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The purpose of this paper is to consider unsteady free convection flow of a dissipative fluid past an exponentially accelerated infinite vertical porous plate in the presence of Newtonian heating and mass diffusion.

The problem is governed by coupled non-linear partial differential equations with appropriate boundary conditions. A Galerkin finite element numerical solution is developed to solve the resulting well-posed two-point boundary value problem. It is a powerful, stable technique which provides excellent convergence and versatility in accommodating coupled systems of ordinary and partial differential equations.

It is found that the skin friction coefficient increases with increases in either of the Eckert number, thermal Grashof number, mass Grashof number or time whereas it decreases with increases in either of the suction parameter, Schmidt number or the acceleration parameter for both air and water. The skin friction coefficient is also found to decrease with increases in the values of the Prandtl number. In addition, it is found that the rate of heat transfer increases with an increase in the suction parameter and decreases with an increase in the Eckert number for both air and water. Lastly, it is found that the rate of heat transfer increases with increasing values of the Prandtl number and decreases with increasing time for all values of the Prandtl number.

The present study has considered only Newtonian fluids. Future studies will address non-Newtonian liquids.

A very useful source of information for researchers on the subject of free convective flow over the surface when the rate of heat transfer from the surface is proportional to the local surface temperature.

This paper is relatively original and illustrates the effects of viscous dissipation on free convective flow past an exponentially accelerated infinite vertical porous plate with Newtonian heating and mass diffusion.

In various kinds of materials processes, heat and mass transfer control in nuclear phenomena, constructing buildings, turbines and electronic circuits, etc., there are numerous problems that cannot be enlightened by uniform wall temperature. To explore such physical phenomena researchers incorporate non-uniform or ramped temperature conditions at the boundary, the purpose of this paper is to achieve the closed-form solution of a time-dependent magnetohydrodynamic (MHD) boundary layer flow with heat and mass transfer of an electrically conducting non-Newtonian Casson fluid toward an infinite vertical plate subject to the ramped temperature and concentration (RTC). The consequences of chemical reaction in the mass equation and thermal radiation in the energy equation are encompassed in this analysis. The flow regime manifests with pertinent physical impacts of the magnetic field, thermal radiation, chemical reaction and heat generation/absorption. A first-order chemical reaction that is proportional to the concentration itself directly is assumed. The Rosseland approximation is adopted to describe the radiative heat flux in the energy equation.

The problem is formulated in terms of partial differential equations with the appropriate physical initial and boundary conditions. To make the governing equations dimensionless, some suitable non-dimensional variables are introduced. The resulting non-dimensional equations are solved analytically by applying the Laplace transform method. The mathematical expressions for skin friction, Nusselt number and Sherwood number are calculated and expressed in closed form. Impacts of various associated physical parameters on the pertinent flow quantities, namely, velocity, temperature and concentration profiles, skin friction, Nusselt number and Sherwood number, are demonstrated and analyzed via graphs and tables.

Graphical analysis reveals that the boundary layer flow and heat and mass transfer attributes are significantly varied for the embedded physical parameters in the case of constant temperature and concentration (CTC) as compared to RTC. It is worthy to note that the fluid velocity is high with CTC and lower for RTC. Also, the fluid velocity declines with the augmentation of the magnetic parameter. Moreover, growth in thermal radiation leads to a declination in the temperature profile.

The proposed model has relevance in numerous engineering and technical procedures including industries related to polymers, area of chemical productions, nuclear energy, electronics and aerodynamics. Encouraged by such applications, the present work is undertaken.

Literature review unveils that sundry studies have been carried out in the presence of uniform wall temperature. Few studies have been conducted by considering non-uniform or ramped wall temperature and concentration. The authors are focused on an analytical investigation of an unsteady MHD boundary layer flow with heat and mass transfer of non-Newtonian Casson fluid past a moving plate subject to the RTC at the plate. Based on the authors’ knowledge, the present study has, so far, not appeared in scientific communications. Obtained analytical solutions are verified by considering particular cases of the published works.

