INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,

MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)

ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XIV, Issue XI, November 2025

MHD Flow Over A Rotating Vertical Porous Plate with

Exponentially Accelerating Velocity, Temperature, and Mass in the

Presence of Hall Current and Heat Source

Dr D. Lakshmikaanth¹, M. Krishnakumari²

¹Department of Mathematics, College of Fish Nutrition & Food Technology (CFNFT), Tamilnadu Dr. J.

Jayalalithaa Fisheries University (TNJFU), Chennai-600051, India

²Department of Mathematics, Mahalashmi Women’s College of Arts and Science , No.!,Mahalashmi

nagar ,Paruthipattu., Avadi, Chennai, Tamilnadu

DOI : https://doi.org/10.51583/IJLTEMAS.2025.1411000116

Received: 29 November 2025; Accepted: 05 December 2025; Published: 24 December 2025

ABSTRACT:

This study analyzes exponentially accelerating fluid through vertically porous plate with a heat source. The

effects of rotation, porosity, and Thermal Radiation on velocity (Speed), temperature (Warmth), and

concentration(accumulation) profiles are investigated. Results indicate that velocity rises with heat source

increase but decreases with radiation and rotation. Temperature increases with heat generation raises while

concentration drops with higher Schmidt numbers. Also, Skin friction, Nusselt & Sherwood values tabulated.

Keywords: Exponential, Sherwood, Generation, Plate, Concentration.

INTRODUCTION

Heat sources are used a lot in the processing of chemicals and polymers, like film coating, extrusion, and drying,

because they speed up reaction and production rates. In the food industry, heat sources are used in processes like

pasteurisation, and film coating. Controlled heating speeds up reactions, improves texture, and makes products

more stable. [1] Kota et al. studied transient MHD flow across a vertically speeding permeable plate with viscous

heating and warmth generation. [2] A. Selvaraj and E. Jothi looked into how the temperature of the plate rises

in a straight line over time, with the highest values happening close to the surface of the plate. [3]-[4] Nath and

Deka compared the behaviour of nanofluids with two stratifications to that without any stratification without and

with Chemical reaction. [5] Rakesh Rabha and Rudra K. Deka analyzed the flow with and without stratification,

observing that steady state(independent of time) is reached faster in the presence of stratification. [6] K.Balu

and his collegue examines MHD across rapidly sloped plate and concentrating on the region adjacent to the

plate. [7] Pratibha P. Ubale Patil et al. found that axial skin friction goes down as water permeability goes up,

changes in an irregular way in air, and oscillates in both fluids when a heat source is present.[8]-[11] D.

Lakshmikanth and his team looked into how a heat source with and without rotation, as well as the Dufour effect,

affected a vertically accelerated isothermal plate that was undergoing chemical reaction and radiation.[12] R.

Muthukumaraswamy and a coworker used MATLAB to make graphs of skin friction, temperature,

concentration, and velocity profiles for different thermophysical parameters. [13]-[14] Hetnarski introduces an

algorithm for the formulas of inverse Laplace transforms.

Mathematical Formulation

We are looking at a non-conductive vertical plate at 푧 = 0, with a viscous incompressible conducting fluid

flowing past it. The plate is vertical and the 푧 axis is normal to it. The velocity, temperature and concentration

all are e^atat t=0. The velocity components make the flow characteristics when there is constant pressure across

flow and continuity is met. Taking these assumptions into account, the governing equations for the transient flow

are written like this:

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INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,

MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)

ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XIV, Issue XI, November 2025

2

~

B





u



m v



u

 u

~



u

~

0

1

 2u  

 gT  T  gC  C







1



~



2

~

t

K

1

z





1 m

1

2

~

~ ~

~

B  m u  v

v

 v

v

~

0

1

 2v  





2



~

2

~

t

K

1

z





1 m



1

~

2



1  

~



 R  Q

3

 

~

2

~

t

Pr

z

~

2

C

1  C



4



~

2

~

t

Sc

z

The conditions are

~

t  0: u  v  0,T  T ,C  C , z  0,



~

at

~









t  0: u  u

e

, v  0,T  T  C  C  0z  0,



5



0







~

t  0: u  0, v  0,T  T ,C  C as z  ,



The consequent dimensionless aggregate is

~

2

0

~

u

zu

tu

T  T

C  C



0



Z 

, t 

,U 

, 

,C   

~



u

T  T

C

 C

o

w



w



1/ 3

~

2







gT  T



g

C

 C



B

o



2

w



w





Gr 

,Gc 

,M 



6



3

2











u

o

1/ 3







Cp



2





Pr 

,K  K

,Sc 

1









k

D

u

o

(1)+ i×(2) and putting velocity q = u+iv we get ,

2

q

t

 q

q

M

 G   G C 

 mq 

where m 

 2i

r

c

2

K



1 hi

z

1

2



t

1  

P

r



 R  Q

2

z

2

C

1  C



2

t

S

c

z

With conditions

q  0,   C  0 for all z,t  0

at

q  e ,   e

,C  e

for all z,t  0

q  0,   0 ,C  0 as z  .

