Abstract
Heat transfer phenomena has become significant in engineering and industrial processes due to application of nanoparticles with enhanced thermal characteristics. The major goal of this study is to examine the heat transfer of Casson nanofluid with the suspension of Copper Cu into the base fluid water in the presence of temperature dependent thermal conductivity, heat source and thermal slip. Casson fluid is a type of non-Newtonian fluid and has gained attention for their distinct rheological properties and has potential practical applications in heat exchangers, food industry, manufacturing processes, biomedical treatments, etc. The flow is considered over horizontal and exponentially stretching cylinders. Nonlinear ordinary differential equations are attained by reforming the governing equations with the contribution of similarity variables. The dimensionless system is solved by MATLAB package \(\text{bvp}4\text{c}\). The results are obtained graphically and numerically. Consequences of various dimensionless quantities such as curvature parameter \(k\), Eckert number \(\text{Ec}\), Casson fluid parameter β, Thermal slip parameter \(\gamma \), stretching parameter λ, nano-shapes \(n\), heat source parameter \({Q}_{\text{H}}\) and volume fraction ϕ on temperature and velocity field for both horizontal and exponential cylinders are presented graphically and in tabular form. In this comparative study, we find out that the momentum boundary layer is dominant for exponential cylinder while the thermal boundary layer is more effective for horizontal cylinder as compared to exponential. Moreover, temperature enhances for horizontal and reduces for exponential cylinder with varying values of thermal slip.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10973-024-13378-z/MediaObjects/10973_2024_13378_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10973-024-13378-z/MediaObjects/10973_2024_13378_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10973-024-13378-z/MediaObjects/10973_2024_13378_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10973-024-13378-z/MediaObjects/10973_2024_13378_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10973-024-13378-z/MediaObjects/10973_2024_13378_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10973-024-13378-z/MediaObjects/10973_2024_13378_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10973-024-13378-z/MediaObjects/10973_2024_13378_Fig7_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10973-024-13378-z/MediaObjects/10973_2024_13378_Fig8_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10973-024-13378-z/MediaObjects/10973_2024_13378_Fig9_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10973-024-13378-z/MediaObjects/10973_2024_13378_Fig10_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10973-024-13378-z/MediaObjects/10973_2024_13378_Fig11_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10973-024-13378-z/MediaObjects/10973_2024_13378_Fig12_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10973-024-13378-z/MediaObjects/10973_2024_13378_Fig13_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10973-024-13378-z/MediaObjects/10973_2024_13378_Fig14_HTML.png)
References
Crane LJ. Flow past a stretching plate. Zeitschrift für angewandte Mathematik und Physik ZAMP. 1970;21(4):645–7.
Wang CY. Fluid flow due to a stretching cylinder. Phys fluids. 1988;31(3):466–8.
Brady JF, Acrivos A. Steady flow in a channel or tube with an accelerating surface velocity. An exact solution to the Navier stokes equations with reverse flow. J Fluid Mech. 1981;112:127–50.
Ishak A, Nazar R, Pop I. Uniform suction/blowing effect on flow and heat transfer due to a stretching cylinder. Appl Math Model. 2008;32(10):2059–66.
Wang CY. Natural convection on a vertical stretching cylinder. Commun Nonlinear Sci Numer Simul. 2012;17(3):1098–103.
Ishak A, Nazar R, Pop I. Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching cylinder. Energy Convers Manag. 2008;49(11):3265–9.
Munawar S, Ali A, Mehmood A. Thermal analysis of the flow over an oscillatory stretching cylinder. Phys Scr. 2012;86(6):065401.
Mukhopadhyay S. MHD boundary layer slip flow along a stretching cylinder. Ain Shams Eng J. 2013;4(2):317–24.
Khan M, Malik R, Hussain M. Nonlinear radiative heat transfer to stagnation-point flow of Sisko fluid past a stretching cylinder. AIP Adv. 2016;6(5):055315.
Pandey AK, Kumar M. Boundary layer flow and heat transfer analysis on Cu-water nanofluid flow over a stretching cylinder with slip. Alex Eng J. 2017;56(4):671–7.
Rangi RR, Ahmad N. Boundary layer flow past a stretching cylinder and heat transfer with variable thermal conductivity. Appl Math. 2012;3:205.
Choi SU, Eastman JA. Enhancing thermal conductivity of fluids with nanoparticles (No. ANL/MSD/CP-84938; CONF-951135–29). Argonne National Lab., IL (United States). 1995.
Kakaç S, Pramuanjaroenkij A. Review of convective heat transfer enhancement with nanofluids. Int J Heat Mass Trans. 2009;52(13–14):3187–96.
Khan WA, Pop I. Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Trans. 2010;53(11–12):2477–83.
Sheikholeslami M, Ganji DD, Ashorynejad HR, Rokni HB. Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method. Appl Math Mech. 2012;33(1):25–36.
Ibrahim W, Shankar B, Nandeppanavar MM. MHD stagnation point flow and heat transfer due to nanofluid towards a stretching sheet. Int J Heat Mass Transf. 2013;56(1–2):1–9.
Das SK, Putra N, Thiesen P, Roetzel W. Temperature dependence of thermal conductivity enhancement for nanofluids, communicated to J Heat Transfer. Trans ASME. 2001
Nadeem S, Rehman A. Axisymmetric stagnation flow of a nanofluid in a moving cylinder. Comput Math Model. 2013;24(2):293–306.
