.

This paper is a new work related to comparative study of TiO₂ and SiO₂ nanoparticles in heat transfer of dusty fluid flow.

The theory of micropolar fluids was formulated by Eringen. A similarity solution is used to investigate the flow of such a fluid driven by a continuous porous plate. Continuous surfaces are surfaces such as polymer sheets or filaments continuously drawn from a dye. Within the framework of the boundary‐layer theory, similarity transformation is used for the specific case when the wall velocity varies linearly with component. A physical characteristic of the fluid is used as a perturbation parameter to obtain a first estimate solution. Using a perturbation technique, analytical solutions for large transfer rates are presented. Then, a quasilinearization is used to obtain a complete solution. Good agreement is found between solutions obtained with these different methods and with the numerical data in Hassanien and Gorla (1990).

The purpose of this paper is to study two-dimensional nonlinear radiative-convective, steady-state boundary layer flow of non-Newtonian power-law nanofluids along a flat vertical plate in a saturated porous medium taking into account thermal and mass convective boundary conditions numerically.

The governing equations are reduced to a set of coupled nonlinear ordinary differential equations with relevant boundary conditions. The transformed equations are then solved using the Runge-Kutta-Fehlberg fourth-fifth order numerical method with Maple 17 and Adomian decomposition method (ADM) in Mathematica.

The transformed equations are controlled by the parameter: power-law exponent, n; temperature ratio, Tr; Rosseland radiation-conduction, R; conduction-convection, Nc; and diffusion-convection, Nd. Temperature and nanoparticle concentration is enhanced with convection-diffusion parameter as are temperatures. Velocities are depressed with greater power-law rheological index whereas temperatures are elevated. Increasing thermal radiation flux accelerate the flow but to strongly heat the boundary layer. Very good correlation of the Maple solutions with previous stationary free stream and ADM solutions for a moving free stream, are obtained.

The study is relevant to high temperature nano-polymer manufacturing systems.

Lie symmetry group is used for the first time to transform the governing equations into a set of coupled nonlinear ordinary differential equations with relevant boundary conditions. The study is relevant to high temperature nano-polymer manufacturing systems.

The study of the electro-osmotic forces (EOF) in the flow of the boundary layer has been a topic of interest in biomedical engineering and other engineering fields. The purpose of this paper is to develop an innovative mathematical model for electro-osmotic boundary layer flow. This type of fluid flow requires sophisticated mathematical models and numerical simulations.

The effect of EOF on the boundary layer Williamson fluid model containing a gyrotactic microorganism through a non-Darcian flow (Forchheimer model) is investigated. The problem is formulated mathematically by a system of non-linear partial differential equations (PDEs). By using suitable transformations, the PDEs system is transformed into a system of non-linear ordinary differential equations subjected to the appropriate boundary conditions. Those equations are solved numerically using the finite difference method.

The boundary layer velocity is lower in the case of non-Newtonian fluid when it is compared with that for a Newtonian fluid. The electro-osmotic parameter makes an increase in the velocity of the boundary layer. The boundary layer velocity is lower in the case of non-Darcian fluid when it is compared with Darcian fluid and as the Forchheimer parameter increases the behavior of the velocity becomes more closely. Entropy generation decays speedily far away from the wall and an opposite effect occurs on the Bejan number behavior.

The present outcomes are enriched to give valuable information for the research scientists in the field of biomedical engineering and other engineering fields. Also, the proposed outcomes are hopefully beneficial for the experimental investigation of the electroosmotic forces on flows with non-Newtonian models and containing a gyrotactic microorganism.

The study of novel exponential heat source (EHS) phenomena across a flowing fluid with the suspension of nanoparticles over a rotating plate in the presence of Hall current and chemical reaction has been an open question. Therefore, the purpose of this paper is to investigate the impact of EHS in the transport of nanofluid under the influence of strong magnetic dipole (Hall effect), chemical reaction and temperature-dependent heat source (THS) effects. The Khanafer-Vafai-Lightstone model is used for nanofluid and the thermophysical properties of nanofluid are calculated from mixture theory and phenomenological laws. The simulation of the flow is also carried out using the appropriate values of the empirical shape factor for five different particle shapes (i.e. sphere, hexahedron, tetrahedron, column and lamina).

Using Laplace transform technique, exact solutions are presented for the governing nonlinear equations. Graphical illustrations are pointed out to represent the impact of involved parameters in a comprehensive way. The numeric data of the density, thermal conductivity, dynamic viscosity, specific heat, Prandtl number and Nusselt number for 20 different nanofluids are presented.

It is established that the nanofluid enhances the heat transfer rate of the working fluids; the nanoparticles also cause an increase of viscous. The impact of EHS advances the heat transfer characteristics significantly than usual thermal-based heat source (THS).

The effectiveness of EHS phenomena in the dynamics of nanofluid over a rotating plate with Hall current, chemical reaction and THS effects is first time investigated.

We determine the effects of micro‐inertia density and the vortex viscosity on laminar free convection boundary layer flow of a thermomicropolar fluid past a vertical plate with exponentially varying surface temperature as well as surface heat flux. The governing nonsimilarity boundary layer equations are analyzed using: first, a series solution for small ξ (a scaled streamwise distribution of micro‐inertia density), second, an asymptotic solution for large ξ and, third, a full numerical solution implicit finite difference method together with Keller‐box scheme. Results are expressed in terms of local skin friction and local Nusselt number. The effects of varying the vortex viscosity parameter, Δ, surface temperature and the surface heat flux gradient n and m respectively against ξ for fluids having Prandtl number equals 0.72 and 7.0 are determined.

