Dimensionlessnumber in heat transfer

dimensionless no in heat transfer

1. DIMENSIONLESS NUMBER

2. GROUP MEMBERS:

3. DIMENSIONAL ANALYSIS: Dimensional analysis is a topic that deal with dimension. There are two types of dimensions. Fundamental dimension Derived dimension Dimensional analysis is use wo check the correction of given formula. Two terms are add when the dimensions of both quantities is same.

4. DIMENSIONAL ANALYSIS

5. Reynold’s Number (Re) It gives a measure of the ratio of inertial and viscous forces in fluid flow. It is often used to determine if the flow is either laminar or turbulent: In laminar flow, viscous forces dominate. The flow paths are smooth, streamline and constant. In turbulent flow, inertial forces dominate. The flow regime is unstable, generating eddies and vortices. The Kind of flow depends on value of R e If Re < 2000 the flow is Laminar If Re > 4000 the flow is turbulent If 2000 < Re < 4000 it is called transition flow .

6. Prandtl Numbe r (Pr) The Prandtl number, Pr, is the ratio of kinematic viscosity to the thermal diffusivity. It is used in many calculations involving heat transfer in flowing fluids. it gives a measure of the relative thickness of the thermal and momentum boundary layers. Where, Cp = Fluid specific heat capacity μ = Dynamic viscosity k = Thermal conductivity

7. Nusselt Number (Nu) The Nusselt Number, Nu, is the ratio of convective to conductive heat transfer in a fluid over a given length, l: For heat transfer in pipes, the characteristic length is the pipe diameter. At a Nusselt number of around one means that convection and conduction are about equal. Where, h = Heat transfer coefficient l = Characteristic length k = Thermal conductivity

8. Grashof Number: The Grashof number is used to determine the heat transfer coefficient under free convection conditions. It is basically a ratio between the buoyancy forces and viscous forces .

9. Biot N umber (Bi) It the ratio of the heat transfer resistances inside of and at the surface of a body. The Biot number (Bi) is used in heat transfer calculations . Where, h = Heat transfer coefficient l = Characteristic length kb = Thermal conductivity of the body

10. Fourier Number (Fo) Ratio of rate of heat conduction to the rate of heat storage. Used along with Biot number to solve transient state heat transfer problems. For mass transfer by diffusion, Fourier number for MT is used. Where, α = Thermal Diffusivity t = Characteristic time L = Length through which conduction occurs D = Diffusivity

11. Lewis Number (Le) Ratio of thermal diffusivity to mass diffusivity. Fluid flow with simultaneous Heat & mass transfer by convection. It is also ratio of Schmidt number to Prandtl number.

12. Mach Number (Ma) The Mach Number, Ma, is the ratio of the fluid velocity to the velocity of sound in that medium. In Chemical Engineering, the Mach Number is commonly used in calculations involving high velocity gas flow. Where, u = Velocity of fluid a = Speed of sound in fluid medium

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