scholarly journals Differential Transform Technique on the Effect of Baffle Convective Nanofluid Flow in Saturated Porous Channel

2019 ◽  
Vol 8 (4) ◽  
pp. 10349-10360
Keyword(s):  
Porous Medium ◽  
Perturbation Method ◽  
Vertical Channel ◽  
Differential Transform Method ◽  
Regular Perturbation ◽  
Nanofluid Flow ◽  
Transform Method ◽  
Differential Transform ◽  
Perturbation Parameters ◽  
Energy Equations

Simulations are shown for steady nanofluid saturated with porous medium in a vertical channel divided into two way by placing a thin baffle. Tiwari and Das model applied for continuity, momentum and energy equations are written using to define the nanofluid and non-Darcy model used for porous medium. The nonlinear equations are solved analytically using regular perturbation method and by semi analytical method using differential transform method. The validity of the solutions obtained by perturbation method and differential transform method are compared and found that they agree very well for small values of perturbation parameters. The numerical values of the velocity and temperature are shown graphically at different baffle positions for all the pertinent parameters. The Nusselt number for both regular and nanofluids are evaluated and tabulated.

scholarly journals Mixed Convective Fully Developed Flow in a Vertical Channel in the Presence of Thermal Radiation and Viscous Dissipation

2017 ◽  
Vol 22 (1) ◽  
pp. 123-144 ◽  
Author(s):  
K.V. Prasad ◽  
P. Mallikarjun ◽  
H. Vaidya
Keyword(s):  
Thermal Radiation ◽  
Perturbation Method ◽  
Viscous Dissipation ◽  
Vertical Channel ◽  
Differential Transform Method ◽  
Physical Parameters ◽  
Regular Perturbation ◽  
Transform Method ◽  
Fully Developed Flow ◽  
Differential Transform

Abstract The effect of thermal radiation and viscous dissipation on a combined free and forced convective flow in a vertical channel is investigated for a fully developed flow regime. Boussinesq and Roseseland approximations are considered in the modeling of the conduction radiation heat transfer with thermal boundary conditions (isothermal-thermal, isoflux-thermal, and isothermal-flux). The coupled nonlinear governing equations are also solved analytically using the Differential Transform Method (DTM) and regular perturbation method (PM). The results are analyzed graphically for various governing parameters such as the mixed convection parameter, radiation parameter, Brinkman number and perturbation parameter for equal and different wall temperatures. It is found that the viscous dissipation enhances the flow reversal in the case of a downward flow while it counters the flow in the case of an upward flow. A comparison of the Differential Transform Method (DTM) and regular perturbation method (PM) methods shows the versatility of the Differential Transform Method (DTM). The skin friction and the wall temperature gradient are presented for different values of the physical parameters and the salient features are analyzed.

scholarly journals Effect of viscous dissipation on mixed convection flow in a vertical double passage channel using Robin boundary conditions

1970 ◽  
Vol 8 (3) ◽  
pp. 27-47
Author(s):  
J. Prathap Kumar ◽  
J.C. Umavathi ◽  
M. Karuna Prasad
Keyword(s):  
Boundary Conditions ◽  
Mixed Convection ◽  
Perturbation Method ◽  
Viscous Dissipation ◽  
Perturbation Parameter ◽  
Differential Transform Method ◽  
Robin Boundary Conditions ◽  
Transform Method ◽  
Differential Transform ◽  
Robin Boundary

The laminar fully developed flow in a vertical double passage channel filled with clear fluid has been discussed using Robin boundary conditions. The thin perfectly conductive baffle is inserted in the channel. The governing equations of the fluid which are coupled and nonlinear are solved analytically by the perturbation method and semi analytically using differential transform method (DTM). The reference temperature of the external fluid is considered to be equal and different. The perturbation method which is valid for small values of perturbation parameter is used to find the combined effects of buoyancy forces and viscous dissipation. The limitation imposed on the perturbation parameter is relaxed by solving the basic equations using differential transform method. The influence of mixed convection parameter, Biot number for symmetric and asymmetric wall temperatures on the velocity, temperature and the Nusselt number is explored at different positions of the baffle. The solutions obtained by differential transform method are justified by comparing with the solutions obtained by perturbation method and the solutions agree very well for small values of the perturbation parameter.Keywords: Baffle, Differential Transform Method, Perturbation Method, Viscous dissipation, Robin Boundary Conditions, Double passage channel.

scholarly journals Differential transform method for unsteady nanofluid flow and heat transfer

2018 ◽  
Vol 57 (3) ◽  
pp. 1867-1875 ◽  
Author(s):  
Muhammad Usman ◽  
Muhammad Hamid ◽  
Umar Khan ◽  
Syed Tauseef Mohyud Din ◽  
Muhammad Asad Iqbal ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Transform Method ◽  
Nanofluid Flow ◽  
Transform Method ◽  
Flow And Heat Transfer ◽  
Differential Transform

scholarly journals Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Zhoujin Cui ◽  
Zisen Mao ◽  
Sujuan Yang ◽  
Pinneng Yu
Keyword(s):  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Time Derivative ◽  
Differential Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Differential Transform ◽  
Reduced Differential Transform Method

The approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization, or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the form of periodic functions and the results are depicted through graphs. The two different cases have studied and proved that the method is extremely effective due to its simplistic approach and performance.

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