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Numerical Analysis of Unsteady MHD Mixed Convection Flow in a Lid-Driven Square Cavity with Central Heating on Left Vertical Wall

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Applications of Fluid Dynamics

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Abstract

The article presents a numerical study performed on analysis of unsteady magneto-convective heat transfer in a square enclosure with partial active wall. The thermally insulated top and bottom wall while the left vertical wall is heated at Centre the rest of the left vertical wall is adiabatic and right vertical wall maintained at a lower temperature T c. MAC (Marker-and-Cell) method is used to solve numerically set of dimensionless governing partial differential equations. The effect of local heat source on left wall is evaluated. The influence of the governing of thermophysical parameters, namely Prandtl number, Rayleigh number \(\left( {Ra} \right)\), Hartmann number \(\left( {Ha} \right)\), Grashof number \(\left( {Gr} \right)\) and Reynolds number \(\left( {Re} \right)\), is obtained. The results of streamlines and temperature are presented graphically and discussed.

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Abbreviations

\(Ha\) :

Hartmann number

\(g\) :

Acceleration due to gravity, m s−2

\(k\) :

Thermal conductivity, Wm−1 K−1

H :

Height square cavity, m

\(K\) :

Permeability, m2

\(N\) :

Total number of nodes

\(Nu\) :

Local Nusselt number

\(Gr\) :

Grashof number

\(T\) :

Temperature, K

\(u\) :

\(x\) component of velocity, m s−1

\(U\) :

\(x\) component of dimensionless velocity

\(U_{0}\) :

\(x\) lid velocity, m s−1

\(V\) :

\(y\) component of dimensionless velocity

\(X\) :

Dimensionless distance along \(x\)

\(Y\) :

Dimensionless distance along \(y\)

\(v\) :

\(y\) component of velocity, m s−1

\(p\) :

Pressure, \(Pa\)

\(P\) :

Dimensionless pressure

\({ \Pr }\) :

Prandtl number

\({\text{Re}}\) :

Reynolds number

\(Ri\) :

Richardson number

\(\alpha\) :

Thermal diffusivity, m2s−1

\(\beta\) :

Volume expansion coefficient, K−1

\(\gamma\) :

Penalty parameter

\(T\) :

Dimensionless temperature

\(\upsilon\) :

Kinematic viscosity, m2s−1

\(\rho\) :

Density, kg m−3

\(\Psi\) :

Stream function

References

  • Aydin M, Fener RT (2001) Boundary element analysis of driven cavity flow for low and moderate Reynolds numbers. Int J Numer Methods Fluids 37:45–64

    Article  MATH  Google Scholar 

  • Barragy E, Carey GF (1997) Stream function-vorticity driven cavity solutions using p finite elements. Comput Fluids 26:453–468

    Article  MATH  Google Scholar 

  • Batchelor GK (1967) An introduction to fluid dynamics. Cambridge University Press, UK

    Google Scholar 

  • Benjamin AS, Denny VE (1979) On the convergence of numerical solutions for 2-D flows in a cavity at large Re. J Comput Phys 33:340–358

    Article  MATH  Google Scholar 

  • Chamkha AJ (2002) Hydromagnetic mixed convection flow with vertical lid driven cavity in presence of internal heat generation or absorption. Numer Heat Transfer A 41:529–546

    Article  Google Scholar 

  • Davis GD, Jones IP (1983) Natural convection in a square cavity: a comparison exercise. Int J Numer Methods Fluids 3:227–248

    Article  MATH  Google Scholar 

  • Erturk E, Corke TC, GÄokcÄol C (2005) Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers. Int J Numer Methods Fluids 48:747–774

    Google Scholar 

  • Ghia U, Ghia KN, Shin CT (1982) High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J Comput Phys 48:387–411

    Article  MATH  Google Scholar 

  • Guo Guanghong, Sharif Muhammad AR (2004) The study of mixed convection in rectangular cavity moving cold vertical walls with various aspect ratios in presence of linear flux heat source on the bottom wall. Int J Therm Sci 43:465–475