RESULTS & DISCUSSION

Solving Using Inverse technique of Laplace we have

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INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,

MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)

ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XIV, Issue XI, November 2025

at

e

2 atSc

z atSc





C

e

erfc Sc  ate

erfc Sc  at







2 

at

 4²P atRtQt

4²P aRQ

t













e















2

r



e

erfc  P  at  Rt  Qt  e

erfc  P  at  Rt  Qt











r

2

















1

2











m a 4 t

at



























e

t

k₁













q 

e

erfc  mt 

 at e

erfc  mt 

 at





2

k

1































t

2







mt  at 4















t

k₁









e

erfc  mt 

 at



at

k

e

1

2





t

2





mt  at 4











t

k₁







 e

erfc   mt 

 at



k

1





G

1

r



















P 1 a  b

t

2

r









mt  bt 4















t

k₁













e

erfc 

mt 

 bt









k

bt



1



e



2





t

2





mt  bt 4 t













t

k₁







 





 e

erfc 

mt 

 bt







 

k







1

 































t

2







mt  at 4















t

k₁









e

erfc 

mt 

 at











k

 ^at

e

1







2







t

2





mt  at 4













t

k₁













e

erfc  

mt 

 at





k



1







 

G

1





c











S 1 a  c













c

t

2







mt  ct 4













t

k₁











e

erfc  

mt 

 ct













k

ct

1



e



2





t

2





mt  at 4















t

k₁











 e

erfc  

mt 

 ct



k



1

 





















R Qa4t²Pr























2

e

erfc  Pr  Rt  Qt  at







at

e

R Qa4t²Pr

2 









2

 e

erfc  Pr  Rt  Qt  at



















G

1



r



R Qb4t²Pr

P 1 a  b





r







 

2

e

erfc  Pr  Rt  Qt  bt











bt



e



R Qb4t²Pr

2 





 

2

e

erfc  Pr  Rt  Qt  bt





















at





e

2 atSc

2 atSc





ct





e

erfc Sc  ate

erfc Sc  at













G

1

2

c

S 1 a  c

c

e



2 ctSc

2 ctSc











e

erfc Sc  ct e

erfc Sc  ct















2

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Page 1220

INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,

MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)

ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XIV, Issue XI, November 2025

1

m 



R  QPr

m 

k

z

k

1

where  

b 

,

c 

Pr1

Sc 1

2 t

Skin

Friction

1

(Sk)





1













 mt t

at



































q

1

1









k₁

at









 e



e

 1 erfc

mt  t

 at

m 

 a















z

k

1

t











1









z0

















1











 mt t

at































1

k₁

at















e



e

 1 erfc

mt  t

 at

m 

 a













k

1

t







1













G

r



P 1a  b





1









r





 mt t

bt































1

k₁

bt

















 e

 



e

 1 erfc

mt  t

 bt

m 

 b













k

1

t









1































1











 mt t

at















































1

k₁

at

e





















e

 1 erfc

mt  t

 bt

m 

 a













k

1

t







1











G

c









Sc 1a  c









1







 mt t

ct



































1

k₁

bt

















 e



e

 1 erfc

mt  t

 bt

m 

 c













k

1

t







1



































Pr

at



RtQtat

e

 



e





1 erfc Rt  Qt  at





R  Q  aPr











t









G

r



P 1a  b











Pr

r

bt



RtQtbt

 e



e





1 erfc Rt  Qt  bt







R  Q  bPr















t











Nusselt





































G

 Sc

at

at

bt

bt

c

































e

 1 erfc at

aSc  e

e

 1 erfc bt

bSc





Sc 1a  c

t









































 Pr







at



Rt Qtat





 e

e





1 erfc Rt  Qt  at





R Pr QPr a Pr

Number (Nu)







z



t









z0

Sherwood Number (Sh)



















C

 Sc









at

 e^at

e





1 erfc at







aSc



z

t



_z0









Nusselt Number (Nu)

R

Q

Pr

t

Nu

2.0

7.0

0.4

-3.4646

-5.0003

-6.2683

3.0

5.0

7.0

R

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5.0

7.0

0.71

7.0

0.4

0.1

0.2

0.4

-5.9710

-5.0003

-3.4646

-1.5925

-5.0003

-6.1739

-5.3226

-5.0003

0.5

2.0

4.0

2.0

Q

Pr

T

Sherwood Number (Sh)

