Solution of the Boundary Layer Equation of the Power-Law Pseudoplastic Fluid Using Differential Transform Method

The boundary layer equation of the pseudoplastic fluid over a flat plate is considered. This equation is a boundary value problem (BVP) with the high nonlinearity and a boundary condition at infinity. To solve such problems, powerful numerical techniques are usually used. Here, through using differential transform method (DTM), the BVP is replaced by two initial value problems (IVP) and then multi-step differential transform method (MDTM) is applied to solve them. The differential equation and its boundary conditions are transformed to a set of algebraic equations, and the Taylor series of solution is calculated in every sub domain. In this solution, there is no need for restrictive assumptions or linearization. Finally, DTM results are compared with the numerical solution of the problem, and a good accuracy of the proposed method is observed

Investigation of Transient MHD Couette flow and Heat Transfer of Dusty Fluid with Temperature-Dependent Oroperties

In the present study, transient MHD Couette flow and heat transfer of dusty fluid between two parallel plates and the effect of the temperature dependent properties has been investigated. The thermal conductivity and viscosity of the fluid are assumed as linear and exponential functions of temperature, respectively. A constant pressure gradient and an external uniform magnetic field are considered in the main flow direction and perpendicular to the plates, respectively. A hybrid treatment based on finite difference method (FDM) and differential transform method (DTM) is used to solve the coupled flow and heat transfer equations. The effects of the variable properties, Hartman number, Hall current, Reynolds number and suction velocity on the Nusselt number and skin friction factor have been discussed. It is found that when Hartman number increases, skin friction of the upper and lower plates increases

Application of differential transform method to unsteady free convective heat transfer of a couple stress fluid over a stretching sheet

In the present article, the transient rheological boundary layer flow over a stretching sheet with heat transfer is investigated, a topic of relevance to non-Newtonian thermal materials processing. Stokes couple stress model is deployed to simulate non-Newtonian characteristics. Similarity transformations are utilized to convert the governing partial differential equations into nonlinear ordinary differential equations with appropriate wall and free stream boundary conditions. The non-dimensional boundary value problem emerging is shown to be controlled by a number of key thermophysical and rheological parameters, namely the rheological couple stress parameter, unsteadiness parameter, Prandtl number (Pr), buoyancy parameter. The semi-analytical Differential Transform Method (DTM) is used to solve the reduced nonlinear coupled ordinary differential boundary value problem. A numerical solution is also obtained via the MATLAB built in solver ‘bvp4c’ to validate the results. Further validation with published results from the literature is included. Fluid velocity is enhanced with increasing couple stress parameter whereas it is decreased with unsteadiness parameter. Temperature is elevated with couple stress parameter whereas it is initially reduced with unsteadiness parameter. The flow is accelerated with increasing positive buoyancy parameter (for heating of the fluid) whereas it is decelerated with increasing negative buoyancy parameter (cooling of the fluid). Temperature and thermal boundary layer thickness are boosted with increasing positive values of buoyancy parameter. Increasing Prandtl number decelerates the flow, reduces temperatures, increases momentum boundary layer thickness and decreases thermal boundary layer thickness. Excellent accuracy is achieved with the DTM approach

Energy conservation of bio-nanofluids past a needle in the presence of Stefan blowing : lie symmetry and numerical simulation

Thermal energy management associated with the transmission of heat is one of the main problems in many industrial setups (e.g. pharmaceutical, chemical and food) and bioengineering devices (e.g. hospital ventilation, heating, cooling devices, heat exchanger and drying food, etc). The current study aims to examine thermo-bioconvection of oxytactic microorganisms taking place in a nanofluid-saturated needle with the magnetic field. Stefanblowing is applied. The leading equations of continuity, momentum and energy, species transport equations for oxygen concentration and population density of microorganisms are reduced dimensionless and Lie symmetry group transformations are used to generate appropriate invariant transformations. The resulting similarity boundary value problem (in which the blowing parameter is coupled with concentration) have been simulated using MATLAB (2015a) bvp5c built in function. The impact of the emerging factors on the nondimensional velocity, temperature, nanoparticle concentration and motile microorganism density functions and their slopes at the wall, are pictured and tabulated. Justification with published results are included. It is found that all physical quantities decrease with Stefan blowing and increase with power law index parameter. With elevation in magnetic field parameter i.e., Lorentzian drag force, the friction factor reduces while the local Nusselt number, local Sherwood number, and the local motile microorganism density wall gradient increase. Present study could be used in food and pharmaceutical industries, chemical processing equipment, fuel cell technology, enhanced oil recovery, etc

Investigation of the viscoelastic flow and species diffusion in a porous channel with high permeability

In this study, effect of mass transfer on laminar flow of viscoelastic fluid in a porous channel with high permeability medium is investigated. The viscoelastic model used in this work is the upper convected Maxwell (UCM) model. Applying the similarity transformation, the governing partial equations are converted to ordinary differential equations. The problem is studied by a hybrid technique based on Differential Transformation Method (DTM) and iterative Newton’s method (INM). Also a numerical solution is done to validate the present analytical method. The effects of active parameters such as Darcy number (Da), transpiration Reynolds number (ReT) Deborah number (De) and Schmidt number (Sc) on the both velocity components and concentration function are discussed in this work. The results indicate that the stream function increases for large Deborah and Darcy numbers. The axial velocity is initially decreased by increasing the Deborah number but then increased while approaching the upper channel wall

Approximate solution of the nonlinear heat transfer equation of a fin with the power-law temperature-dependent thermal conductivity and heat transfer coefficient

In this paper, differential transform method (DTM) is used to solve the nonlinear heat transfer equation of a fin with the power-law temperature-dependent both thermal conductivity and heat transfer coefficient. Using DTM, the differential equation and the related boundary conditions transformed into a recurrence set of equations and finally, the coefficients of power series are obtained based on the solution of this set of equations. DTM overcame on nonlinearity without using restrictive assumptions or linearization. Results are presented for the dimensionless temperature distribution and fin efficiency for different values of the problem parameters. DTM results are compared with special case of the problem that has an exact closed-form solution, and an excellent accuracy is observed