Consequence of exponential heat generation on non-DarcyForchheimer flow of water based carbon nanotubes driven by a curved stretching sheet

doi:10.1007/s10483-020-2647-7

Abstract

Abstract: The present article comprises the study on the influence of exponential space based heat generation on the non-Darcy-Forchheimer flow of carbon nanotubes (CNTs). The flow is considered over a curved stretching sheet. Similarity variables are used to reduce the flow descriptive nonlinear partial derivative equations to simple equations. Simplified equations are then solved by the exploiting Runge-Kutta-Fehlberg fourth- and fifth-order methods. Obtained numerical solutions are shown in graphs and tables. Comparison between single and multi-walled CNTs has been established through the tabulated values and plotted graphs. It is concluded that the heat source parameter plays a prime role in enhancement of temperature, and the curvature parameter has adverse impact on velocity and temperature panels. Both the inertial parameter and inverse-Darcy number affect the fluid velocity.

Key words: exponential heat generation, non-Darcy-Forchheimer flow, carbon nanotube (CNT), curved stretching sheet

2010 MSC Number:

76A05

B. J. GIREESHA, B. NAGARAJA, S. SINDHU, G. SOWMYA. Consequence of exponential heat generation on non-DarcyForchheimer flow of water based carbon nanotubes driven by a curved stretching sheet. Applied Mathematics and Mechanics (English Edition), 2020, 41(11): 1723-1734.

