Diffusion-thermo Effects in Stagnation Point Flow of Second ‎Grade Fluid past a Stretching Plate

Document Type : Research Paper

Authors

1 College of Applied Science, Beijing University of Technology, Beijing 100124, P.R. China

2 Govt Postgraduate College Attock, Pakistan

3 College of Applied Science, Beijing University of Technology, Beijing 100124, P.R. China‎

Abstract

Transmission of heat and mass in boundary layer flows over stretching surfaces play a significant role in metallurgy and polymer industry. In Current article the assisting and opposing flow of a second grade fluid towards a stretching sheet is analyzed to examine the heat and mass transfer in stagnation point boundary layer flow. Different flow parameters such as concentration, surface temperature and stretching velocity are supposed to variate linearly. The basic transport equations are transformed into non-linear ordinary differential equations by means of boundary layer approximation and similarity transmutations, which are then solved by employing nonlinear shooting (NLS) and Keller-box methods (KBM). These techniques are very useful for solving boundary-layer problems and are applicable to other general situations than that presented current study. The outcomes of velocity, temperature, concentration profile, skin-friction coefficient, heat and mass transfer coefficients are analyzed briefly in graphical and tabular formats. The mass transmission rate was found to be in direct relation with Schmidt number. Moreover, we predict that a rise in Prandtl number leads to a decline in temperature and thermal layer of boundary thickness for both supporting and contrasting flows. The outcomes of this article are important for the analysts in the field of second grade fluids. We believe that the article is very well prepared and the results are original and useful from both theoretical and application point of views.

