Abstract
Cattaneo–Christov heat flux model was proposed to remedy the weakness of the traditional Fourier heat flux model to maintain the finite travel time of heat. The literature is replete with numerical studies to understand the heat transfer enhancement property. The present effort is to provide a mathematical rigor and to analytically demonstrate why the new model should act toward cooling and thus, in the way of enhancing the heat transfer rate from the surfaces. The derived and presented formulae here prove this assertion through comparison with a few selected examples from the open literature.
Issue Section:
Technical Briefs
References
1.
Cattaneo
,
C.
, 1948
, “
Sulla Condizione Del Calore
,” Atti del Seminario Matematico e Fisico dell' Universita di Modena e Reggio Emilia
, Vol.
3
, pp. 83
–101
.2.
Christov
,
C. I.
, 2009
, “
On Frame Indifferent Formulation of the Maxwell-Cattaneo Model of Finite-Speed Heat Conduction
,” Mech. Res. Commun.
,
36
(4
), pp. 481
–486
.10.1016/j.mechrescom.2008.11.0033.
Fourier
,
J. B. J.
, 1822
, Theorie Analytique ee la Chaleur
,
Cambridge University Press
,
Paris
.4.
Han
,
S.
,
Zheng
,
L.
,
Li
,
C.
, and
Zhang
,
X.
, 2014
, “
Coupled Flow and Heat Transfer in Viscoelastic Fluid With Cattaneo-Christov Heat Flux Model
,” Appl. Math. Lett.
,
38
, pp. 87
–93
.10.1016/j.aml.2014.07.0135.
Salahuddin
,
T.
,
Malik
,
M. Y.
,
Hussain
,
A.
,
Bilal
,
S.
, and
Awais
,
M.
, 2016
, “
Mhd Flow of Cattanneo-Christov Heat Flux Model for Williamson Fluid Over a Stretching Sheet With Variable Thickness: Using Numerical Approach
,” J. Magn. Magn. Mater.
,
401
, pp. 991
–997
.10.1016/j.jmmm.2015.11.0226.
Acharya
,
N.
,
Das
,
K.
, and
Kundu
,
P. K.
, 2017
, “
Cattaneo-Christov Intensity of Magnetised Upper-Convected Maxwell Nanofluid Flow Over an Inclined Stretching Sheet: A Generalised Fourier and Fick's Perspective
,” Int. J. Mech. Sci.
,
130
, pp. 167
–173
.10.1016/j.ijmecsci.2017.05.0437.
Hayat
,
T.
,
Muhammad
,
T.
, and
Alsaedi
,
A.
, 2017
, “
On Three-Dimensional Flow of Couple Stress Fluid With Cattaneo-Christov Heat Flux
,” Chin. J. Phys.
,
55
(3
), pp. 930
–938
.10.1016/j.cjph.2017.03.0038.
Hayat
,
T.
,
Aziz
,
A.
,
Muhammad
,
T.
, and
Alsaedi
,
A.
, 2018
, “
Three-Dimensional Flow of Prandtl Fluid With Cattaneo-Christov Double Diffusion
,” Results Phys.
,
9
, pp. 290
–296
.10.1016/j.rinp.2018.02.0659.
Upadhya, Mahesha
,
S. M.
, and
Raju
,
C. S. K.
, 2018
, “
Unsteady Flow of Carreau Fluid in a Suspension of Dust and Graphene Nanoparticles With Cattaneo-Christov Heat Flux
,” ASME J. Heat Transfer-Trans. ASME
,
140
(9
), p. 092401
.10.1115/1.403990410.
F. A.
Sulti
, 2019
, “
Impact of Cattaneo-Christov Heat Flux Model on Stagnation-Point Flow Toward a Stretching Sheet With Slip Effects
,” ASME J. Heat Transfer-Trans. ASME
,
141
(2
), p. 022003
.10.1115/1.404195911.
Zhang
,
X.
,
Zheng
,
L.
,
Liu
,
L.
, and
Zhang
,
X.
, 2020
, “
Modeling and Simulation on Heat Transfer in Blood Vessels Subject to a Transient Laser Irradiation
,” ASME J. Heat Transfer-Trans. ASME
,
142
(3
), p. 031201
.10.1115/1.404566912.
Sharma
,
R.
,
Hussain
,
S. M.
,
Raju
,
C. S. K.
,
Seth
,
G. S.
, and
Chamkha
,
A. J.
, 2020
, “
Study of Graphene Maxwell Nanofluid Flow Past a Linearly Stretched Sheet: A Numerical and Statistical Approach
,” Chin. J. Phys.
,
68
, pp. 671
–683
.10.1016/j.cjph.2020.10.01313.
Shankar
,
D. G.
,
Raju
,
C. S. K.
,
Kumar
,
M. S. J.
, and
Makinde
,
O. D.
, 2020
, “
Cattaneo-Christov Heat Flux on an Mhd 3D Free Convection Casson Fluid Flow Over a Stretching Sheet
,” Eng. Trans.
,
68
(3
), pp. 223
–238
.10.24423/EngTrans.1099.2020072014.
Upadhya
,
S. M.
,
Devi
,
R. L. V. R.
,
Raju
,
C. S. K.
, and
Ali
,
H. M.
, 2021
, “
Magnetohydrodynamic Nonlinear Thermal Convection Nanofluid Flow Over a Radiated Porous Rotating Disk With Internal Heating
,” J. Therm. Anal. Calorim.
,
143
(3
), pp. 1973
–1984
.10.1007/s10973-020-09669-w15.
Crane
,
L.
, 1970
, “
Flow Past a Stretching Plate
,” Z. Angew. Math. Phys.
,
21
(4
), pp. 645
–647
.10.1007/BF0158769516.
Wang
,
C. Y.
, 1989
, “
Free Convection on a Vertical Stretching Surface With Suction and Blowing
,” Appl. Math. Mech.
,
69
(11
), pp. 418
–420
.Copyright © 2021 by ASME
You do not currently have access to this content.
