The Nusselt number is the key parameter in the field of heat transfer analysis. It is the well-known dimensionless physical parameter, which is always used to determine the rate of heat transfer. This topic is also an important part of the M.Sc. Mathematics (Fluid Dynamics) syllabus at Biyani Girls College. In mathematics, it can be represented as the ratio of convective heat transfer to the conductive heat transfer and denoted by Nu.
Nu = Convective heat transfer Conductive heat transfer = h α(x) κ
by using Newton’s law of cooling and Fourier law, the above relation can be written as
Nu = h (Tw − T∞) ( ∂T / ∂y )y=0
Here (xα) represents the coefficient of convective heat transfer, h is denoted the characteristic length and κ shows the thermal conductivity of the fluid. The thermal conductivity is the property of the material to conduct the heat. It is an inherited property of materials, which is used for designing the cooling and heating devices in the field of thermal industries.
The Nusselt number is also used in the field of fluid dynamics. It is defined as the relative importance of mode of heat transfer. In the study of heat transfer analysis, we noticed that heat transfer is possible in three modes such as convection, conduction, and radiation.
The mode of heat transfer through convection is also classified into two categories such as natural convection and forced convection. Natural and forced convection has versatile practical applications in the field of science and technology.
If the numerical value of the Nusselt number is high, then the heat transfer is possible due to convection, while the small value of the Nusselt number explains the heat transfer through conduction. If the Nusselt number is 1, then it reflects the equal contribution of convection and conduction in heat transfer analysis.
In other words, we can say that the high numerical value of the Nusselt number represents the Turbulent flow (dominance of heat transfer through convection), whereas small value represents the laminar flow (dominance of heat transfer through conduction).
In the study of fluid dynamics, we have governing equations of fluid flow, such as continuity equation, momentum equation and equation of energy. The solution of the momentum equation provides the velocity distribution profile, whereas the equation of energy gives the temperature distribution profile of fluid flow through.
Later, the solution of the energy equation provides the rate of heat transfer in terms of Nusselt number, and their numerical interpretation is defined with the help of involved physical parameters.
In the literature, it is seen that the high intensity of the magnetic field boosts the rate of heat transfer. The rate of heat transfer also plays an important role in the irreversibility distribution profile of flow.
It was observed that sometimes the high intensity of the magnetic field improves the rate of heat transfer and consequently the total irreversibility in terms of entropy generation profile increases during the fluid motion.
The irreversibility distribution is possible due to a change in temperature difference during the flow, fluid friction and existence of applied magnetic field. The irreversibility distribution can control by sufficient change in the fluid flow governing parameter.
Frequently Asked Questions (FAQs)
1. What is the Nusselt number?
The Nusselt number is a dimensionless parameter that represents the ratio of convective heat transfer to conductive heat transfer. It helps in determining how effectively heat is transferred in a system.
2. What does a high or low Nusselt number indicate?
A high Nusselt number indicates dominant heat transfer by convection (often turbulent flow), while a low value suggests conduction-dominated heat transfer (usually laminar flow). If Nu = 1, both modes contribute equally.
3. Why is the Nusselt number important in engineering applications?
It is widely used in designing heating and cooling systems, analyzing fluid flow, and improving thermal efficiency in industries. It also helps predict temperature distribution and heat transfer rates.
Author:
Mr. Santosh Kumar Choudhary
Assistant Professor,Departent of Science
Biyani Girls College,Jaipur