Keywords

Main Subjects

[1]     Sakiadis, B. C. Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow. AIChE Journal7(1), 1961, 26-28.
[2]     Crane, L. J., Flow past a stretching plate. Zeitschrift für Angewandte Mathematik und Physik ZAMP21(4), 1970, 645-647.
[3]     Erickson, L. E., Fan, L. T., & Fox, V. G., Heat and mass transfer on moving continuous flat plate with suction or injection. Industrial & Engineering Chemistry Fundamentals5(1), 1966, 19-25.
[4]     Gupta, P. S., & Gupta, A. S., Heat and mass transfer on a stretching sheet with suction or blowing. The Canadian Journal of Chemical Engineering55(6), 1977, 744-746.
[5]     Grubka, L. J., & Bobba, K. M., Heat transfer characteristics of a continuous stretching surface with variable temperature. ASME J. Heat Transfer107(1), 1985, 248-250.
[6]     Char, M. I., Heat transfer of a continuous, stretching surface with suction or blowing. Journal of Mathematical Analysis and Applications135(2), 1988, 568-580.
[7]     M.E. Ali. Heat transfer characteristics of a continuous stretching surface. Heat Mass Transfer, 29, 1994, 227-234.
[8]     Chen, C. H., Laminar mixed convection adjacent to vertical, continuously stretching sheets. Heat and Mass Transfer33(56), 1998, 471-476.
[9]     Wang, C. Y., Analysis of viscous flow due to a stretching sheet with surface slip and suction. Nonlinear Analysis: Real World Applications10(1), 375-380.
[10]   Cortell, R., MHD flow and mass transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet with chemically reactive species. Chemical Engineering and Processing: Process Intensification46(8), 2009, 721-728.
[11]   Cortell, R., Toward an understanding of the motion and mass transfer with chemically reactive species for two classes of viscoelastic fluid over a porous stretching sheet. Chemical Engineering and Processing-Process Intensification46(10), 2007, 982-989.
[12]   Mansour, M. A., El-Anssary, N. F., & Aly, A. M., Effects of chemical reaction and thermal stratification on MHD free convective heat and mass transfer over a vertical stretching surface embedded in a porous media considering Soret and Dufour numbers. Chemical Engineering Journal145(2), 2008, 340-345.
[13]   Hayat, T., Abbas, Z., & Ali, N., MHD flow and mass transfer of a upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species. Physics Letters A372(26), 2008, 4698-4704.
[14]   Bhattacharyya, K., & Layek, G. C., Chemically reactive solute distribution in MHD boundary layer flow over a permeable stretching sheet with suction or blowing. Chemical Engineering Communications197(12), 2010, 1527-1540.
[15]   Hiemenz, K. , Die Grenzschicht an einem in den gleichformigen Flussigkeitsstrom eingetauchten geraden Kreiszylinder. Dinglers Polytech. J.326, 1911, 321-324.
[16]   TC, Chiam., Stagnation-point flow towards a stretching plate. Journal of the Physical Society of Japan63(6), 1994, 2443-2444.
[17]   Nazar, R., Amin, N., Filip, D., & Pop, I., Stagnation point flow of a micropolar fluid towards a stretching sheet. International Journal of Non-Linear Mechanics39(7), 2004, 1227-1235.
[18]   Layek, G. C., Mukhopadhyay, S., & Samad, S. A., Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing. International Communications in Heat and Mass Transfer34(3), 2007, 347-356.
[19]   Nadeem, S., Hussain, A., & Khan, M., HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet. Communications in Nonlinear Science and Numerical Simulation15(3), 2010, 475-481.
[20]   Singh, J., Mahabaleshwar, U. S., & Bognár, G., Mass transpiration in nonlinear MHD flow Due to porous Stretching Sheet. Scientific Reports, 9(1), 2019, 1-15.
[21]   Hayat, T., Abbas, Z., Pop, I., & Asghar, S., Effects of radiation and magnetic field on the mixed convection stagnation-point flow over a vertical stretching sheet in a porous medium. International Journal of Heat and Mass Transfer53(1-3), 2010, 466-474.
[22]   Ishak, A., Nazar, R., Arifin, N. M., & Pop, I., Dual solutions in mixed convection flow near a stagnation point on a vertical porous plate. International Journal of Thermal Sciences47(4), 2008, 417-422.
[23]   Ishak, A., Nazar, R., & Pop, I., Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet. Meccanica41(5), 2006, 509-518.
[24]   Ishak, A., Nazar, R., Arifin, N. M., & Pop, I., Mixed convection of the stagnation-point flow towards a stretching vertical permeable sheet. Malaysian Journal of Mathematical Sciences2, 2007, 217-226.
[25]   Garg, V. K., & Rajagopal, K. R., Stagnation point flow of a non-Newtonian fluid. Mechanics Research Communications,17(6), 1990, 415-421.
[26]   Wang, C. Y., Stagnation flow towards a shrinking sheet. International Journal of Non-Linear Mechanics, 43(5), 2008, 377-382.