TrendMD

References

[1] AKBAR, N. S., KHAN, Z. H., and NADEEM, S. The combined effects of slip and convective boundary conditions on stagnation-point flow of CNT suspended nanofluid over a stretching sheet. Journal of Molecular Liquids, 196, 21-25(2014)
[2] RIZWAN, U. H., NADEEM, S., KHAN, Z. H., and NOOR, N. F. M. Convective heat transfer in MHD slip flow over a stretching surface in the presence of carbon nanotubes. Physica B:Condensed Matter, 457, 40-47(2015)
[3] GIREESHA, B. J., MAHANTHESH, B., SHASHIKUMAR, N. S., and SHEHZAD, S. A. Marangoni convective MHD flow of SWCNT and MWCNT nanoliquids due to a disk with solar radiation and irregular heat source. Physica E:Low-Dimensional Systems and Nanostructures, 94, 25-30(2017)
[4] HAYAT, T., KHURSHEED, M., ALSAEDI, A., and ASGHAR, S. Numerical study for melting heat transfer and homogeneous-heterogeneous reactions in flow involving carbon nanotubes. Results in Physics, 8, 415-421(2018)
[5] HAYAT, T., RAFIQUE, K., MUHAMMAD, T., ALSAEDI, A., and AYUB, M. Carbon nanotubes significance in Darcy-Forchheimer flow. Results in Physics, 8, 26-33(2018)
[6] REDDY, M. G., KUMAR, K. G., SHEHZAD, S. A., JAVED, T., and AMBREEN, T. Thermal transportation analysis of nanoliquid squeezed flow past a sensor surface with MCWCNT and SWCNT. Heat Transfer-Asian Research, 6, 2262-2275(2019)
[7] JAIN, S. and GUPTA, P. Flow and heat transfer of carbon nanotubes nanofluid flow over a 3-D inclined nonlinear stretching sheet with porous media. Numerical Heat Transfer and Fluid Flow (2019) https://doi.org/10.1007/978-981-13-1903-7-37
[8] ZENG, Z. and GRIGG, R. A criterion for non-Darcy flow in porous media. Transport in Porous Media, 63(1), 57-69(2006)
[9] PAL, D. and CHATTERJEE, S. Heat and mass transfer in MHD non-Darcian flow of a micropolar fluid over a stretching sheet embedded in a porous media with non-uniform heat source and thermal radiation. Communications in Nonlinear Science and Numerical Simulation, 15(7), 1843-1857(2010)
[10] HAYAT, T., HAIDER, F., MUHAMMAD, T., and ALSAEDI, A. Numerical treatment for Darcy-Forchheimer flow of carbon nanotubes due to an exponentially stretching curved surface. Journal of Central South University, 4, 865-872(2019)
[11] KHAN, M. I., RASHID, M., HAYAT, T., KHAN, N. B., and ALSAEDI, A. Physical aspects of Darcy-Forchheimer bidirectional flow in carbon nanotubes (SWCNTs and MWCNTs). International Journal of Numerical Methods for Heat & Fluid Flow (2019) https://doi.org/10.1108/HFF-12-2018-0770
[12] SAIF, R. S., HAYAT, T., ELLAHI, R., MUHAMMAD, T., and ALSAEDI, A. Darcy-Forchheimer flow of nanofluid due to a curved stretching surface. International Journal of Numerical Methods for Heat & Fluid Flow, 29(1), 2-20(2019)
[13] BILAL, S., SOHAIL, M., NAZ, R., and MALIK, M. Y. Dynamical and optimal procedure to analyse the exhibition of physical attribute imparted by sutterby magneto nano fluid in darcy medium yield by axially stretched cylinder. Canadian Journal of Physics (2019) https://doi.org/10.1139/cjp-2018-0581
[14] NANDEPPANAVAR, M. M. and SHAKUNTHALA, S. Impact of Cattaneo-Christov heat flux on magnetohydrodynamic flow and heat transfer of carbon nanofluid due to stretching sheet. Journal of Nanofluids, 8(4), 746-755(2019)
[15] HAYAT, T., HAIDER, F., MUHAMMAD, T., and ALSAEDI, A. Darcy-Forchheimer three-dimensional flow of carbon nanotubes with nonlinear thermal radiation. Journal of Thermal Analysis and Calorimetry (2019) https://doi.org/10.1007/s10973-019-09016-8
[16] HOSSEINZADEH, K. H., ASADI, A., MOGHARREBI, A. R., KHALESI, J., MOUSAVISANI, S., and GANJI, D. D. Entropy generation analysis of (CH₂OH)2 containing CNTs nanofluid flow under effect of MHD and thermal radiation. Case Studies in Thermal Engineering, 14, 100482(2019)
[17] SAKIADIS, B. C. Boundary layer behaviour on continuous solid flat surface. American Institute of Chemical Engineers Journals, 7, 26-28(1961)
[18] CRANE, L. J. Flow past a stretching plate. Journal of Applied Mathematics and Physics (ZAMP), 21, 645-647(1970)
[19] SAJID, M., ALI, N., JAVED, T., and ABBAS, Z. Stretching a curved surface in a viscous fluid. Chinese Physics Letters, 27, 149-152(2010)
[20] ABBAS, Z., NAVEED, M., and SAJID, M. Hydromagnetic slip flow of nanofluid over a curved stretching surface with heat generation and thermal radiation. Journal of Molecular Liquids, 215, 756-762(2016)
[21] HAYAT, T., SAIF, R. S., ELLAHI, R., MUHAMMAD, T., and AHMAD, B. Numerical study of boundary-layer flow due to a nonlinear curved stretching sheet with convective heat and mass conditions. Results in Physics, 7, 2601-2606(2017)
[22] SABA, F., AHMED, N., HUSSAIN, S., KHAN, U., MOHYUD-DIN, S., and DARUS, M. Thermal analysis of nanofluid flow over a curved stretching surface suspended by carbon nanotubes with internal heat generation. Applied Sciences, 8, 395(2018)
[23] HAYAT, T., AYUB, S., and ALSAEDI, A. Homogeneous-heterogeneous reactions in curved channel with porous medium. Results in Physics, 9, 1455-1461(2018)
[24] AHMAD, S., NADEEM, S., and MUHAMMAD, N. Boundary layer flow over a curved surface imbedded in porous medium. Communications in Theoretical Physics, 71, 344(2019)
[25] QAYYUM, S., HAYAT, T., and ALSAEDI, A. Optimization of entropy generation in motion of magnetite-Fe₃O₄ nanoparticles due to curved stretching sheet of variable thickness. International Journal of Numerical Methods for Heat & Fluid Flow (2019) https://doi.org/10.1108/HFF-12-2018-0782.
[26] ANIMASAUN, I. L., ADEBILEE. A., and FAGBADE, A. I. Casson fluid flow with variable thermo-physical property along exponentially stretching sheet with suction and exponentially decaying internal heat generation using the homotopy analysis method. Journal of the Nigerian Mathematical Society, 35(1), 1-17(2016)
[27] MAHANTHESH, B., GIREESHA, B. J., PRASANNAKUMARA, B. C., and SAMPATH-KUMAR, P. B. Magneto-thermo-marangoni convective flow of Cu-H₂O nanoliquid past an infinite disk with particle shape and exponential space based heat source effects. Results in Physics, 7, 2990-2996(2017)
[28] ZIA, Q. M., ULLAH, I., WAQAS, M., ALSAEDI, A., and 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, 1275-1282(2018)
[29] KUMAR, A., REDDY, J. V. R., SUGUNAMMA, V., and SANDEEP, N. Impact of cross diffusion on MHD viscoelastic fluid flow past a melting surface with exponential heat source. Multidiscipline Modelling in Materials and Structures, 8, 90-94(2018)
[30] WAINI, I., ISHAK, A., and POP, I. Unsteady flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid. International Journal of Heat and Mass Transfer, 136, 288-297(2019)
[31] SHEIKHOLESLAMI, M., HAQ, R. U., SHAFEE, A., and LI, Z. Heat transfer behavior of nanoparticle enhanced PCM solidification through an enclosure with V shaped fins. International Journal of Heat and Mass Transfer, 130, 1322-1342(2019)
[32] IMTIAZ, M., SHAHID, F., HAYAT, T., and ALSAEDI, A. Melting heat transfer in Cu-water and Ag-water nanofluids flow with homogeneous-heterogeneous reactions. Applied Mathematics and Mechanics (English Edition), 40(4), 465-480(2019) https://doi.org/10.1007/s10483-019-2462-8