Physical significance of non dimensional numbers

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1. HEAT TRANSFER PHYSICAL SIGNIFICANCE OF NON-DIMENSIONAL NUMBERS

2. NUSSELT NUMBER(Nu) It shows relation between convective hear transfer co- officient h, thermal conductivity k and characteristic length L. Thus, it shows the comparison between convection in the fluid and conduction at the plate. It may also be defined as temperature gradient at the solid surface to the overall temperature gradient.

3. Grashoff Number( Gr ) It shows relative dominance of inertia and buoyant force over viscous force. It is used in free convection similarly as Reynolds No. is used in forced convection. Chances of free convection is very less,at very low value of Gr,at some critical value of Gr,free convection starts it increase as value of Gr increases

4. Prandtl number(pr) It is the ratio of kinematic viscosity to thermal diffusivity. Kinematic viscosity indicates energy transport due to friction. Thermal diffusivity shows energy transport due to conduction.

5. It shows relative comparison of energy transport due to viscous action and conduction. It shows comparison between velocity and thermal boundary layer. For gases value of number is almost unity,but for liquids metals pr=0.003 to 0.1 which shows that energy transport due to thermal conduction is more as compared to viscous action.

6. Reynolds number(Re) It is a ratio of the inertia force ton the viscous force. Inertia force= mass x acceleration =density x volume x acceleration

7. Viscous force= shear stress x area Reynolds number is, It shows magnitude of inertia force compared to viscous force.if Re value is high ,inertia force is more as compared to viscous force and turbulence in flow will be higher. If Re value is low viscous force has dominance over inertia force, thus turbulence in the flow will be low. it is mostly used for force convection process.

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