The purpose of this paper is to study the flow, heat and mass transfer of MHD Casson nanofluid due to an inclined stretching sheet using similarity transformation, the governing PDE’S equations of flow, heat and mass transfer are converted into ODE’S. The resulting non-linear ODE’S are solved numerically using an implicit finite difference method, which is known as Kellor-box method. The effects of various governing parameters on velocity, temperature and concentration are plotted for both Newtonian and non-Newtonian cases. The numerical values of skin friction, Nusselt number and Sherwood number are calculated and tabulated in various tables for different values of physical parameters. It is noticed that the effect of angle of inclination enhances the temperature and concentration profile whereas velocity decreases. The temperature decreases due to the increase in the parametric values of Pr and Gr due to thickening in the boundary layer.

Numerical method is applied to find the results.

Flow and heat transfer analysis w.r.t various flow and temperature are analyzed for different values of the physical parameters.

The numerical values of skin friction, Nusselt number and Sherwood number are calculated and tabulated in various tables for different values of physical parameters.

The study of the boundary layer flow, heat and mass transfer is important due to its applications in industries and many manufacturing processes such as aerodynamic extrusion of plastic sheets and cooling of metallic sheets in a cooling bath.

Here in this paper the authors have investigated the MHD boundary layer flow of a Casson nanofluid over an inclined stretching sheet along with the Newtonian nanofluid as a limited.

The purpose of this paper is to focus on MHD unsteady flow of Carreau fluid over a variable thickness melting surface in the presence of chemical reaction and non-uniform heat sink/source.

The flow governing partial differential equations are transformed into ordinary ones with the help of similarity transformations. The set of ODEs are solved by a shooting technique together with the R.K.–Fehlberg method. Further, the graphs are depicted to scrutinize the velocity, concentration and temperature fields of the Carreau fluid flow. The numerical values of friction factor, heat and mass transfer rates are tabulated.

The results are presented for both Newtonian and non-Newtonian fluid flow cases. The authors conclude that the nature of three typical fields and the physical quantities are alike in both cases. An increase in melting parameter slows down the velocity field and enhances the temperature and concentration fields. But an opposite outcome is noticed with thermal relaxation parameter. Also the elevating values of thermal relaxation parameter/ wall thickness parameter/Prandtl number inflate the mass and heat transfer rates.

This is a new research article in the field of heat and mass transfer in fluid flows. Cattaneo–Christov heat flux model is used. The surface of the flow is assumed to be melting.

Using turbulators, obstacles, ribs, corrugations, baffles and different tube geometry, and also various arrangements of these components have a noticeable effect on the shell and tube heat exchangers (STHEs) thermal-hydraulic performance. This study aims to investigate non-Newtonian fluid flow characteristics and heat transfer features of water and carboxyl methyl cellulose (H₂O 99.5%:0.5% CMC)-based Al₂O₃ nanofluid inside the STHE equipped with corrugated tubes and baffles using two-phase mixture model.

Five different corrugated tubes and two baffle shapes are studied numerically using finite volume method based on SIMPLEC algorithm using ANSYS-Fluent software.

Based on the obtained results, it is shown that for low-mass flow rates, the disk baffle (DB) has more heat transfer coefficient than that of segmental baffle (SB) configuration, while for mass flow rate more than 1 kg/s, using the SB leads to more heat transfer coefficient than that of DB configuration. Using the DB leads to higher thermal-hydraulic performance evaluation criteria (THPEC) than that of SB configuration in heat exchanger. The THPEC values are between 1.32 and 1.45.

Using inner, outer or inner/outer corrugations (outer circular rib and inner circular rib [OCR+ICR]) tubes for all mass flow rates can increase the THPEC significantly. Based on the present study, STHE with DB and OCR+ICR tubes configuration filled with water/CMC/Al₂O₃ with f = 1.5% and d_np = 100 nm is the optimum configuration. The value of THPEC in referred case was 1.73, while for outer corrugations and inner smooth, this value is between 1.34 and 1.57, and for outer smooth and inner corrugations, this value is between 1.33 and 1.52.

