## 5 Conclusions  
The current research was carried out to analyse the convection analysis of heated Jeffrey fluid in a conduit having elliptic domain and ciliated boundaries. The key outcomes are given below. The velocity gains its highest magnitude in the middle region of the conduit and a parabolic velocity profile is seen. The velocity gains magnitude with the increasing value of \(\beta\) in the middle of the duct but it declines with increasing \(\beta\) near the ciliated boundaries. An axial symmetry and parabolic velocity profile is observed. An axially symmetrical temperature behaviour is also observed in these temperature graphs. The temperature has high magnitude in the middle and low sections near the ciliated boundaries. A decline in the temperature profile is observed for increasing values of \(\lambda_{1}\). If we set \(\lambda_{1}=0\) then the problem is simply a Newtonian flow problem. The increase in the value of \(\lambda_{1}\) changes the problem to a non-Newtonian flow problem. It is observed that the temperature reduces if the problem is transformed from Newtonian analysis to a non-Newtonian one. The temperature rapidly increases for the increasing value of \(B_{r}\). The trapped close contours show an increase in size for rising \(Q\). Data curation, S.N. ; Formal analysis, S.N. ; Funding acquisition, S.E.E. ; Methodology, S.N. and S.A. ([PERSON]); Project administration, S.N. ; Resources, S.A. ([PERSON]); Supervision, S.N. ; Validation, S.A. ([PERSON]) and H.A.G. ; Writing--original draft, S.A. ([PERSON]); Writing--review & editing, S.A. ([PERSON]). All authors have read and agreed to the published version of the manuscript. This research received no external funding. The authors  
[PERSON]; [PERSON] Influence of heat transfer on a peristaltic flow of Johnson Segalman fluid in a non uniform tube. _Int. Commun. Heat Mass Transf._**2009**, _36_, 1050-1059. [CrossRef]
* [7] [PERSON]; [PERSON]; [PERSON]; [PERSON] Peristaltic flow of a nanofluid in a non-uniform tube. _Heat Mass Transf._**2012**, _48_, 451-459. [CrossRef]
* [8] [PERSON]; [PERSON] Peristaltic flow of a Phan-Thien-Tanner nanofluid in a diverging tube. _Heat Transf.--Asian Res._**2012**, _41_, 10-22. [CrossRef]
* [9] [PERSON]; [PERSON] Combined effects of heat and chemical reactions on the peristaltic flow of Carreau fluid model in a diverging tube. _Int. J. Numer. Methods Fluids_**2011**, _67_, 1818-1832. [CrossRef]
* [10] [PERSON]; [PERSON] The mathematical analysis for peristaltic flow of hyperbolic tangent fluid in a curved channel. _Commun. Theor. Phys._**2013**, _59_, 729. [CrossRef]
* [11] [PERSON]; [PERSON] Mathematical analysis for peristaltic flow of two phase nanofluid in a curved channel. _Commun. Theor. Phys._**2015**, _64_, 547. [CrossRef]
* [12] [PERSON]; [PERSON] Peristaltic flow of a Jeffrey fluid in a rectangular duct. _Nonlinear Anal. Real World Appl._**2010**, _11_, 4238-4247. [CrossRef]
* [13] [PERSON]; [PERSON]; [PERSON] Three dimensional peristaltic flow of [PERSON] fluid in a rectangular duct. _Indian J. Phys._**2013**, _87_, 1275-1281. [CrossRef]
* [14] [PERSON]; [PERSON] Analysis of Heating Effects and Different Wave Forms on Peristaltic Flow of Carreau Fluid in Rectangular Duct. _Adv. Math. Phys._**2020**, _2020_, 8294318. [CrossRef]
* [15] [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Mathematical computations for Peristaltic flow of heated non-Newtonian fluid inside a sinusoidal elliptic duct. _Phys. Scr._**2020**, _95_, 105009. [CrossRef]
* [16] [PERSON]; [PERSON] Heat transfer analysis of viscoelastic fluid flow due to metachronal wave of cilia. _Int. J. Biomath._**2014**, \(7\), 1450066. [CrossRef]
* [17] [PERSON]; [PERSON] Influence of magnetic field for metachronical beating of cilia for nanofluid with Newtonian heating. _J. Magn. Magn. Mater._**2015**, _381_, 235-242. [CrossRef]
* [18] [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Physical aspects of peristaltic flow of hybrid nano fluid inside a curved tube having ciliated wall. _Results Phys._**2020**, _19_, 103431.