All fluids have its resistance to relative motion between surfaces and is called Viscosity. This property is about the friction between the particles of a fluid. A fluid that is forced in a tube has the liquid moving faster as it is closer the axis of the tube and slower when farther from it.
3.1.1 Dimensionless Parameters
In analysis of convection heat transfer, it is convenient to convert to non-dimensional the governing equations and combine the variables, which makes the group of dimensionless numbers in order to reduce the number of total variables.
3.1.1.1 Prandtl Number
The Prandtl number is the ratio of the momentum diffusivity or viscous diffusuion rate and thermal diffusivity or thermal diffusion rate expressed as
where is the specific heat, is the thermal diffusivity, is the thermal conductivity, and & are the kinematic and dynamic viscosity, respectively. Generally, it is used to describe how heat diffuses in a moving fluid. Relative to momentum, a low Prandtl number like in liquid metals (Pr 1) means faster heat diffusion, and a higher Prandtl number like in oil (Pr 1) means slower heat diffusion. 3.1.1.2 Reynolds Number The Reynolds number is the ratio of inertia forces to viscous forces in the fluid. For an external flow, it is expressed as where is the density of the fluid, is the velocity of the fluid, and is the characteristic length of the geometry. For an internal flow, it is expressed as in which the internal pipe diameter is used instead of . The Reynolds number governs the flow regime in forced convection and is used to determine the degree of laminar and turbulent flow. A large Reynolds number signifies the flow is turbulent and a small Reynold number for laminar. 3.1.1.3 Grashof Number The Grashof Number is used for similar function of Reynolds Number but governs the flow regime in natural convection. It represents the ratio of the buoyancy force to the viscous force acting on the fluid expressed as where g is gravitational acceleration, is the coefficient of volume expansion, and & are the temperature of the surface and of the viscous force acting on the fluid, respectively. 3.1.1.4 Nusselt Number The Nusselt number represents the enhancement of heat transfer through a fluid layer as a result of convection relative to conduction across the same fluid layer. …show more content…
It is the dimensionless number, which is basically the ratio of the heat flux for convection and for conduction, defined as
where is the convective heat transfer coefficient. A larger Nusselt number represents a more effective convection heat transfer. In natural convection, there are complexities in fluid motion that makes difficult for analytical analysis of relations for heat transfer. However, simple empirical correlations with claimed accuracy for the average Nusselt number is used for heat transfer analysis in natural convection expressed as
where and are the constants depending on the geometry of the surface and flow regime. For value of for laminar flow and turbulent flow are usually equal to and , respectively (Cengel, Y.A. 2007).
3.2 Basic Heat Transfer
Heat is normally absorbed or rejected by a working substance at a constant pressure. The heat transferred without a phase change results in a change of temperature is called sensible heat and can be measured by the expression where is the mass, is the specific heat at constant pressure, and is the temperature change of the
3.1.1 Dimensionless Parameters
In analysis of convection heat transfer, it is convenient to convert to non-dimensional the governing equations and combine the variables, which makes the group of dimensionless numbers in order to reduce the number of total variables.
3.1.1.1 Prandtl Number
The Prandtl number is the ratio of the momentum diffusivity or viscous diffusuion rate and thermal diffusivity or thermal diffusion rate expressed as
where is the specific heat, is the thermal diffusivity, is the thermal conductivity, and & are the kinematic and dynamic viscosity, respectively. Generally, it is used to describe how heat diffuses in a moving fluid. Relative to momentum, a low Prandtl number like in liquid metals (Pr 1) means faster heat diffusion, and a higher Prandtl number like in oil (Pr 1) means slower heat diffusion. 3.1.1.2 Reynolds Number The Reynolds number is the ratio of inertia forces to viscous forces in the fluid. For an external flow, it is expressed as where is the density of the fluid, is the velocity of the fluid, and is the characteristic length of the geometry. For an internal flow, it is expressed as in which the internal pipe diameter is used instead of . The Reynolds number governs the flow regime in forced convection and is used to determine the degree of laminar and turbulent flow. A large Reynolds number signifies the flow is turbulent and a small Reynold number for laminar. 3.1.1.3 Grashof Number The Grashof Number is used for similar function of Reynolds Number but governs the flow regime in natural convection. It represents the ratio of the buoyancy force to the viscous force acting on the fluid expressed as where g is gravitational acceleration, is the coefficient of volume expansion, and & are the temperature of the surface and of the viscous force acting on the fluid, respectively. 3.1.1.4 Nusselt Number The Nusselt number represents the enhancement of heat transfer through a fluid layer as a result of convection relative to conduction across the same fluid layer. …show more content…
It is the dimensionless number, which is basically the ratio of the heat flux for convection and for conduction, defined as
where is the convective heat transfer coefficient. A larger Nusselt number represents a more effective convection heat transfer. In natural convection, there are complexities in fluid motion that makes difficult for analytical analysis of relations for heat transfer. However, simple empirical correlations with claimed accuracy for the average Nusselt number is used for heat transfer analysis in natural convection expressed as
where and are the constants depending on the geometry of the surface and flow regime. For value of for laminar flow and turbulent flow are usually equal to and , respectively (Cengel, Y.A. 2007).
3.2 Basic Heat Transfer
Heat is normally absorbed or rejected by a working substance at a constant pressure. The heat transferred without a phase change results in a change of temperature is called sensible heat and can be measured by the expression where is the mass, is the specific heat at constant pressure, and is the temperature change of the