Transient Analysis of Heat Transfer by Natural Convection Along a Vertical Wavy Surface
-
Sadia Siddiqa
,
M. Mahfooz
Abstract
The problem considered in this paper deal with the transient behavior of heat transfer by natural convection flow of fluid along an infinite vertical heated wavy surface. The governing equations are transformed into dimensionless form and solutions are obtained for the two dimensional flow for both pure (α=0) and uneven surface (α ≠ 0). For pure vertical surface boundary layer equations are solved in the (i) upstream (small τ) (ii) downstream (large τ) and (iii) entire (0<τ<∞) regimes using analytical and numerical techniques. A very good agreement is found when results of above mentioned regimes are compared. Further, for wavy surface solutions are obtained for the entire time regime and results are discussed in terms of average Nusselt number coefficient and isotherms. Numerical results are served to reveal the influence of the physical parameters such as the Prandtl number, Pr, and wavy geometry, α, for the surface conditions.
Nomenclature
- x, y
Coordinate system (m)
- X, Y
Dimensionless coordinate system
- u, v
Dimensional x and y component of velocity (ms–1)
- U, V
Dimensionless X and Y component of velocity
Characteristic velocity
- F
Dimensionless stream function
- T
Dimensional time (s)
- T
Dimensional temperature (K)
- Pr
Prandtl number
- P
Pressure (Nm–2)
- qx
Nusselt number
- L
Wavelength of the wavy surface (m)
- K
Conductivity (Wm–1K–1)
- G
Gravitational acceleration (ms–2)
- Cp
Specific heat of fluid at constant pressure (kJkg–1K–1)
- τw
Skin-friction
- Gr
Grashof number
- Greek symbols
- ε
Amplitude of the wavy surface (m)
- α
Amplitude-wavelength ratio, ε/L
- βT
Volumetric coefficient of thermal expansion
- σ
Dimensionless coordinate of the wavy surface
Coordinate of the wavy surface, eq. (1)
- μ
Dynamic viscosity (kgm–1s–1)
- υ
Kinematic viscosity (m2s–1)
- ρ
Fluid density (kgm–3)
- θ
Dimensionless temperature
Dimensionless time
- ψ
Stream function
- η
Non-dimensional similarity variable
- Subscripts
- ∞
Free stream condition
- W
Surface condition
- T
Temperature
- X
Local value
- i, j
Evaluated at the ith and jth nodal point in the y- and x-directions, respectively
- Superscripts
- ’
Differentiation with respect to η
- N
Evaluated at the nth point in the τ-direction
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© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Transient Analysis of Heat Transfer by Natural Convection Along a Vertical Wavy Surface
- Three-Dimensional Flow Problems in a Lid-Driven Cubical Cavity with a Circular Cylinder
- Complete Controllability of Fractional Impulsive Multivalued Stochastic Partial Integrodifferential Equations with State-Dependent Delay
- Dynamic Stability of a Thin Film Bonded to a Compliant Substrate Subjected to a Step Load with Damping
- Existence Results to Some Damped-Like Fractional Differential Equations
- A Numerical Method for Solving Two-Dimensional Elliptic Interface Problems with Nonhomogeneous Flux Jump Condition and Nonlinear Jump Condition
- Numerical Simulation of Free Surface and Flow Field Turbulence in a Circular Channel with the Side Weir in Subcritical Flow
- Comparative Analysis of Various Control Strategies for a Nonlinear CSTR System
- Non-Polynomial Spline Method for One Dimensional Nonlinear Benjamin-Bona-Mahony-Burgers Equation
- The Binary Nonlinearization of the Super Integrable System and Its Self-Consistent Sources
Articles in the same Issue
- Frontmatter
- Transient Analysis of Heat Transfer by Natural Convection Along a Vertical Wavy Surface
- Three-Dimensional Flow Problems in a Lid-Driven Cubical Cavity with a Circular Cylinder
- Complete Controllability of Fractional Impulsive Multivalued Stochastic Partial Integrodifferential Equations with State-Dependent Delay
- Dynamic Stability of a Thin Film Bonded to a Compliant Substrate Subjected to a Step Load with Damping
- Existence Results to Some Damped-Like Fractional Differential Equations
- A Numerical Method for Solving Two-Dimensional Elliptic Interface Problems with Nonhomogeneous Flux Jump Condition and Nonlinear Jump Condition
- Numerical Simulation of Free Surface and Flow Field Turbulence in a Circular Channel with the Side Weir in Subcritical Flow
- Comparative Analysis of Various Control Strategies for a Nonlinear CSTR System
- Non-Polynomial Spline Method for One Dimensional Nonlinear Benjamin-Bona-Mahony-Burgers Equation
- The Binary Nonlinearization of the Super Integrable System and Its Self-Consistent Sources
