The present work examines the effects of temperature and velocity jump conditions on heat transfer, fluid flow, and entropy generation. As the physical model, the axially symmetrical steady flow of a Newtonian ambient fluid over a single rotating disk is chosen. The related nonlinear governing equations for flow and thermal fields are reduced to ordinary differential equations by applying so-called classical approach, which was first introduced by von Karman. Instead of a numerical method, a recently developed popular semi numerical-analytical technique; differential transform method is employed to solve the reduced governing equations under the assumptions of velocity and thermal jump conditions on the disk surface. The combined effects of the velocity slip and temperature jump on the thermal and flow fields are investigated in great detail for different values of the nondimensional field parameters. In order to evaluate the efficiency of such rotating fluidic system, the entropy generation equation is derived and nondimensionalized. Additionally, special attention has been given to entropy generation, its characteristic and dependency on various parameters, i.e., group parameter, Kn and Re numbers, etc. It is observed that thermal and velocity jump strongly reduce the magnitude of entropy generation throughout the flow domain. As a result, the efficiency of the related physical system increases. A noticeable objective of this study is to give an open form solution of nonlinear field equations. The reduced recurative form of the governing equations presented gives the reader an opportunity to see the solution in open series form.

1.
Bejan
,
A.
, 1980, “
Second Law Analysis in Heat Transfer
,”
Energy
0360-5442,
5
, pp.
720
732
.
2.
Erbay
,
L. B.
,
Ercan
,
M. S.
,
Sulus
,
B.
, and
Yalcin
,
M. M.
, 2003, “
Entropy Generation During Fluid Flow Between Two Parallel Plates With Moving Bottom Plate
,”
Entropy
1099-4300,
5
(
5
), pp.
506
518
.
3.
Mahmud
,
S.
, and
Fraser
,
R. A.
, 2003, “
The Second Law Analysis in Fundamental Convective Heat Transfer Problems
,”
Int. J. Therm. Sci.
1290-0729,
42
(
2
), pp.
177
186
.
4.
Yilbas
,
B. S.
, 2001, “
Entropy Analysis of Concentric Annuli With Rotating Outer Cylinder
,”
Int. J. Exergy
1742-8297,
1
(
1
), pp.
60
66
.
5.
Abu-Hijleh
,
B. A. K.
, and
Heilen
,
W. N.
, 1999, “
Entropy Generation Due to Laminar Natural Convection Over a Heated Rotating Cylinder
,”
Int. J. Heat Mass Transfer
0017-9310,
42
(
22
), pp.
4225
4233
.
6.
Owen
,
J. M.
, and
Roger
,
R. H.
, 1989, “
Flow and Heat Transfer in Rotating-Disc Systems
,”
Research Studies Press
,
Wiley
,
New York
.
7.
Attia
,
H. A.
, 2009, “
Steady Flow Over a Rotating Disk in Porous Medium With Heat Transfer
,”
Nonlinear Analysis: Modelling and Control
,
14
(
1
), pp.
21
26
.
8.
Sibanda
,
P.
, 2010, “
On steady MHD flow and Heat Transfer Past a Rotating Disk in a Porous Medium With Ohmic Heating and Viscous Dissipation
,”
Int. J. Numer. Methods Heat Fluid Flow
0961-5539,
20
(
3
), pp.
269
285
.
9.
Osalusi
,
E.
,
Side
,
J.
, and
Harris
,
R.
, 2007, “
The Effects of Ohmic Heating and Viscous Dissipation on Unsteady MHD and Slip Flow Over a Porous Rotating Disk With Variable Properties in the Presence of Hall and Ion-Slip Currents
,”
Int. Commun. Heat Mass Transfer
0735-1933,
34
, pp.
1017
1029
.
10.
Shevchuk
,
I. V.
, and
Buschmann
,
M. H.
, 2005, “
Rotating Disk Heat Transfer in a Fluid Swirling as a Forced Vortex
,”
Heat Mass Transfer
0947-7411,
41
, pp.
1112
1121
.
11.
Shevchuk
,
I. V.
, 2009,
Convective Heat and Mass Transfer in Rotating Disk Systems
,
Springer
,
Berlin
.
12.