    Article  Google Scholar 

  • Gupta MM, Manohar RP (1979) Boundary approximations and accuracy in viscous flow computations. J Comput Phys 31:265–288

    Article  MATH  MathSciNet  Google Scholar 

  • Harlow FH, Welch JE (1965) Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys Fluids 8:2182–2190

    Article  MATH  MathSciNet  Google Scholar 

  • Iwatsu R, Hyun JM, Kuwahara K (1992) Numerical simulation of flows driven by a torsionally-oscillating lid. J Fluid Eng 114:143–151

    Article  Google Scholar 

  • Kandaswamy P, Muthtamilselvan M, Lee J (2008) Prandtl number effects on mixed Convection in a lid-driven porous cavity. J Porous Media 11:791–801

    Google Scholar 

  • Khanafer KM, Al-Amiri AM, Pop I (2007) Numerical simulation of unsteady convection in a driven cavity using an externally exited sliding lid. Eur J Mech B/Fluids 26:669–687

    Article  MATH  MathSciNet  Google Scholar 

  • Mohamad AA, Viskanta R (1995) Flow and heat transfer in a lid-driven cavity filled with a stably stratified fluid. Appl Math Model 19:465–472

    Article  MATH  Google Scholar 

  • Nguyen TH, Prudhomme M (2001) Bifurcation of convection flows in a rectangular cavity subjected to uniform heat fluxes. Int Comm Heat Mass Transfer 28:23–30

    Article  Google Scholar 

  • Nishimura T, Kunitsugu K (1997) Fluid mixing and mass transfer in two-dimensional cavities with time-periodic lid velocity. Int J Heat Fluid Flow 18:497–506

    Article  Google Scholar 

  • Peng YF, Shiau YH, Hwang RR (2003) Transition in a 2-D lid-driven cavity flow. Comput Fluids 32:337–352

    Article  MATH  Google Scholar 

  • Prasad AK, Koseff JR (1996) Mixed convection heat transfer in a deep lid-driven cavity flow with cold top wall moving constant velocity. Int J Heat Fluid Flow 17:460–467

    Article  Google Scholar 

  • Schreiber R, Keller HB (1983) Driven cavity flows by efficient numerical techniques. J Comput Phys 49:310–333

    Article  MATH  Google Scholar 

  • Soh WH, Goodrich JW (1988) Unsteady solution of incompressible Navier-Stokes equations. J Comput Phys 79:113–134

    Article  MATH  MathSciNet  Google Scholar 

  • Sriram S, Deshpande AP, Pushpavanam S (2006) Analysis of spatiotemporal variations and flow structures in a periodically driven cavity. J Fluid Eng 128:413–420

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Madanapalle Institute of Technology & Science, Madanapalle, 517325, AP, India

    K. Venkatadri & S. Gouse Mohiddin

  2. Department of Mathematics, JNTUA College of Engineering, Pulivendula, 516390, AP, India

    M. Suryanarayana Reddy

Authors
  1. K. Venkatadri
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  2. S. Gouse Mohiddin
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  3. M. Suryanarayana Reddy
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Corresponding author

Correspondence to K. Venkatadri .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India

    M.K. Singh

  2. Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India

    B.S. Kushvah

  3. Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India

    G.S. Seth

  4. University of Botswana, Gaborone, Botswana

    J. Prakash

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Venkatadri, K., Gouse Mohiddin, S., Suryanarayana Reddy, M. (2018). Numerical Analysis of Unsteady MHD Mixed Convection Flow in a Lid-Driven Square Cavity with Central Heating on Left Vertical Wall. In: Singh, M., Kushvah, B., Seth, G., Prakash, J. (eds) Applications of Fluid Dynamics . Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-5329-0_26

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  • DOI: https://doi.org/10.1007/978-981-10-5329-0_26

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  • Print ISBN: 978-981-10-5328-3

  • Online ISBN: 978-981-10-5329-0

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