## THERMAL SCIENCE

International Scientific Journal

### IMPACT OF TEMPERATURE DEPENDENT HEAT SOURCE AND NON-LINEAR RADIATIVE FLOW OF THIRD GRADE FLUID WITH CHEMICAL ASPECTS

**ABSTRACT**

This communication explores the MHD flow of third grade fluid bounded by a stretching surface with homogeneous-heterogeneous reactions. Incompressible fluid is electrically conducting in the presence of constant magnetic field. Heat transfer is performed through exponential based space internal heat source, non-linear thermal radiation and convective boundary condition. Non-linear differential systems are computed by homotopic technique. Intervals of convergence through numerical data and plots are explicitly determined. The dimensionless velocity, temperature, and concentration distributions manifesting the characteristics of various influential parameters are addressed. The skin friction coefficient and local Nusselt number are also addressed. Clearly temperature is enhanced by radiation, temperature ratio, and magnetic parameters.

**KEYWORDS**

PAPER SUBMITTED: 2018-04-09

PAPER REVISED: 2018-08-09

PAPER ACCEPTED: 2018-08-11

PUBLISHED ONLINE: 2018-09-30

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**2**, PAGES [1173 - 1182]

- Okoya, S. S., Flow, thermal criticality and transition of a reactive third-grade fluid in a pipe with Reynolds model viscosity, Journal of Hydrodynamics, Ser. B, 28 (2016), 1, pp. 84-94
- Li, S. X., Jian, Y. J., Xie, Z. Y., Liu, Q. S., Li, F. Q., Rotating electro-osmatic flow of third grade fluids between two microparallel plates, Collids and Surfaces A, 470 (2015), pp. 240-247
- Aziz, T., Mahomed, F. M., Auyb, M. Mason, D. P., Nonlinear time-dependent flow models of third grade fluids: A conditional symmetry approch, International Journal of Non-Linear Mechanics, 54 (2013), pp. 55-65
- Abdelhameed, M., Varnhorn, W., Hashim, I., Roslan, R., The unsteady flow of third grade fluid caused by the periodic motion of an infinite wall with transpiration, Alexandria Engineering 10 Journal, 54 (2015), 4, pp. 1233-1241
- Sinha, A., MHD flow and heat transfer of third order fluid in a porous channel with stretching wall: Application to hemodynamics, Alexandria Engineering Journal, 54 (2015), 4, pp. 1243-1252
- Abbasbandy, S., Hayat, T., Mahomed, F. M., Ellahi, R., On comparison of exact and series solutions for thin film flow of a third grade fluid, International Journal for Numerical Methods in Fluids, 61 (2009), pp. 987-994
- Hussain, T., Hayat, T., Shehzad, S. A., Alsaedi, A., Chen, B., A model of solar radiation and Joule heating in flow of third grade nanofluid, Zeitschrift für Naturforschung A, 70 (2015), 3, pp. 177-184
- Sahoo B., Poncet S., Flow and heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition, International Journal of Heat and Mass Transfer, 54 (2011), pp. 5010-5019
- Sahoo B., Do Y., Effects of slip on sheet-driven flow and heat transfer of a third grade fluid past a stretching sheet, International Communications in Heat and Mass Transfer, 37 (2010), pp. 1064-1071
- Sahoo B., Effects of slip on sheet-driven flow and heat transfer of a non-Newtonian fluid past a stretching sheet, Computers and Mathematics with Applications, 61 (2011), pp. 1442-1456
- Hayat, T., Ullah, I., Muhammad, T., Alsaedi, A., A revised model for stretched flow of third grade fluid subject to magneto nanoparticles and convective condition, Journal of Molecular Liquids, 230 (2017), pp. 608-615
- Crane, L. J., Flow past a stretching plate, Zeitschrift für angewandte Mathematik und Physik ZAMP, 21 (1970), 4, pp. 645-647
