The objective of this study is to determine the characteristics of hydromagnetic flow over a slendering stretching sheet in slip flow regime. Steady, two dimensional, nonlinear, hydromagnetic laminar flow of an incompressible, viscous and electrically conducting fluid over a stretching sheet with variable thickness in the presence of variable magnetic field and slip flow regime is considered. Govern-ing equations of the problem are converted into ordinary differential equations utilizing similarity transformations. The resulting non-linear differential equations are solved numerically by utilizing Nachtsheim-swigert shooting iterative scheme for satisfaction of asymptotic boundary conditions along with fourth order Runge-Kutta integration method. Numerical computations are carried out for various values of the physical parameters and their effects over the velocity and temperature are analyzed. Numerical values of dimensionless skin friction coefficient and non-dimensional rate of heat transfer are also obtained.

The current study investigates the mixed convective flow of MHD tangent hyperbolic nanofluid due to a stretching surface with motile micro-organisms via convective heat transfer and slip conditions. The flow analysis's governing equations were converted into a non-dimensional relation by using the proper alteration. The PDE model equations are computed for these transformed equations using the MATLAB- bvp4c scheme. Skin friction, Sherwood number, Nusselt number, and the profiles of motile microorganisms are engineering-relevant quantities when compared to various physical variables. In comparison to recent literature, Skin friction is consistent for magnetic parameter; the results demonstrated a good consistency. Furthermore, an enhancement in the radiation and mixed convection parameter's magnitude enhances the velocity profile. Weissenberg number and magnetic field are used to study the reverse impact. The impact of thermal radiation parameter, Brownian movement, and thermophoretic effects are additional factors that frequently improve heat transfer. Through graphical and tabular explanations, the physical interpretation has been presented.

Effects of the uniform transverse magnetic field on the transient free convective flows of a nanofluid with generalized thermal transport between two vertical parallel plates have been analyzed. The fluid temperature is described by a time-fractional differential equation with Caputo derivatives. Closed form of the temperature field is obtained by using the Laplace transform and fractional derivatives of the Wright’ s functions. A semi-analytical solution for the velocity field is obtained by using the Laplace transform coupled with the numerical algorithms for the inverse Laplace transform elaborated by Stehfest and Tzou. Effects of the derivative fractional order and physical parameters on the nanofluid flow and heat transfer are graphically investigated.

A free convective unsteady visco-elastic flow through porous medium of variable permeability bounded by an infinite vertical porous plate with variable suction, constant heat flux under the influence of transverse uniform magnetic field has been investigated in the present study. The permeability of porous medium fluctuates with time about the constant mean. Approximate solutions for mean velocity, transient velocity, mean temperature and transient temperature of non-Newtonian flow and skin friction are obtained. The effects of various parameters such as Pr (Prandtl number), Gr (Grashof number), M (Hartmann number),  w (frequency parameter) and k0 (mean permeability parameter) on the above are depicted, skin friction, amplitude and phase are shown graphically and discussed. Expressions for fluctuating parts of velocity ‘Mr’ and ‘Mi’ are found and plotted graphically, effects of different parameters on them are discussed.

An experimental investigation was carried out to study convective heat transfer of nanofluid flow inside an inclined copper tube under uniform heat flux condition. Required data are acquired for laminar and hydrodynamically fully developed flow inside a round tube. The stable CuO-base oil nanofluid with different nanoparticle weight fractions of 0.5%, 1% and 2% was produced by means of ultrasonic device in two steps method. In this study, the effect of different parameters such as tube inclination, nanofluid weight fraction and Reynolds number on heat transfer coefficient was considered. Results show that the heat transfer coefficient of nanofluid with different weight fractions increases with the increasing Reynolds number inside horizontal and inclined round tubes. Also, nanofluid flow inside the inclined tube at 30 degrees exhibit the most heat transfer enhancement amongst other tube inclinations at same Reynolds number.

The current article has investigated unsteady convective flow for MHD non-Newtonian Powell-Eyring fluid embedded porous medium over inclined permeable stretching sheet. We have pondered the thermophoresis parameter, chemical reaction, variable thermal conductivity, Brownian motion, variable heat source and variable thermal radiation in temperature and concentration profiles. Using similar transformation, the PDEs are converted by couple ODEs and solve by R– K– Fehlberg 4th– 5th order method. The physical features of nondimensional radiation parameter, non-Newtonian fluid parameters, suction /injection parameter, mass Grashof number porosity parameter, temperature ratio parameter, thermal Grashof number, Biot number of temperature and Biot number of concentration have been analyzed by plotting the graphs of graphical representations of momentum, heat, and mass profiles. Cf Re 1/2, Nu Re x-1/2 and Sh Re x-1/2 have been analyzed. The transfer rate of temperature is decreased whereas the flow rate offluid grows with an enhancement in (K) and (Gr). The transfer rate of the temperature is distinctly boosted whereas the fluid flow rate is distinctly declined with an enhancement in (M), (Kp).

Entropy generation due to viscous incompressible MHD forced convective dissipative fluid flow through a horizontal channel of finite depth in the existence of an inclined magnetic field and heat source effect has been examined. The governing non-linear partial differential equations for momentum, energy, and entropy generation are derived and solved by using the analytical method. In addition, the skin friction coefficient and Nusselt number are calculated numerically and their values are presented through the tables for the upper and the bottom wall of the channel. It was concluded that the total entropy generation rate and Bejan number are reduced due to a rise in the inclination angle of the magnetic field. Also, an increment in the heat source props up the fluid temperature and total entropy generation rate. This study will help to reduce the energy loss due to reversible process and heat dissipation. The results are also useful for chemical and metallurgy industries.

The study of flow and convective heat transfer from a rotary sphere in fluid mechanics, astrophysics, and astronaut subjects is important. Today, use of porous media has become widespread because of heat transfer characteristics as well as their lightweight and low volume. Many numerical studies on heat transfer and fluid mechanics in the rotary sphere have been done. The present project studies the phenomena of flow and heat transfer due to the rotation of the sphere at a constant temperature around itself in a porous medium, assuming a laminar, steady and incompressible flow. Analytical solution of the equations used is based on power series and the porosity coefficient is assumed to be between 0 and 1 in this problem. In the spherical coordinate system used here, changes in the azimuthal angle direction are ignored and the body force and pressure gradient for the problem are considered zero. The presence of the porous medium is expected to increase the value of thermal parameters.