The purpose of this paper is to conduct a numerical study of the convection heat transfer in porous media by the homotopy analysis method (HAM). The geometry considered is that of a rectangular profile fin. The porous fin allows the flow to infiltrate through it and solid-fluid interaction takes place. This study is performed using Darcy's model to formulate heat transfer equation. To study the thermal performance, three types of cases are considered namely long fin, finite length fin with insulated tip and finite length fin with tip exposed. The theory section addresses the derived governing equation. The effects of the porosity parameter Sh, radiation parameter G and temperature ratio CT on the dimensionless temperature distribution and heat transfer rate are discussed. The results suggest that the radiation transfers more heat than a similar model without radiation. The auxiliary parameter in the HAM is derived by using the averaged residual error concept which significantly reduces the computational time. The use of optimal auxiliary parameter provides a superior control on the convergence and accuracy of the analytic solution.

This study is performed using Darcy's model to formulate heat transfer equation. To study the thermal performance, three types of cases are considered namely long fin, finite length fin with insulated tip and finite length fin with tip exposed. The effects of the porosity parameter Sh, radiation parameter G and temperature ratio CT on the dimensionless temperature distribution and heat transfer rate are discussed.

The HAM has been successfully applied for the thermal performance of a porous fin of rectangular profile. Solutions are derived for three cases of tip condition: an infinitely long fin with tip in thermal equilibrium with the ambient, a finite fin with an insulated tip and a finite fin with a convective tip. The performance of the fin depends on three dimensionless parameters; porosity parameter Sh, radiation-conduction parameter G and a dimensionless temperature relating the ambient and base temperatures. The results show that the base heat flow increases when the permeability of the medium is high and/or when the buoyancy effect induced in the fluid is strong. The base heat flow is enhanced as the surface radiation or the tip Biot number increases.

The analysis is made for the Darcy's model. Non-Darcy effects will be investigated in a future work.

The approach is useful in enhancing heat transfer rates.

The results of the study will be interested to the researchers of the field of heat exchanger designers.

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.

In this paper, temperature distribution and fin efficiency in a moving porous fin have been discussed. The heat transfer equation is formulated by using Darcy's model. Heat transfer coefficient and thermal conductivity vary with temperature. The surface emissivity of the fin varies with temperature as well as with wavelength. Thermal conductivity is taken as a linear and quadratic form of temperature. The entire analysis of the paper is presented in non-dimensional form.

In this study, a new mathematical model is investigated. The novelty of this model is surface emissivity which is considered temperature and wavelength dependent. Another interesting point is the addition of porous material. The Legendre wavelet collocation method has been used to solve the nonlinear heat transfer equation. Numerical simulations are carried out in MATLAB software.

An attempt has been made to discuss temperature distribution in the presence of porosity and wavelength-temperature-dependent surface emissivity. The effect of various parameters on temperature has been discussed, including thermal conductivity, emissivity, convection-radiation, Peclet number, sink temperature, exponent “n” and porosity. Fin efficiency is also calculated for some parameters. According to the study, heat transfer rate increases with higher radiation-convection, emissivity, wavelength and porosity parameters.

The numerical results are carried out by using the Legendre wavelet collocation method, which has been compared with exact results in a particular case and found to be in good agreement. The percent error is calculated to find the error between the current method and the exact result. A comparison of the obtained results with the previous data is presented to validate the numerical results.

The purpose of this paper is to numerically solve the problem of an unsteady squeezing three-dimensional flow and heat transfer of a nanofluid in rotating vertical channel of stretching left plane. The fluid is assumed to be Newtonian, incompressible and electrically conducting embedded with nanoparticles. Effect of internal heat generation/ absorption is also considered in energy equation. Four different types of nanoparticles are considered, namely, copper (Cu), alumina (Al₂O₃), silver (Ag) and titanium oxide (TiO₂) with the base fluid as water. Maxwell-Garnetts and Brinkman models are, respectively, employed to calculate the effective thermal conductivity and viscosity of the nanofluid.

Using suitable similarity transformations, the governing partial differential equations are transformed into set of ordinary differential equations. Resultant equations have been solved numerically using Runge-Kutta-Fehlberg fourth fifth order method for different values of the governing parameters. Effects of pertinent parameters on normal, axial and tangential components of velocity and temperature distributions are presented through graphs and discussed in detail. Further, effects of nanoparticle volume fraction, squeezing parameter, suction/injection parameter and heat source/sink parameter on skin friction and local Nusselt number profiles for different nanoparticles are presented in tables and analyzed.

Squeezing effect enhances the temperature field and consequently reduces the heat transfer rate. Large values of mixed convection parameter showed a significant effect on velocity components. Also, in many heat transfer applications, nanofluids are potentially useful because of their novel properties. They exhibit high-thermal conductivity compared to the base fluids. Further, squeezing and rotation effects are desirable in control the heat transfer.

Three-dimensional mixed convection flows over in rotating vertical channel filled with nanofluid are very rare in the literature. Mixed convection squeezing three-dimensional flow in a rotating channel filled with nanofluid is first time investigated.