Numerical Solution for the Effect of Variable Fluid Properties on the Flow and Heat Transfer in a Non-Newtonian Maxwell Fluid qver an Unsteady Stretching Sheet with Internal Heat Generation
DOI:
https://doi.org/10.15407/ujpe58.04.0353Keywords:
Maxwell fluid, unsteady stretching sheet, variable fluid properties, internal heat generation, Chebyshev spectral methodAbstract
This article looks at the flow and heat transfer in the unsteady two-dimensional boundary layer of a non-Newtonian Maxwell fluid over a stretching sheet in the presence of variable fluid properties and internal heat generation. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved numerically, by using the appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary-value problem is based on applying the Chebyshev spectral method over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, heat generation parameter, Maxwell parameter, and Prandtl number on the flow and temperature profiles, as well as on the local skin-friction coefficient and the local Nusselt number, are presented and discussed. Comparison of numerical results is made with the earlier published results in limiting cases. A special attention is given to the effect of the viscosity parameter, thermal conductivity parameter, and heat generation parameter on the velocity and temperature fields above the sheet.
References
<li> L.J. Crane, Z. Angew Math. Phys. 21, 645 (1970). <a href="https://doi.org/10.1007/BF01587695">https://doi.org/10.1007/BF01587695</a></li>
<li> P.S. Gupta and A.S. Gupta, Can. J. Chem. Eng. 55, 744 (1977). <a href="https://doi.org/10.1002/cjce.5450550619">https://doi.org/10.1002/cjce.5450550619</a></li>
<li> W.H.H. Banks, J. Mech. Theor. Appl. 2, 375 (1983).</li>
<li> L.J. Grubka and K.M. Bobba, AME J. Heat Transfer 107, 248 (1985). <a href="https://doi.org/10.1115/1.3247387">https://doi.org/10.1115/1.3247387</a></li>
<li> C.K. Chen and M. Char, J. Math. Anal. Appl. 35, 568 (1988). <a href="https://doi.org/10.1016/0022-247X(88)90172-2">https://doi.org/10.1016/0022-247X(88)90172-2</a></li>
<li> E. Magyari and B. Keller, J. Phys. D. Appl. Phys. 32, 2876 (1999). <a href="https://doi.org/10.1088/0022-3727/32/22/308">https://doi.org/10.1088/0022-3727/32/22/308</a></li>
<li> T.R. Mahapatra and A.S. Gupta, Canad. J. of Chem. Engin. 81, 258 (2003). <a href="https://doi.org/10.1002/cjce.5450810210">https://doi.org/10.1002/cjce.5450810210</a></li>
<li> I. Pop and T. Na, Mech. Res. Comm. 23, 413 (1996). <a href="https://doi.org/10.1016/0093-6413(96)00040-7">https://doi.org/10.1016/0093-6413(96)00040-7</a></li>
<li> E.M.A. Elbashbeshy and M.A.A. Bazid, Appl. Math. and Comp. 138, 239 (2003). <a href="https://doi.org/10.1016/S0096-3003(02)00106-6">https://doi.org/10.1016/S0096-3003(02)00106-6</a></li>
<li> E.M.A. Elbashbeshy and M.A.A. Bazid, J. of Heat and Mass Transfer 41, 1 (2004). <a href="https://doi.org/10.1007/s00231-004-0520-x">https://doi.org/10.1007/s00231-004-0520-x</a></li>
<li> M.E. Ali and E. Magyari, Int. J. of Heat Mass Transfer 50, 188 (2007). <a href="https://doi.org/10.1016/j.ijheatmasstransfer.2006.06.021">CrossRef</a></li>
<li> M.A. El-Aziz, Int. Commun. Heat and Mass Transfer 36, 521 (2009). <a href="https://doi.org/10.1016/j.icheatmasstransfer.2009.01.016">https://doi.org/10.1016/j.icheatmasstransfer.2009.01.016</a></li>
<li> A. Ishak, R. Nazar, and I. Pop, Nonlin. Analysis: Real World Appl. 10, 2909 (2009).</li>
<li> M.A. El-Aziz, Meccanica 45, 97 (2010). <a href="https://doi.org/10.1007/s11012-009-9227-x">https://doi.org/10.1007/s11012-009-9227-x</a></li>
<li> K.R. Rajagopal, Int. J. Non-Linear Mech. 17, 369 (1982). <a href="https://doi.org/10.1016/0020-7462(82)90006-3">https://doi.org/10.1016/0020-7462(82)90006-3</a></li>
<li> W.C. Tan, P.W. Xiao, and X.M. Yu, Int. J. Non-Linear Mech. 38, 645 (2003). <a href="https://doi.org/10.1016/S0020-7462(01)00121-4">https://doi.org/10.1016/S0020-7462(01)00121-4</a></li>
<li> C.H. Chen, J. of Heat and Mass Transfer 39, 791 (2003). <a href="https://doi.org/10.1007/s00231-002-0363-2">https://doi.org/10.1007/s00231-002-0363-2</a></li>
<li> C.H. Chen, J. Non-Newton. Fluid Mech. 135, 128 (2006).</li>
<li> C. Fetecau, M. Athar, and C. Fetecau, Comput. Math. Appl. 57, 596 (2009). <a href="https://doi.org/10.1016/j.camwa.2008.09.052">https://doi.org/10.1016/j.camwa.2008.09.052</a></li>
<li> M.S. Abel, J. Tawade, and M.M. Nandeppanavar, Int. J. Non-Linear Mech. 44, 990 (2009). <a href="https://doi.org/10.1016/j.ijnonlinmec.2009.07.004">https://doi.org/10.1016/j.ijnonlinmec.2009.07.004</a></li>
<li> M.A.A. Mahmoud and A.M. Megahed, Canad. J. of Phys. 87, 1065 (2009). <a href="https://doi.org/10.1139/P09-066">https://doi.org/10.1139/P09-066</a></li>
<li> W.W. Bell, Special Functions for Scientists and Engineers (Dover, New York, 2004).</li>
<li> S.E. El-Gendi, Computer J. 12, 282 (1969). <a href="https://doi.org/10.1093/comjnl/12.3.282">https://doi.org/10.1093/comjnl/12.3.282</a></li>
<li> M.M. Khader, Comm. in Nonlin. Sci. and Numer. Sim. 16, 2535 (2011).</li>
<li> N.H. Sweilam and M.M. Khader, ANZIAM 51, 464 (2010). <a href="https://doi.org/10.1017/S1446181110000830">https://doi.org/10.1017/S1446181110000830</a></li>
<li> A.J. Chamkha and A.A. Khaled, J. of Heat Mass Transfer. 37, 117 (2001). <a href="https://doi.org/10.1007/s002310000131">https://doi.org/10.1007/s002310000131</a></li>
<li> M.S. Abel, J. Tawade, and M.M. Nandeppanavar, Meccanica, DOI 10.1007/s11012-011-9448-7. <a href="https://doi.org/10.1007/s11012-011-9448-7">https://doi.org/10.1007/s11012-011-9448-7</a></li>
<li> P.G. Siddheshwar and U.S. Mahabaleswar, Int. J. NonLinear Mech. 40, 807 (2005). <a href="https://doi.org/10.1016/j.ijnonlinmec.2004.04.006">https://doi.org/10.1016/j.ijnonlinmec.2004.04.006</a></li>
</ol>
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