- Bhattacharyya, K., Boundary layer flow and heat transfer over an exponentially shrinking sheet, Chinese Physics Letters, 28 (2011), pp. 074701
- Mukhopadhyay, S., Effects of slip on unsteady mixed convective flow and heat transfer past a stretching surface, Chinese Physics Letters, 27 (2010), pp. 124401
- Turkyilmazoglu, M., Multiple solutions of hydromagnetic permeable flow and heat transfer for viscoelastic fluid, Journal of Thermophysics and Heat Transfer, 25 (2011), pp. 595-605
- Zheng, L., Niu, J., Zhang, X., Gao, Y., MHD flow and heat transfer over a porous shrinking surface with velocity slip and temperature jump, Mathematical and Computer Modelling, 56 (2012), 5-6, pp. 133-144
- Hayat, T., Ullah, I., Alsaedi A., Ahmad, B., Radiative flow of Carreau liquid in presence of Newtonian heating and chemical reaction, Results in Physics, 7 (2017), pp. 715-722
- Hayat, T., Anwar, M. S., Farooq, M., Alsaedi, A, Mixed convection flow of viscoelastic fluid by a stretching cylinder with heat transfer, PLoS One, 10 (2015), pp. e0118815
- Hayat, T., Ullah, I., Alsaedi A., Ahmad, B., Modeling tangent hyperbolic nanoliquid flow with heat and mass flux conditions, The European Physical Journal Plus, 132 (2017), pp. 112
- Rehman K. U., Malik M. Y., Salahuddin T., Naseer M., Dual stratified mixed convection flow of Eyring-Powell fluid over an inclined stretching cylinder with heat generation/absorption effect, AIP Advances, 6 (2016), pp. 075112
- Hayat, T., Ullah, I., Alsaedi, A., Farooq, M., MHD flow of Powell-Eyring nanofluid over a non-linear stretching sheet with variable thickness, Results in Physics, 7 (2017), pp. 189-196
- Bibi M., Rehman K. U., Malik M. Y., Tahir M., Numerical study of unsteady Williamson fluid flow and heat transfer in the presence of MHD through a permeable stretching surface, The European Physical Journal Plus, 133 (2018), pp. 154
- Hayat, T., Ullah, I., Muhammad, T., and Alsaedi, A., Magnetohydrodynamic (MHD) three-dimensional flow of second grade nanofluid by a convectively heated exponentially stretching surface, Journal of Molecular Liquids, 220 (2016), pp. 1004-1012
- Rehman K. U., Khan A. A., Malik M. Y., Makinde O. D., Thermophysical aspects of stagnation point magnetonanofluid flow yields by an inclined stretching cylindrical surface: a non-Newtonian fluid model, Journal of the Brazilian Society of Mechanical Sciences and Engineering 39 (2017), pp. 3669-3682
- Hayat, T., Ullah, I., Muhammad, T., Alsaedi, A., Radiative three-dimensional flow with Soret and Dufour effects, International Journal of Mechanical Sciences, 133 (2017), pp. 829-837
- Hayat, T., Ullah, I., Muhammad, T., Asghar, S., MHD stagnation-point flow of Sisko liquid with melting heat transfer and heat generation/absorption, Journal of Thermal Sciences and Engineering Applications, (2018) pp. 051015
- Rehman K. U., Khan A. A., Malik M. Y., Magneto-nanofluid numerical modelling of chemically reactive Eyring-Powell fluid flow towards both flat and cylindrical an inclined surfaces: A comparative study, AIP Advances 7 (2017), pp. 065103
- Rehman K. U., Malik M. Y., Bilal S., Bibi M., Numerical analysis for MHD thermal and solutal stratified stagnation point flow of Powell-Eyring fluid induced by cylindrical surface with dual convection and heat generation effects, Results in physics, 7 (2017), pp. 482-492
- Merkin, J. H., A model for isothermal homogeneous-heterogeneous reactions in boundary layer flow, Mathematical and Computer Modelling, 24 (1996), pp. 125-136
