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.

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.2008.11.003
3.
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.2014.07.013
5.
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.2015.11.022
6.
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.2017.05.043
7.
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.2017.03.003
8.
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.2018.02.065
9.
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
.10.1115/1.4039904
10.
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
.10.1115/1.4041959
11.
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
.10.1115/1.4045669
12.
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.2020.10.013
13.
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.1099.20200720
14.
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-w
15.
Crane
,
L.
,
1970
, “
Flow Past a Stretching Plate
,”
Z. Angew. Math. Phys.
,
21
(
4
), pp.
645
647
.10.1007/BF01587695
16.
Wang
,
C. Y.
,
1989
, “
Free Convection on a Vertical Stretching Surface With Suction and Blowing
,”
Appl. Math. Mech.
,
69
(
11
), pp.
418
420
.
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