Shevchuk
,
I. V.
, 2008, “
A New Evaluation Method for Nusselt Numbers in Naphthalene Sublimation Experiments in Rotating-Disk Systems
,”
Heat Mass Transfer
0947-7411,
44
, pp.
1409
1415
.
13.
Shevchuk
,
I. V.
, 2009, “
Turbulent Heat and Mass Transfer Over a Rotating Disk for the Prandtl or Schmidt Numbers Much Larger Than Unity: An Integral Method
,”
Heat Mass Transfer
0947-7411,
45
, pp.
1313
1321
.
14.
Hooman
,
K.
,
Hooman
,
F.
, and
Famouri
,
M.
, 2009, “
Scaling Effects for Flow in Micro-Channels: Variable Property, Viscous Heating, Velocity Slip, and Temperature Jump
,”
Int. Commun. Heat Mass Transfer
0735-1933,
36
, pp.
192
196
.
15.
Sparrow
,
E. M.
, and
Haji-Sheikh
,
A.
, 1964, “
Velocity Profile and Other Local Quantities in Free-Molecule Tube Flow
,”
Phys. Fluids
1070-6631,
7
, pp.
1256
1251
.
16.
Hooman
,
K.
, 2007, “
Entropy Generation for Microscale Forced Convection: Effects of Different Thermal Boundary Conditions, Velocity Slip, Temperature Jump, Viscous Dissipation, and Duct Geometry
,”
Int. Commun. Heat Mass Transfer
0735-1933,
34
, pp.
945
957
.
17.
Colin
,
S.
, 2005, “
Rarefaction and Compressibility Effects on Steady and Transient Gas Flows in Microchannels
,”
Microfluid. Nanofluid.
1613-4982,
1
, pp.
268
279
.
18.
Renksizbulut
,
M.
,
Niazmand
,
H.
, and
Tercan
,
G.
, 2006, “
Slip-Flow and Heat Transfer in Rectangular Microchannels With Constant Wall Temperature
,”
Int. J. Therm. Sci.
1290-0729,
45
, pp.
870
881
.
19.
Xiao
,
N.
,
Elsnab
,
J.
, and
Ameel
,
T.
, 2009, “
Microtube Gas Flows With Second-Order Slip Flow and Temperature Jump Boundary Conditions
,”
Int. J. Therm. Sci.
1290-0729,
48
, pp.
243
251
.
20.
Meolans
,
J. G.
, 2003, “
Thermal Slip Boundary Conditions in Vibrational Nonequilibrium Flows
,”
Mech. Res. Commun.
0093-6413,
30
, pp.
629
637
.
21.
,
M.
, 1999, “
The Fluid Mechanics of Microdevices—The Freeman Scholar Lecture
,”
ASME J. Fluids Eng.
0098-2202,
121
(
1
), pp.
5
33
.
22.
Ozkol
,
I.
,
Komurgoz
,
G.
, and
Arikoglu
,
A.
, 2007, “
Entropy Generation in the Laminar Natural Convection From a Constant Temperature Vertical Plate in an Infinite Fluid
,”
Proc. Inst. Mech. Eng., Part A
0957-6509,
221
, (A5), pp.
609
616
.
23.
Baytaş
,
A. C.
, 1997, “
Optimisation in an Inclined Enclosure for Minimum Entropy Generation in Natural Convection
,”
J. Non-Equil. Thermodyn.
0304-0204,
22
(
2
), pp.
145
155
.
24.
Ogulata
,
R. T.
,
Doba
,
F.
, and
Yilmaz
,
T.
, 1999, “
Second-Law and Experimental Analysis of a Cross-Flow Heat Exchanger
,”
J. Heat Transfer Eng.
,
20
(
2
), pp.
20
27
.
25.
Yari
,
M.
, 2009, “
Second-Law Analysis of Flow and Heat Transfer Inside a Microannulus
,”
Int. Commun. Heat Mass Transfer
0735-1933,
36
(
1
), pp.
78
87
.
26.
Hooman
,
K.
, 2008, “
Heat Transfer and Entropy Generation for Forced Convection Through a Microduct of Rectangular Cross-Section: Effects of Velocity Slip, Temperature Jump, and Duct Geometry
,”
Int. Commun. Heat Mass Transfer
0735-1933,
35
(
9
), pp.