[27]   M. Awais, T. Hayat, M. Mustafa, K. Bhattacharyya, M. A. Farooq., Analytic and numeric solutions for stagnation-point flow with melting, thermal- diffusion and diffusion-thermo effects. International Journal of Numerical Methods Heat Fluid Flow, 24(2), 2014, 438-454.
[28]   T. Hayat, Z. Iqbal, M. Mustafa, A. Alsaedi., Stagnation-point flow of Jerey fluid with melting heat transfer and Soret and Dufour effects. International Journal of Numerical Methods for Heat and Fluid Flow, 24(2), 2014, 402-418.
[29]   Schmidt, E., Verdunstung und wärmeübergang. International Journal of Heat and Mass Transfer, 19(1), 1976, 3-8.
[30]   Nusselt, W., Wärmeübergang, diffusion und verdunstung. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik10(2), 1930, 105-121.
[31]   Damtie, M. M., Woo, Y. C., Kim, B., Park, K. D., Hailemariam, R. H., Shon, H. K., & Choi, J. S., Analysis of mass transfer behavior in membrane distillation, Mathematical modeling under various conditions. Chemosphere236, 2019, 124289.
[32]   Yaïci, W., & Entchev, E., Coupled unsteady computational fluid dynamics with heat and mass transfer analysis of a solar/heat powered adsorption cooling system for use in buildings. International Journal of Heat and Mass Transfer144, 2019, 118648.
[33]   Das, K., Effects of thermophoresis and thermal radiation on MHD mixed convective heat and mass transfer flow. Afrika Matematika24(4), 2013, 511-524.
[34]   De, P., Mondal, H., & Bera, U. K., Influence of nanofluids on magnetohydrodynamic heat and mass transfer over a non-isothermal wedge with variable viscosity and thermal radiation. Journal of Nanofluids3(4), 2014, 391-398.
[35]   Pal, D., & Mandal, G., Influence of thermal radiation on mixed convection heat and mass transfer stagnation-point flow in nanofluids over stretching/shrinking sheet in a porous medium with chemical reaction. Nuclear Engineering and Design273, 2014, 644-652
[36]   Alam, M. S., Rahman, M. M., & Sattar, M. A., MHD free convective heat and mass transfer flow past an inclined surface with heat generation. Science & Technology Asia, 2006, 1-8.
[37]   Pal, D., & Mondal, H., Soret-Dufour Effects on Hydromagnetic Non-Darcy Convective-Radiative Heat and Mass Transfer over a Stretching Sheet in Porous Medium with Viscous Dissipation and Ohmic Heating. Journal of Applied Fluid Mechanics7(3), 2014, 513–523.
[38]   Bhargava, R., Kumar, L., & Takhar, H. S., Numerical solution of free convection MHD micropolar fluid flow between two parallel porous vertical plates. International Journal of Engineering Science41(2), 2003, 123-136.
[39]   Anwar, T., Kumam, P., & Watthayu, W., An exact analysis of unsteady MHD free convection flow of some nanofluids with ramped wall velocity and ramped wall temperature accounting heat radiation and injection/consumption. Scientific Reports10(1), 2020, 1-19.
[40]   Ellahi, R., Zeeshan, A., Shehzad, N., & Alamri, S. Z., Structural impact of Kerosene-Al2O3 nanoliquid on MHD Poiseuille flow with variable thermal conductivity: application of cooling process. Journal of Molecular Liquids264, 2018, 607-615.
[41]   Sheikholeslami, M., et al. Performance of solar collector with turbulator involving nanomaterial turbulent regime. Renewable Energy163, 2021, 1222-1237.
[42]   Sheikholeslami, M., and Seyyed Ali, F., Nanoparticle transportation inside a tube with quad-channel tapes involving solar radiation. Powder Technology, 378, 2021, 145-159.
[43]   Hayat, T., Abbas, Z., & Pop, I., Mixed convection in the stagnation point flow adjacent to a vertical surface in a viscoelastic fluid. International Journal of Heat and Mass Transfer51(11-12), 2008, 3200-3206.
[44]   N. Ramachandran, T.S. Chen, B.F. Armaly., Mixed convection in stagnation flows adjacent to vertical surfaces. ASME J. Heat Transfer, 110, 1988, 373–377.
[45]   Lok, Y. Y., Amin, N., Campean, D., & Pop, I., Steady mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface. International Journal of Numerical Methods for Heat & Fluid Flow, 15, 2005, 654–670.
[46]   Golafshan, B., & Rahimi, A. B., Effects of radiation on mixed convection stagnation-point flow of MHD third-grade nanofluid over a vertical stretching sheet. Journal of Thermal Analysis and Calorimetry135(1), 2019, 533-549.
[47]   Ali, M. E., The effect of variable viscosity on mixed convection heat transfer along a vertical moving surface. International Journal of Thermal Sciences45(1), 2006, 60-69.
[48]   Ali, M., & Al-Yousef, F., Laminar mixed convection from a continuously moving vertical surface with suction or injection. Heat and Mass Transfer33(4), 1998, 301-306.
[49]   Mahapatra, T. R., Gupta, A. S., Heat transfer in stagnation-point flow towards a stretching sheet. Heat Mass Transfer, 38, 2002, 517-521.
[50]   Kudenatti, R. B., Hydrodynamic flow of non-Newtonian power-law fluid past a moving wedge or a stretching sheet: a unified computational approach. Scientific Reports10(1), 2020, 1-16.