INTERACTION OF HEAT TRANSFER AND PERISTALTIC PUMPING OF FRACTIONAL SECOND GRADE FLUID THROUGH A VERTICAL CYLINDRCAL TUBE
Abstract
This paper deals with a theoretical investigation of interaction of heat transfer with peristaltic pumping of a fractional second grade fluid through a tube, under the assumption of low Reynolds number and long wave length approximation. Analytical solution of problem is obtained by using Caputo's definition. Effect of different physical parameters, material constant, amplitude ratio, friction force, temperature and heat transfer on pumping action and frictional force are discussed with particular emphasis. The computed results are presented in graphical form.
Dates
- Submission Date2011-10-22
- Revision Date2012-07-13
- Acceptance Date2012-07-27
References
- Fung, Y.C., Yih, C.S., Peristaltic transport, J. Applied. Mech, 35 (1968), pp. 669-675
- Burns, J.C., Parkers, T., Peristaltic motion, J. Fluid Mech, 29 (1970), pp.731-743
- Abd El Naby. A.E.H., El Misiery. A.E.H., Effects of an endoscope and generalized Newtonian fluid on peristaltic motion, Applied Mathematics and Computation, 128 (2002), pp.19-35
- Abd El Hakeem., Abd El Naby., El Misiery, A.E.M., hydro magnetic flow of generalized Newtonian fluid through a uniform tube with peristalsis, Mathematics and computation, 173 (2006), pp. 856-871
- Rathod,V.P., Channakote, M.M., A study of ureteral peristalsis in cylindrical tube through porous medium, Advance in Applied Science Research, 2 (2011), pp.134-140
- Nadeem, S., Akbar, N.S., Influence of heat transfer on peristaltic flow of Johnson Segalmn fluid in non uniform tube, Int. Communication in Heat and Mass Transfer, 36 (2009), pp.1050-1059
- Nadeem, S., Akbar, N.S., Effect of heat transfer on the peristaltic transport of MHD Newtonian fluid with variable viscosity: Application of Adomian decomposition method, Communication in Nonlinear Science and Numerical Simulation, 14 (2009), pp.3844-3855
- Nadeem, S., Akram, N. S., Heat transfer in a peristaltic flow of MHD fluid with partial slip, Communication in Nonlinear Science and Numerical Simulation, 15 (2010), pp. 312-321
- Nadeem, S., Akbar, N. S., Influence of heat transfer on a peristaltic transport of Herschel-Bulkley fluid in a non-uniform inclined tube, Communication in Nonlinear Science and Numerical Simulation 14 (2009), pp. 4100-13
- Hayat,T., Abbasi, F. M., Peristaltic mechanism in a symmetric channel with heat transfer, Mathematics Computation Applied, 15(2010), pp. 621-637
- Vasudev, C., Rajeswar Rao, U., Prabhakar Rao, G., Subba Reddy, M., peristaltic flow of a Newtonian fluid through a porous medium in vertical tube under the effect of magnetic field, Int. J of Current Scientific Research, 1(2011), pp.105-110
- Vajravelu, K., Sreenadh, S., Lakshiminarayana, P., The influence of heat transfer on peristaltic transport of Jeffrey fluid in vertical porous stratum, Communication in Nonlinear Science and Numerical Simulation, 16 (2011), pp. 3107-3125
- Vasudev, C., Rajeswar Rao,U., Prabhakar Rao, G., Subba Reddy, M., Effect of heat transfer on the peristaltic flow of a Jeffrey fluid through a porous medium in a vertical channel, J. of Basic Applied Science Research, 1(2011), pp.751-758
- Srinivas, S., Kothandapani, M., Peristaltic transport in a symmetric channel with heat transfer-A note, International Communication in Heat and mass transfer, 35 (2008), pp. 514-522
- Qi, H., Xu, M., Stokes first problem for a viscoelastic fluid with the generalized Oldroyd-B model, Acta Mechanica Sinica, 23 (2007), pp. 463-469
- Tan, W., Pan, W., Xu, Mi., A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates, Int. J. of Non-Linear Mech, 38 (2003), pp. 645-650
- Khan, M,S., Ali, H., Qi, H., On accelerated flows of a viscoelastic fluid with the fractional Burgers' model, Nonlinear Analysis: Real World Applications, 10 (2009), pp. 2286-2296
- Friedrich, C., Relaxation and retardation functions of the Maxwell model with fractional derivatives, Rheologica Acta, 30 (1991), pp. 151-158
- Qi, H., Jin, H., Unsteady rotating flows of a viscoelastic fluid with the fractional Maxwell model between coaxial cylinders, Acta Mechanica Sinica, 22 (2006), pp. 301-305
- Wang, S., Xu, M., Axial Couette flow of two kinds of fractional viscoelastic fluids in an annulus, Nonlinear Analysis: Real World Applications, 10 (2009), pp. 1087-1096
- Tripathi, D., Pandey, S.K., Das, S., Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel, Applied Mathematics Computation, 215 (2010), pp. 3645-3654
- Tripathi, D., Numerical study on peristaltic flow of generalized burgers fluids in uniform tubes in the presence of an endoscope, Int. J of Numerical Methods in Biomedical Engineering, 27 (2011), pp. 812-1828
- Tripathi, D., Peristaltic flow of a fractional second grade fluid through a cylindrical tube, Thermal Science, 15(2011), pp. 5167-5173
- Tripathi, D., Numerical and analytical simulation of peristaltic flows of generalized Oldroyd-B fluids, Int. J of Numerical Methods in Fluids, 67 (2011), pp.1932-1943
- Tripathi, D., A mathematical model for the peristaltic flow of chyme movement in small intestine, Mathematical Biosciences, 233 (2011), pp. 90-97
- Tripathi, D., Peristaltic transport of fractional Maxwell fluids in uniform tubes: applications in endoscopy, Computers and Mathematics with Applications, 62 (2011), pp.1116-1126
- Tripathi, D., Peristaltic transport of a viscoelastic fluid in a channel, Acta Astronautica, 68 (2011), pp.1379-1385
- Tripathi, D., Numerical study on peristaltic transport of fractional bio fluids model, Journal of Mechanics in Medicine and Biology, 11 (2011), pp.1045-1058
- Tripathi, D., A mathematical model for swallowing of food bolus through the oesophagus under the influence of heat transfer, Int. J. of Thermal science, 51 (2012), pp. 99-101
- Tripathi, D., Pandey, S.K., Das, S., Peristaltic transport of a generalized Burgers' fluid: Application to the movement of chyme in small intestine, Acta Astronautica, 69 (2011), pp. 30-38
- Nadeem, S., Akbar, N. S., Effects of heat and mass transfer peristaltic flow of Williamson fluid in a vertical annulus, Meccanica, 47 (2012), pp.141-151
- Nadeem, S., Akbar, N. S., Characteristics of heating scheme and mass transfer on the peristaltic flow for an Eyring-Powell fluid in an endoscope, International Journal of Heat and Mass Transfer, 52(2012), pp.375-383
- Nadeem, S., Akbar, N. S., Endoscopic and heat transfer effects on the peristaltic flow of a third order fluid with chemical reactions, Asia Pacific Journal of Chemical Engineering, 7(2012),pp.45-54
- Akbar, N.S., Hayat , T., Nadeem, S., Obaidat, S., Peristaltic flow of a Williamson fluid in an inclined asymmetric channel with partial slip and heat transfer, Int. J. of Heat and Mass Transfer, 55 (2012), pp. 1855-1862
Volume
18,
Issue
4,
Pages1109 -1118