1065
1068
.
27.
,
O.
,
Abuzzaid
,
M.
, and
Al-Nimr
,
M.
, 2004, “
Entropy Generation Due to Laminar Incompressible Forced Convection Flow Through Parallel-Plates Microchannel
,”
Entropy
1099-4300,
6
(
5
), pp.
413
426
.
28.
,
G. E.
, and
Beskok
,
A.
, 2002,
Microflows: Fundamentals and Simulation
,
Springer-Verlag
,
New York
, p.
56
.
29.
Arikoglu
,
A.
, and
Ozkol
,
I.
, 2005, “
Analysis for Slip Flow Over a Single Free Disk With Heat Transfer
,”
ASME J. Fluids Eng.
0098-2202,
127
(
3
), pp.
624
627
.
30.
Karman
,
T.
, 1921, “
Über Laminare und Turbulente Reibung
,”
Z. Angew. Math. Mech.
0044-2267,
1
, pp.
233
252
.
31.
Arikoglu
,
A.
, and
Ozkol
,
I.
, 2006, “
On the MHD and Slip Flow Over a Rotating Disk With Heat Transfer
,”
Int. J. Numer. Methods Heat Fluid Flow
0961-5539,
16
(
2
), pp.
172
184
.
32.
Benton
,
E. R.
, 1966, “
On the Flow Due to a Rotating Disk
,”
J. Fluid Mech.
0022-1120,
24
, pp.
781
800
.
33.
Attia
,
H. A.
, 2008, “
Rotating Disk Flow and Heat Transfer Through a Porous Medium of a Non-Newtonian Fluid With Suction and Injection
,”
Commun. Nonlinear Sci. Numer. Simul.
1007-5704,
13
(
8
), pp.
1571
1580
.
34.
Arikoglu
,
A.
, and
Ozkol
,
I.
, 2005, “
Solution of Boundary Value Problems for Integro-Differential Equations by Using Differential Transform Method
,”
Appl. Math. Comput.
0096-3003,
168
(
2
), pp.
1145
1158
.
35.
Arikoglu
,
A.
, and
Ozkol
,
I.
, 2006, “
Solution of Difference Equations by Using Differential Transform Method
,”
Appl. Math. Comput.
0096-3003,
174
(
2
), pp.
1216
1228
.
36.
Arikoglu
,
A.
,
Komurgoz
,
G.
, and
Ozkol
,
I.
, 2008, “
Effect of Slip on the Entropy Generation From a Single Rotating Disk
,”
ASME J. Fluids Eng.
0098-2202,
130
(
10
), p.
101202
.
37.
Miklavcic
,
M.
, and
Wang
,
C. Y.
, 2004, “
The Flow Due to a Rough Rotating Disk
,”
Z. Angew. Math. Phys.
0044-2275,
55
, pp.
235
46
.
38.
Lin
,
H. T.
, and
Lin
,
L. K.
, 1987, “
Heat-Transfer From a Rotatıng Cone or Disk to Fluids of Any Prandtl Number
,”
Int. Commun. Heat Mass Transfer
0735-1933,
14
(
3
), pp.
323
332
.
39.
Oehlbeck
,
D. L.
, and
Erian
,
F. F.
, 1979, “
Heat-Transfer From Axisymmetric Sources at the Surface of a Rotating-Disk
,”
Int. J. Heat Mass Transfer
0017-9310,
22
(
4
), pp.
601
610
.
40.
Komurgoz
,
G.
,
Arikoglu
,
A.
,
Turker
,
E.
, and
Ozkol
,
I.
, 2010, “
Second-Law Analysis for an Inclined Channel Containing Porous-Clear Fluid Layers by Using the Differential Transform Method
,”
Numer. Heat Transfer, Part A
1040-7782,
57
(
8
), pp.
603
623
.
41.
Attia
,
H. A.
, 2001, “
Transient Flow a Conducting Fluid With Heat Transfer Due to an Infinite Rotating Disk
,”
Heat Mass Transfer
0947-7411,
28
(
3
), pp.
439
448
.