The purpose of this paper is to investigate the effects of thermal radiation and viscous dissipation on steady natural convection flow of a viscous incompressible fluid along a uniformly moving infinite vertical porous plate with Newtonian heating in the presence of transverse magnetic field. The governing non-linear boundary layer equations are solved by using homotopy analysis method (HAM). The effects of various system parameters on velocity and temperature fields are discussed graphically, and the numerical values for skin friction and Nusselt number are presented in tabular form.

The problem is formulated using the Boussinesq approximation under the effects of thermal radiation and transverse magnetic field. The resulting coupled system of non-linear differential equations is solved using HAM with appropriate boundary conditions for Newtonian heating of the plate. HAM is a powerful method which provides rapidly converging series solution for the velocity and temperature fields. The effects of Prandtl number, Grashof number, suction parameter, magnetic field parameter, radiation parameter and Eckert number on the fluid velocity, temperature, skin friction and Nusselt number have been investigated.

The HAM solution has been successfully applied to find the converging series solution for velocity and temperature fields in terms of pertinent system parameters. Comparison of the exact solution results agree well with the HAM solution results in the absence of Eckert number and this indicates that the HAM solutions are accurate. It is found that the velocity and temperature profiles decreases with the increase of thermal radiation and suction parameters. An increase in the magnetic field parameter leads to a rise in the fluid temperature and fall in the fluid velocity.

The present analysis is limited to steady state laminar natural convection flow only. Unsteady natural- /mixed-convection laminar flow in the presence of thermal radiation, chemical reaction and transverse magnetic field will be investigated in a future work.

The study provides very useful information for heat transfer engineers to understand the heat transfer rate when the moving vertical porous surface temperature is not known a prior. The present results have immediate relevance in the design of nuclear reactors where vertical moving porous plates are using as control rods.

The present research work is relatively original and illustrates the effects of thermal radiation, viscous dissipation and transverse magnetic field on natural convection flow past a uniformly moving infinite vertical porous plate with Newtonian heating.

The purpose of this paper is to highlight the effect of combined heat and mass transfer characteristics of magnetohydrodynamic (MHD) free convection flow of an electrically conducting Newtonian fluid on circular cylinder with uniform heat/mass flux, taking into consideration the effects of uniform transverse magnetic field and thermal radiation.

An analysis is performed to study the momentum, combined heat and mass transfer characteristics of MHD free convection flow past a circular cylinder surface under the effect of thermal radiation with uniform heat and mass flux. By using Lie group method, the infinitesimal generators of governing equations are calculated. Using the resulting generators for the boundary value problem, the equations are transformed into an ordinary differential system. Numerical solutions of the outcoming non‐linear differential equations are found by using a combination of a Runge–Kutta algorithm and shooting technique.

Application of a magnetic field normal to the flow of an electrically conducting fluid gives rise to a resistive force that acts in the direction opposite to that of the flow. This resistive force tends to slow down the motion of the fluid along the cylinder and causes increases in its temperature and concentration and hence the respective changes in the wall shear stress, local Nusselt and Sherwood numbers as the magnetic parameter, respectively are changed with various values of angle which is measured in degrees from the front stagnation point on the surface. It is noted that these coefficients reduced as the magnetic parameter increases. Also, the effect of thermal radiation works as a heat source and so the quantity of heat added to the fluid increases, therefore the local Nusselt number reduced as the radiation parameter increases.

An analysis is performed to study the momentum, combined heat and mass transfer characteristics of MHD free convection flow of an electrically conducting Newtonian fluid on circular cylinder with uniform heat/mass flux with the effects of uniform transverse magnetic field and thermal radiation.

This paper provides a very useful source of coefficient of heat and mass transfer values for engineers planning to transfer heat and mass by using electrically conducting gases with uniform heat/mass flux.

The combined heat and mass transfer of an electrically conducting gases on free convection flow in the presence of magneto and thermal radiation effects are investigated and can be used by different engineers working on industry, geothermal, geophysical, technological and engineering applications.

