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 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.

Solution of Free Vibration Equations of Euler-Bernoulli Cracked Beams by Using Differential Transform Method

2011 ◽  
Vol 110-116 ◽  
pp. 4532-4536 ◽  
Author(s):  
K. Torabi ◽  
J. Nafar Dastgerdi ◽  
S. Marzban
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Differential Transform Method ◽  
Beam Model ◽  
Cracked Beam ◽  
Transform Method ◽  
Simple Method ◽  
Differential Transform

In this paper, free vibration differential equations of cracked beam are solved by using differential transform method (DTM) that is one of the numerical methods for ordinary and partial differential equations. The Euler–Bernoulli beam model is proposed to study the frequency factors for bending vibration of cracked beam with ant symmetric boundary conditions (as one end is clamped and the other is simply supported). The beam is modeled as two segments connected by a rotational spring located at the cracked section. This model promotes discontinuities in both vertical displacement and rotational due to bending. The differential equations for the free bending vibrations are established and then solved individually for each segment with the corresponding boundary conditions and the appropriated compatibility conditions at the cracked section by using DTM and analytical solution. The results show that DTM provides simple method for solving equations and the results obtained by DTM converge to the analytical solution with much more accurate for both shallow and deep cracks. This study demonstrates that the differential transform is a feasible tool for obtaining the analytical form solution of free vibration differential equation of cracked beam with simple expression.

Free vibration analysis of Euler–Bernoulli nanobeam using differential transform method

2018 ◽  
Vol 07 (03) ◽  
pp. 1850020 ◽  
Author(s):  
Subrat Kumar Jena ◽  
S. Chakraverty
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Differential Transform Method ◽  
Inverse Transformation ◽  
Algebraic Equations ◽  
Transform Method ◽  
Differential Transform

In this paper, a semi analytical-numerical technique called differential transform method (DTM) is applied to investigate free vibration of nanobeams based on non-local Euler–Bernoulli beam theory. The essential steps of the DTM application include transforming the governing equations of motion into algebraic equations, solving the transformed equations and then applying a process of inverse transformation to obtain accurate mode frequency. All the steps of the DTM are very straightforward, and the application of the DTM to both the equations of motion and the boundary conditions seems to be very involved computationally. Besides all these, the analysis of the convergence of the results shows that DTM solutions converge fast. In this paper, a detailed investigation has been reported and MATLAB code has been developed to analyze the numerical results for different scaling parameters as well as for four types of boundary conditions. Present results are compared with other available results and are found to be in good agreement.

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.

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