Thermal Analysis of Fluid Flow with Heat Generation for Different Logarithmic Surfaces

Document Type : Original Article


1 Department of Mechanical Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran


This study investigated the effect of temperature changes on different logarithmic surfaces. One-dimensional heat transfer was considered. The heat generation source term is added to the governing equations. Most scientific problems and phenomena such as heat transfer occur nonlinearly, and it is not easy to find exact analytical solutions. Using the appropriate similarity transformation for temperature and the generation components causes the basic equations governing flow and heat transfer to be reduced to a set of ordinary differential equations. These equations have been solved approximately subject to the relevant boundary conditions with numerical and analytical techniques. According to the given boundary conditions, Collocation, Galerkin, and least squares methods were used to find an answer to the governing differential equations. The validation of the present techniques has been done with the fourth-order Runge-Kutta method as a numerical method. The temperature profiles for different values of β and α have been obtained. The results showed that the proposed methods could consider nonlinear equations in heat transfer. Therefore, the results accepted by current analytical methods are very close to those of numerical methods. Comparing the results provides a more realistic solution and reinforces the conclusions regarding the efficiency of these methods. Furthermore, changes in temperature profiles occur with decreasing and increasing β and α numbers.


Main Subjects

  1. Jalili, B., Jalili, P., Sadighi, S. and Ganji, D.D., "Effect of magnetic and boundary parameters on flow characteristics analysis of micropolar ferrofluid through the shrinking sheet with effective thermal conductivity", Chinese Journal of Physics, Vol. 71, (2021), 136-150.
  2. Jalili, B., Sadighi, S., Jalili, P. and Ganji, D.D., "Characteristics of ferrofluid flow over a stretching sheet with suction and injection", Case Studies in Thermal Engineering, Vol. 14, (2019), 100470.
  3. Zangooee, M., Hosseinzadeh, K. and Ganji, D., "Hydrothermal analysis of mhd nanofluid (tio2-go) flow between two radiative stretchable rotating disks using agm", Case Studies in Thermal Engineering, Vol. 14, (2019), 100460.
  4. Ghadikolaei, S., Hosseinzadeh, K. and Ganji, D., "Analysis of unsteady mhd eyring-powell squeezing flow in stretching channel with considering thermal radiation and joule heating effect using agm", Case Studies in Thermal Engineering, Vol. 10, (2017), 579-594.
  5. Al-Sankoor, K., Al-Gayyim, H., Al-Musaedi, S., Asadi, Z. and Ganji, D., "Analytically investigating of heat transfer parameters with presence of graphene oxide nanoparticles in williamson-magnetic fluid by agm and hpm methods", Case Studies in Thermal Engineering, Vol. 27, (2021), 101236.
  6. Amouzadeh, F., Tondro, M., Asadi, Z. and Ganji, D., "Suction and injection effect on magnetohydrodynamic fluid flow within a vertical annulus for electrical wire cooling", Case Studies in Thermal Engineering, Vol. 27, (2021), 101241.
  7. Etbaeitabari, A., Barakat, M., Imani, A., Domairry, G. and Jalili, P., "An analytical heat transfer assessment and modeling in a natural convection between two infinite vertical parallel flat plates", Journal of Molecular Liquids, Vol. 188, (2013), 252-257.
  8. Ozisik, M.N., "Boundary value problems of heat conduction, courier Corporation, (2002).
  9. Stern, R.H. and Rasmussen, H., "Left ventricular ejection: Model solution by collocation, an approximate analytical method", Computers in biology and medicine, Vol. 26, No. 3, (1996), 255-261.
  10. Sun, Y., Li, X., Zhao, J., Hu, Y., Jing, X., Ma, J. and Zhou, R., "Investigation of transient coupled conduction and radiation heat transfer in the linearly anisotropic scattering cylindrical medium by spectral collocation method", International Journal of Thermal Sciences, Vol. 172, (2022), 107308.
  11. Basha, H.T. and Sivaraj, R., "Exploring the heat transfer and entropy generation of ag/fe $$ _3 $$3 o $$ _4 $$4-blood nanofluid flow in a porous tube: A collocation solution", The European Physical Journal E, Vol. 44, No. 3, (2021), 1-24.
  12. Çelik, İ. and Öztürk, H.K., "Heat transfer and velocity in the squeezing flow between two parallel disks by gegenbauer wavelet collocation method", Archive of Applied Mechanics, Vol. 91, No. 1, (2021), 443-461.