Although many studies have been conducted on the nanofluid flow in microtubes, this paper, for the first time, aims to investigate the effects of nanoparticle diameter and concentration on the velocity and temperature fields of turbulent non-Newtonian Carboxymethylcellulose (CMC)/copper oxide (CuO) nanofluid in a three-dimensional microtube. Modeling has been done using low- and high-Reynolds turbulent models. CMC/CuO was modeled using power law non-Newtonian model. The authors obtained interesting results, which can be helpful for engineers and researchers that work on cooling of electronic devices such as LED, VLSI circuits and MEMS, as well as similar devices.

Present numerical simulation was performed with finite volume method. For obtaining higher accuracy in the numerical solving procedure, second-order upwind discretization and SIMPLEC algorithm were used. For all Reynolds numbers and volume fractions, a maximum residual of 10⁻⁶ is considered for saving computer memory usage and the time for the numerical solving procedure.

In constant Reynolds number and by decreasing the diameter of nanoparticles, the convection heat transfer coefficient increases. In Reynolds numbers of 2,500, 4,500 and 6,000, using nanoparticles with the diameter of 25 nm compared with 50 nm causes 0.34 per cent enhancement of convection heat transfer coefficient and Nusselt number. Also, in Reynolds number of 2,500, by increasing the concentration of nanoparticles with the diameter of 25 nm from 0.5 to 1 per cent, the average Nusselt number increases by almost 0.1 per cent. Similarly, In Reynolds numbers of 4,500 and 6,000, the average Nusselt number increases by 1.8 per cent.

The numerical simulation was carried out for three nanoparticle diameters of 25, 50 and 100 nm with three Reynolds numbers of 2,500, 4,500 and 6,000. Constant heat flux is on the channel, and the inlet fluid becomes heated and exists from it.

The authors obtained interesting results, which can be helpful for engineers and researchers that work on cooling of electronic devices such as LED, VLSI circuits and MEMS, as well as similar devices.

This manuscript is an original work, has not been published and is not under consideration for publication elsewhere. About the competing interests, the authors declare that they have no competing interests.

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.

To amend the efficiency of engineering processes and electronic devices, it is very urgent to assess the irreversibility in the term entropy generation (EG). The efficiency of energy transportation in a system can be improved by minimization of the rate of EG. In this context, the aim of the present study is to estimate irreversible losses of an unsteady magnetohydrodynamic (MHD) flow of a viscous incompressible electrically conducting non-Newtonian molybdenum disulfide-polyethylene glycol Casson nanofluid past a moving vertical plate with slip condition under the influence of Hall current, thermal radiation, internal heat generation/absorption and first-order chemical reaction. Molybdenum disulfide (MoS₂) nanoparticles are dispersed in the base fluid polyethylene glycol (PEG) to make Casson nanofluid. Casson fluid model is considered to characterize the rheology of the non-Newtonian fluid, whereas Rosseland approximation is adopted to simulate the thermal radiative heat flux in the energy equation.

The closed-form solutions are obtained for the model equations by using the Laplace transform method (LTM). Graphs and tables are prepared to examine the impact of pertinent flow parameters on the pertinent flow characteristics. The energy efficiency of the system via the Bejan number is studied extensively.

Analysis reveals that Hall current has diminishing behavior on entropy production of the thermal system. Strengthening of the magnetic field declines the velocity components and prop-ups the rate of EG. Adding nanoparticles into the base fluid reduces the EG, whereas there are an optimum volume fraction of nanoparticles for which the EG is minimized. Further, the rate of decay of EG is prominent in molybdenum disulfide-polyethylene glycol in comparison to PEG.

The results of this study would benefit the industrial sector in achieving the maximum heat transfer at the cost of minimum irreversibilities with an optimal choice of embedded thermophysical parameters. In view of this agenda, this study would be adjuvant in powder technology, polymer dynamics, metallurgical process, manufacturing dynamics of nano-polymers, petroleum industries, chemical industries, magnetic field control of material processing, synthesis of smart polymers, etc.

The novelty of this study is to encompass the analytical solution by using the LTM. Such an exact solution of non-Newtonian fluid flow is rare in the literature. Limited research articles are available in the field of EG analysis during the flow of non-Newtonian nanoliquid subject to a strong magnetic field.