- Chaudhary, M. A., Merkin, J. H., A simple isothermal model for homogeneous-heterogeneous reactions in boundary layer flow: I. Equal diffusivities, Fluid Dynamics Research, 16 (1995), 6, pp. 311-333
- Khan, W. A., Pop, I., Effects of homogeneous-heterogeneous reactions on the viscoelastic fluid towards a stretching sheet, Journal of Heat Transfer | ASME DC, 134 (2012), pp. 064506
- Hayat, T., Imtiaz, M., Almezal, S., Modeling and analysis for three-dimensional flow with homogeneous-heterogeneous reactions, AIP Advances, 5 (2015), pp. 107209
- Hayat, T., Hussain, Z., Farooq, M. Alsaedi, A., Effects of homogeneous and heterogeneous reactions and melting heat in the viscoelastic fluid flow, Journal of Molecular Liquids, 215 (2016), pp. 749-755
- Liao, S. J., Homotopy analysis method in nonlinear differential equations, Springer & Higher Education Press, Heidelberg, 2012.
- Turkyilmazoglu, M., Solution of the Thomas-Fermi equation with a convergent approach, Communications in Nonlinear Science and Numerical Simulation, 17 (2012), pp. 4097-4103
- Abbasbandy, S., Hayat, T., Alsaedi, A. Rashidi, M. M., Numerical and analytical solutions for Falkner-Skan flow of MHD Oldroyd-B fluid, International Journal of Numerical Methods for Heat and Fluid Flow, 24 (2014), pp. 390-401
- Hayat, T., Ullah, I., Alsaedi, A., Waqas, M., Ahmad, B., Three-dimensional mixed convection flow of Sisko nanoliquid, International Journal of Mechanical Sciences, 133 (2017), pp. 273-282
- Ullah I., Waqas M., Hayat T., Alsaedi A. and Khan M. I., Thermally radiated squeezed flow of magneto-nanofluid between two parallel disks with chemical reaction, J. Therm. Anal. Calorim., (2018) Doi.org/10.1007/s10973-018-7482-6.
- Rashidi, M. M., Ashraf, M., Rostami, B., Rastegari, M. T., Bashir, S., Mixed convection boundary layer flow of micro polar fluid towards a heated shrinking sheet by homotopy analysis method, Thermal science, 20 (2016), pp. 21-34
- S. Ahmad, Khan, M. I., Khan, M. W. A., Tufail, A., Hayat, T., Ahmed. A., Impact of arrhenius activation energy in viscoelastic nanomaterial flow subject to binary chemical reaction and nonlinear mixed convection, Thermal Science, (2018) pp. 212-212
- Hayat, T., Ullah, I., Muhammad, T., Asghar, S., Flow of magneto Williamson nanoliquid towards stretching sheet with variable thickness and double stratification, Radiation Physics Chemistry (2018), doi.org/10.1016/j.radphyschem.2018.07.006
- Sui, J., Zheng, L., Zhang, X., Chen, G., Mixed convection heat transfer in power law fluids over a moving conveyor along an inclined plate, International Journal of Heat and Mass Transfer, 85 (2015), pp. 1023-1033
- Hayat, T., Ullah, I., Ahmed, B., Alsaedi A., MHD mixed convection flow of third grade liquid subject to non-linear thermal radiation and convective condition, Results Physics, 7 (2017), pp. 2804-2811
- Zaigham Zia, Q. M., Ullah, I., Waqas, M., Alsaedi, A., Hayat, T., Cross diffusion and exponential space dependent heat source impacts in radiated three-dimensional (3D) flow of Casson fluid by heated surface, Results in Physics, 8 (2018), pp. 1275-1282
- Hayat, T., Ullah, I., Alsaedi, A., Ahmed, B., Numerical simulation for homogeneous-heterogeneous reactions in flow of Sisko fluid, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40 (2018), pp. 73
- Hayat, T., Ullah, I., Alsaedi, A., Ahmed, B., Simultaneous effects of non-linear mixed convection and radiative flow due to Riga-plate with double stratification, Journal of Heat Transfer, 140 (2018), pp. 102008