Sc

t

Sh

0.4

0.1

0.2

0.4

-0.5287

-0.7478

-1.3686

-2.5804

-1.8611

-1.3686

0.3

0.6

Sc

2.01

t



Skin Friction ( )

Gr

Gc

R

Q

k1

M

hc

w

흉

25.0

10.0

18.0

25.0

5.0

2.0

3.0

5.0

2.0

0.5

1.0

1.5

3.0

2.0

0.7275

1.7715

2.6849

1.5370

2.1493

2.6849

3.4668

3.1615

2.6849

2.4134

10.0

18.0

25.0

Gr

Gc

R

Q

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25.0

5.0

1.0

0.5

1.0

4.0

1.0

1.5

2.5

3.0

1.5

3.0

0.25

1.0

3.0

2.0

3.0

4.0

2.6849

3.1615

-1.7834

2.6849

6.1627

2.6849

1.3032

0.2148

0.9419

1.9332

2.6849

-0.3271

-4.7847

2.0

4.0

2.0

k1

M

Hc

Ω

Geometrical Representation

Figure 1

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Fig 1 :The buoyancy force induced by the difference in temperature stronger as the thermal Grashof number

(Gr) goes up. This higher buoyancy makes the fluid move faster, which speeds up the flow.

Figure 2

Fig 2 It shows that when the Mass Grashof number (Gc) goes up the velocity (speed) goes up also. This is

because a bigger mass-concentration differential makes buoyancy forces greater, which pushes the fluid faster

and raises the flow speed.

Figure 3

Fig 3: It discovers that the speed of the fluid rises as the heat source (Q) gets greater. This is because more

heating increases the buoyancy force, which pushes the fluid faster.

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Figure 4 In Fig 4 As radiation(R) rises, the velocity (speed) drops because more radiation takes heat out from

the fluid, which lowers the buoyancy force and slows down the flow.

Figure 5 In Fig 5 As the rotation (w) speeds up, the velocity (speed) down. This is because higher rotational

effects create Coriolis and centrifugal forces, which slow down the flow by resisting the fluid motion.

Figure 6 In Fig 6 As the Hall current (hc)goes up, the speed (velocity) goes up also. This is because the Hall

effect makes the electromagnetic force stronger in the fluid, which speeds up the motion and raises the flow

speed.

Figure 7In Fig 7 The speed (velocity) goes up when permeability(k1) goes up. This is because increased

permeability makes it easier for the fluid to move through the medium, which lowers resistance and speeds up

flow.

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Figure 8 In Fig 8 As the Prandtl number (Pr) goes up, the velocity (speed) goes down. This is because a higher

Prandtl number indicates that momentum spreads out quicker than heat, which slows down the fluid motion and

stops the thermal boundary layer from growing.

Figure 9 In Fig 9 As radiation (R) rises, the temperature drops. This is because increased radiation takes heat out

from the fluid, lowering its thermal energy and lowering the temperature.

Figure 10 In Fig. 10, the temperature goes up because greater Heat source (Q) contributes more thermal energy

to the fluid, which makes it hotter.

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Figure 11

In Fig 11 The Schmidt number (Sc) goes up, which means that mass diffusion is slower than

momentum. This slows down the flow and diminishes the fluid motion.

CONCLUSION

The fast isothermal flow over a inclined vertical plate is the focus of this easy-to-use and interesting framework

for computer research. This has to do with HMT. These computations allow for the deduction of several crucial

relationships:

(i) Velocity increases when the Heat Source increases, whereas velocity decreases with raise in permeability and

Hall Current

(ii)Temperature drops as radiation levels rise whereas the Heat Source raises, the temperature raises.

(iii)The concentration of the species involved tends to decline as the rate of the schmidth raises.

(iv)The Skin friction decreases as Prandtl, Hartmaann, Permeability, Radiation and Hall Current Values

increases whereas skin friction increases when Rotation, Heat Source, Thermal Grashof and Mass Grashof values

increases.

REFERENCES

1. Santhi Kumari Dharani Kota, Venkata Subrahmanyam Sajja, and Perugu Mohana Kishore. “Transient

MHD Flows Through an Exponentially Accelerated Isothermal Vertical Plate with Viscous Dissipation

and Heat Source Embedded in a Porous Medium.” Journal of Advanced Research in Fluid Mechanics

and Thermal Sciences 106, no. 2 (July 18, 2023): 153–66. https://doi.org/10.37934/arfmts.106.2.153166 .

2. Selvaraj, A., and E. Jothi. “Heat Source Impact on MHD and Radiation Absorption Fluid Flow Past an

Exponentially Accelerated Vertical Plate with Exponentially Variable Temperature and Mass Diffusion

through

a

Porous

Medium.”