  13. Nabati, M., Salehi, G.H. and Taherifar, S., "Numerical solution for a porous fin thermal performance problem by application of sinc collocation method", Mathematical Methods in the Applied Sciences, (2021).
  14. Chandrakant, S., Panchal, H. and Sadasivuni, K.K., "Numerical simulation of flow-through heat exchanger having helical flow passage using high order accurate solution dependent weighted least square based gradient calculations", Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, (2021), 1-26.
  15. Biswal, U., Chakraverty, S., Ojha, B.K. and Hussein, A.K., "Numerical simulation of magnetohydrodynamics nanofluid flow in a semi-porous channel with a new approach in the least square method", International Communications in Heat and Mass Transfer, Vol. 121, (2021), 105085.
  16. Hatami, M. and Ganji, D., "Thermal performance of circular convective–radiative porous fins with different section shapes and materials", Energy Conversion and Management, Vol. 76, (2013), 185-193.
  17. Talarposhti, R., Jalili, P., Rezazadeh, H., Jalili, B., Ganji, D., Adel, W. and Bekir, A., "Optical soliton solutions to the (2+ 1)-dimensional kundu–mukherjee–naskar equation", International Journal of Modern Physics B, Vol. 34, No. 11, (2020), 2050102. doi.
  18. Vahabzadeh, A., Fakour, M., Ganji, D. and Bakhshi, H., "Analytical investigation of the one dimensional heat transfer in logarithmic various surfaces", Alexandria Engineering Journal, Vol. 55, No. 1, (2016), 113-117.
  19. Jalili, P., Ganji, D.D., Jalili, B. and Ganji, D.R.M., "Evaluation of electro-osmotic flow in a nanochannel via semi-analytical method", Thermal Science, Vol. 16, No. 5, (2012), 1297-1302. doi: 10.2298/TSCI1205297J.
  20. Pasha, P., Nabi, H., Peiravi, M., Pourfallah, M. and Domiri Ganji, D., "The application of analytical methods in the investigation effects of magnetic parameter and brownian motion on the fluid flow between two equal plates", International Journal of Engineering, Transactions A: Basics, Vol. 34, No. 10, (2021), 2341-2350. doi: 10.5829/IJE.2021.34.10A.15.
  21. Jalili, B., Aghaee, N., Jalili, P. and Ganji, D.D., "Novel usage of the curved rectangular fin on the heat transfer of a double-pipe heat exchanger with a nanofluid", Case Studies in Thermal Engineering, (2022), 102086.
  22. Humphries, U., Govindaraju, M., Kaewmesri, P., Hammachukiattikul, P., Unyong, B., Rajchakit, G., Vadivel, R. and Gunasekaran, N., "Analytical approach of fe3o4-ethylene glycol radiative magnetohydrodynamic nanofluid on entropy generation in a shrinking wall with porous medium", International Journal of Engineering, Transactions B: Applications, Vol. 34, No. 2, (2021), 517-527. doi: 10.5829/IJE.2021.34.02B.25.
  23. Agrawal, Y., Bhadauria, A. and Sikarwar, B., "Towards an analytical model for film cooling prediction using integral turbulent boundary layer", International Journal of Engineering, Transactions A: Basics, Vol. 29, No. 4, (2016), 554-562. doi: 10.5829/idosi.ije.2016.29.04a.15.
  24. Jalili, P., Kazerani, K., Jalili, B. and Ganji, D., "Investigation of thermal analysis and pressure drop in non-continuous helical baffle with different helix angles and hybrid nano-particles", Case Studies in Thermal Engineering, Vol. 36, (2022), 102209.
  25. Jalili, B., Sadighi, S., Jalili, P. and Ganji, D.D., "Numerical analysis of mhd nanofluid flow and heat transfer in a circular porous medium containing a cassini oval under the influence of the lorentz and buoyancy forces", Heat Transfer,
  26. Abbaszadeh, M., Dehghan, M., Khodadadian, A., Noii, N., Heitzinger, C. and Wick, T., "A reduced-order variational multiscale interpolating element free galerkin technique based on proper orthogonal decomposition for solving navier–stokes equations coupled with a heat transfer equation: Nonstationary incompressible boussinesq equations", Journal of Computational Physics, Vol. 426, (2021), 109875.
  27. Zhang, J., Shen, Y., Hu, H., Gong, S., Wu, S., Wang, Z. and Huang, J., "Transient heat transfer analysis of orthotropic materials considering phase change process based on element-free galerkin method", International Communications in Heat and Mass Transfer, Vol. 125, (2021), 105295.
  28. Fakour, M., Ganji, D. and Abbasi, M., "Scrutiny of underdeveloped nanofluid mhd flow and heat conduction in a channel with porous walls", Case Studies in Thermal Engineering, Vol. 4, (2014), 202-214.