Sheikholeslami M. Effect of uniform suction on nanofluid flow and heat transfer over a cylinder. J Braz Soc Mech Sci Eng. 2015;37(6):1623–33.
Acharya N. Magnetized hybrid nanofluid flow within a cube fitted with circular cylinder and its different thermal boundary conditions. J Magn Magn Mater. 2022;15(564):170167.
Acharya N. On the magnetohydrodynamic natural convective alumina nanofluidic transport inside a triangular enclosure fitted with fins. J Indian Chem Soc. 2022;99(12):100784.
Dawar A, Acharya N. Unsteady mixed convective radiative nanofluid flow in the stagnation point region of a revolving sphere considering the influence of nanoparticles diameter and nanolayer. J Indian Chem Soc. 2022;99(10):100716.
Sulochana C, Sandeep N. Stagnation point flow and heat transfer behavior of Cu–water nanofluid towards horizontal and exponentially stretching/shrinking cylinders. Appl Nanosci. 2016;6:451–9.
Murtaza S, Kumam P, Ahmad Z, Sitthithakerngkiet K, Sutthibutpong T. Fractional model of brinkman-type nanofluid flow with fractional order Fourier’s and Fick’s Laws. Fractals. 2023;20:2340199.
Murtaza S, Kumam P, Ahmad Z, Ramzan M, Ali I, Saeed A. Computational simulation of unsteady squeezing hybrid nanofluid flow through a horizontal channel comprised of metallic nanoparticles. J Nanofluids. 2023;12(5):1327–34.
Acharya N. On the hydrothermal behavior and entropy analysis of buoyancy driven magnetohydrodynamic hybrid nanofluid flow within an octagonal enclosure fitted with fins: application to thermal energy storage. J Energy Storage. 2022;1(53):105198.
Acharya N, Mabood F, Badruddin IA. Thermal performance of unsteady mixed convective Ag/MgO nanohybrid flow near the stagnation point domain of a spinning sphere. Int Commun Heat Mass Trans. 2022;1(134):106019.
Acharya N. Buoyancy driven magnetohydrodynamic hybrid nanofluid flow within a circular enclosure fitted with fins. Int Commun Heat Mass Trans. 2022;1(133):105980.
Acharya N, Chamkha AJ. On the magnetohydrodynamic Al2O3-water nanofluid flow through parallel fins enclosed inside a partially heated hexagonal cavity. Int Commun Heat Mass Trans. 2022;1(132):105885.
Murtaza S, Ahmad Z, Ali IE, Akhtar Z, Tchier F, Ahmad H, Yao SW. Analysis and numerical simulation of fractal-fractional order non-linear couple stress nanofluid with cadmium telluride nanoparticles. J King Saud Univ-Sci. 2023;35(4):102618.
Murtaza S, Kumam P, Bilal M, Sutthibutpong T, Rujisamphan N, Ahmad Z. Parametric simulation of hybrid nanofluid flow consisting of cobalt ferrite nanoparticles with second-order slip and variable viscosity over an extending surface. Nanotechnol Rev. 2023;12(1):20220533.
Murtaza S, Kumam P, Sutthibutpong T, Suttiarporn P, Srisurat T, Ahmad Z. Fractal-fractional analysis and numerical simulation for the heat transfer of ZnO+ Al2O3+ TiO2/DW based ternary hybrid nanofluid. ZAMM-J Appl Math Mech/Zeitschrift für Angewandte Mathematik und Mechanik. 2023;21:e202300459.
Bhattacharyya K. MHD stagnation-point flow of Casson fluid and heat transfer over a stretching sheet with thermal radiation. J Thermodyn. 2013;2013:169674.
Mustafa M, Hayat T, Ioan P, Hendi A. Stagnation-point flow and heat transfer of a Casson fluid towards a stretching sheet. Zeitschrift für Naturforschung A. 2012;67(1–2):70–6.
Raju CSK, Sandeep N, Sugunamma V, Babu MJ, Reddy JR. Heat and mass transfer in magnetohydrodynamic Casson fluid over an exponentially permeable stretching surface. Eng Sci Technol Int J. 2016;19(1):45–52.
Murtaza S, Kumam P, Ahmad Z, Seangwattana T, Ali IE. Numerical analysis of newly developed fractal-fractional model of Casson fluid with exponential memory. Fractals. 2022;30(05):2240151.
Khalid A, Khan I, Shafie S. Exact solutions for unsteady free convection flow of Casson fluid over an oscillating vertical plate with constant wall temperature. Abstr Appl Anal. 2015;2015:1–8.
Akbar NS. Influence of magnetic field on peristaltic flow of a Casson fluid in an asymmetric channel: application in crude oil refinement. J Magn Magn Mater. 2015;378:463–8.
Hayat T, Shehzad SA, Alsaedi A. Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid. Appl Math Mech. 2012;33(10):1301–12.
Hussanan A, Zuki Salleh M, Tahar RM, Khan I. Unsteady boundary layer flow and heat transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating. PLoS ONE. 2014;9(10):e108763.
Najib N, Bachok N, Arifin NM, Ishak A. Stagnation point flow and mass transfer with chemical reaction past a stretching/shrinking cylinder. Sci Rep. 2014;4(1):1–7.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Tumreen, M., Qasim, M. Thermal analysis of Casson nanofluid flow over exponentially/horizontally stretching cylinders with physical conditions. J Therm Anal Calorim (2024). https://doi.org/10.1007/s10973-024-13378-z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10973-024-13378-z