Materials

Today:

Proceedings

46

(2021):

3490–94.

https://doi.org/10.1016/j.matpr.2020.11.919 .

3. Nath, Rupam Shankar, and Rudra Kanta Deka. “Thermal and Mass Stratification Effects on MHD

Nanofluid Past an Exponentially Accelerated Vertical Plate through a Porous Medium with Thermal

Radiation and Heat Source.” International Journal of Modern Physics B 39, no. 07 (April 3, 2024).

https://doi.org/10.1142/s0217979225500456 .

4. Nath, Rupam Shankar, and Rudra Kanta Deka. “Theoretical Study of Thermal and Mass Stratification

Effects on MHD Nanofluid Past an Exponentially Accelerated Vertical Plate in a Porous Medium in

Presence of Heat Source, Thermal Radiation and Chemical Reaction.” International Journal of Applied

and Computational Mathematics 10, no. 2 (April 2024). https://doi.org/10.1007/s40819-024-01721-9 .

www.ijltemas.in

Page 1227

INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,

MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)

ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XIV, Issue XI, November 2025

5. Rabha, Rakesh, and Rudra K. Deka. “Influence of Mass Transfer and Chemical Reaction on MHD Flow

Through a Porous Medium Past an Exponentially Accelerated Vertical Plate With Thermal Stratification

and Radiation.” Heat Transfer 54, no. 5 (April 14, 2025): 3208–19. https://doi.org/10.1002/htj.23353 .

6. Balu, K. “Heat And Mass Transfer on MHD Flow Past an Exponentially Accelerated Vertical Plate

Through Porous Medium.” Interantional Journal of Scientific Research in Engineering and Management

07, no. 09 (September 1, 2023). https://doi.org/10.55041/ijsrem25575 .

7. Pratibha P. Ubale Patil, V. B. Kulkarni, R. M. Lahurikar “Effect of Heat Source on the Rotatory Flow

Past an Accelerated Infinite Vertical Plate through Porous Medium.”

Journal of Intelligent Systems and Applications

https://doi.org/10.17762/ijisae.v12i23s.7329 .

International

Engineering, 2024.

in

8. Lakshmikaanth, D., A. Selvaraj, P. Selvaraju, and S. Dilip Jose. “Hall and Heat Source Effects of Flow

Past a Parabolic Accelerated Isothermal Vertical Plate in the presence of Chemical Reaction and

Radiation.”

JP

Journal

of

Heat

and

Mass

Transfer,

July

14,

2023,

105–26.

https://doi.org/10.17654/0973576323035 .

9. Lakshmikaanth, D., Selvaraj, A., Selvaraju, P., & Jose, S. D. (2023). Heat Source effects of flow past a

parabolic accelerated isothermal vertical plate in the presence of Hall Current , Chemical reaction ,

Rotation and Radiation. Eur. Chem. Bull. 2023,12(4), 3354-3374.

10. D, lakshmikaanth, Selvaraj A., and Bhavani S. “Exploration of the Impacts of Hall Effect, Dufour Effect,

and Heat Source on Parabolic Flow over an Infinite Vertical Plate in the Presence of Rotation, Chemical

Reaction, and Radiation in a Porous Medium.” CFD Letters 17, no. 1 (August 31, 2024): 60–77.

https://doi.org/10.37934/cfdl.17.1.6077 .

11. Jose, S. Dilip, K. Selvaraj, P. N. Sudha, P. Geetha, and D. Lakshmikaanth. “Heat and Mass transfer

Effects on parabolic flow past an accelerated Isothermal Vertical plate in the Presence Of Chemical

Reaction and Hall Current.” JP Journal of Heat and Mass Transfer 35 (September 15, 2023): 55–74.

https://doi.org/10.17654/0973576323042 .

12. Muthucumaraswamy, R., and C. Santhana Lakshmi. “Mass and Heat transfer Effects on MHD Fluid

Flow of an Exponentially Accelerated Isothermal vertical Plate with variable mass diffusion.” Advances

and

Applications

in

Fluid

Mechanics

18,

no.

1

(May

8,

2015):

31–49.

https://doi.org/10.17654/aafmjul2015_031_049 .

13. Hetnarski, Richard B. “An Algorithm for Generating Some Inverse Laplace Transforms of Exponential

Form.” Zeitschrift Für Angewandte Mathematik Und Physik ZAMP 26, no. 2 (March 1975): 249–53.

https://doi.org/10.1007/bf01591514 .

14. Hetnarski, R. “On Inverting the Laplace Transforms Connected with the Error Function.” Applicationes

Mathematicae 7, no. 4 (1964): 399–405. https://doi.org/10.4064/am-7-4-399-405 .

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