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Department of Chemical Engineering
Hea
t Tra
nsfe
r
July 2014by
Tun
de O
jum
u (P
hD) Obafemi Awolowo
University, Ile-Ife, Nigeria
CHE405-Heat Transfer
TV Ojumu (PhD) 2.25 Science Building [email protected]
OAU-CHE405: Heat Transfer Class of 2015
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Department of Chemical Engineering
Hea
t Tra
nsfe
r
July 2014
2
by T
unde
Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
Topics Tasks
Heat Transfer by Convection
Determination of coefficient of Heat Transfer Dimensional analysis of cane experiment Exact boundary-layer analysis Analogy between mass, momentum and heat transfer Correlation for heat transfer coefficient (forced, free and mixed convection)
Heat convection with phase change
Drop wise condensation, film condensation, Pool boiling, flow boiling
Heat Exchange Equipment
Type of heat-exchange equipment; Heat exchanger classification; Heat exchanger modelling; Design of heat exchangers (LMTD model); Rating of heat exchangers (NTU/Effectiveness approach)
Heat Transfer by Radiation
Definitions; Basic Laws of Thermal Radiation; radiation involving b;ack surfaces; gray surfaces and radiating surfaces; Thermal-circuit analysis; Matrix formation; Generating view factors for elongated channels; Gas radiation.
Department of Chemical Engineering
Hea
t Tra
nsfe
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July 2014
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by T
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Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
Convection is the mode of energy transfer between a solid surface and the adjacent fluid that is in motion, and it involves the combined effects of conduction and fluid motion.
The faster the fluid motion, the greater the convection heat transfer. In the absence of any bulk fluid motion, heat transfer between a solid surface and the adjacent fluid is by pure conduction.
The presence of bulk motion of the fluid enhances the heat transfer between the solid surface and the fluid, but it also complicates the determination of heat transfer rates.
Convection mode of Heat transfer
Department of Chemical Engineering
Hea
t Tra
nsfe
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July 2014
4
by T
unde
Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
Convection: mechanism of heat transfer through a fluid in the presence of bulk fluid motion
Conduction and Convection: • In solid, heat is transferred only by conduction, since
molecules of the solid remain at relatively fixed position • In a gas or liquid, heat can be transferred by conduction
and/or convection, depending on the presence of any bulk fluid motion:
Department of Chemical Engineering
Hea
t Tra
nsfe
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July 2014
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by T
unde
Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
» Convection: in the presence of bulk fluid motion » Forced convection » Free (Natural) convection
» Conduction: in the absence of bulk fluid motion Conduction in a fluid is the limiting case convection
Figure 1
Department of Chemical Engineering
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t Tra
nsfe
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July 2014
6
by T
unde
Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
Heat transfer processes that involve change of phase of a fluid are also considered to be convection because of the fluid motion induced during the process, such as the rise of the vapour bubbles during boiling or the fall of the liquid droplets during condensation.Despite the complexity of convection, the rate of convection heat transfer is observed to be proportional to the temperature difference, and is conveniently expressed by Newton’s law of cooling as
Department of Chemical Engineering
Hea
t Tra
nsfe
r
July 2014
7
by T
unde
Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
The convection heat transfer coefficient, h, is not a property of the fluid. It is an experimentally determined parameter whose value depends on all the variables influencing convection such as the surface geometry, the nature of fluid motion, the properties of the fluid, and the bulk fluid velocity. Typical values of h can be found in textbooks (Cengel and Ghajar 2015)
Judging from its units (W/m2K), the convection heat transfer coefficient, h, can be defined as the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature difference.
Department of Chemical Engineering
Hea
t Tra
nsfe
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July 2014
8
by T
unde
Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
Consider the following. A 2 m long and 0.3 cm diameter electrical wire extends across a room at 15°C, as shown below. Heat is generated in the wire as a result of resistance heating, and the surface temperature of the wire is measured to be 152°C in steady operation. Also, the voltage drop and electric current through the wire are measured to be 60 V and by radiation can be neglected, determine the convection heat transfer coefficient for heat transfer between the outer surface of the wire and the air in the room.
Example 1
Department of Chemical Engineering
Hea
t Tra
nsfe
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July 2014
9
by T
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Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
Solution
Department of Chemical Engineering
Hea
t Tra
nsfe
r
July 2014
10
by T
unde
Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
That is, a fluid in direct contact with a solid “sticks” to the surface due to viscous effects, and there is no slip. This is known as the no-slip condition The flow region adjacent to the wall in which the viscous effects are significant is called the boundary layerA consequence of the no-slip condition is that all velocity profiles must have zero values with respect to the surface at the points of contact between a fluid and a solid surface
An implication of the no-slip condition is that heat transfer from the solid surface to the fluid layer adjacent to the surface is by pure conduction, since the fluid layer is motionless, and can be expressed as
Department of Chemical Engineering
Hea
t Tra
nsfe
r
July 2014
11
by T
unde
Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
Note that convection heat transfer from a solid surface to a fluid is merely the conduction heat transfer from the solid surface to the fluid layer adjacent to the surface
The above equation is valid for determination of the convection heat transfer coefficient when the temperature distribution within the fluid is known
In convection studies, it is common practice to nondimensionalize the governing equations and combine the variables, which group together into dimensionless numbers in order to reduce the number of total variables. It is also common practice to nondimensionalize the heat transfer coefficient h with the Nusselt number, defined as
Nusselt number,
Department of Chemical Engineering
Hea
t Tra
nsfe
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July 2014
12
by T
unde
Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
Consider a fluid layer of thickness L and temperature difference = T2 - T1. Heat transfer through the fluid layer is by convection when the fluid involves some motion and by conduction when the fluid layer is motionless. Heat flux (the rate of heat transfer per unit surface area) in either case is given as:
The physical significance of the Nusselt number
Therefore, 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. The larger the Nusselt number, the more effective the convection. A Nusselt number of Nu=1 for a fluid layer means that heat transfer across the layer is purely by conduction.
for convectionfor conduction
Department of Chemical Engineering
Hea
t Tra
nsfe
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July 2014
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by T
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Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria Example 2
During the flow of air at = 20°C over a plate surface maintained at a constant temperature of Ts =160°C, the dimensionless temperature profile within the air layer is given as:
where a=3200 m-1 and y is the vertical distance measured from the plate surface in metres as shown below. Determine the heat flux on the plate surface and the convection heat transfer coefficient.
If temperature profile isThen,
SolutionRecall that heat transfer from the plate to air at the surface is by conduction, heat flux from the solid surface to the fluid layer adjacent to the surface is determined from
Department of Chemical Engineering
Hea
t Tra
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July 2014
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by T
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Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
Substituting, the heat flux is determined to be
Department of Chemical Engineering
Hea
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nsfe
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July 2014
15
by T
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Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
Similarly we can write that for heat transfer from fluid to wall surface as:
hx = local heat transfer coefficient at certain position x in flow direction and for given temperature distribution in the fluid flow.
Note the disappearance -ve sign around k
It is important to note that local heat transfer coefficient may vary along the length of flow, possibly as a result changes in velocity or other parameters in the flow direction. Our interest is in the overall heat transfer coefficient, which is an average over distance say x=0 to x = L
Department of Chemical Engineering
Hea
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July 2014
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by T
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Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
The heat transfer from the fluid to the wall surface over the entire distance, L, and width w is:
Consider that the local heat transfer coefficient, hx, determined experimentally for flow over a flat plate with rough surface as
where a is a constant and x is a distance from the leading edge of the plate. Develop an expression for ratio of average heat transfer coefficient, h, for a plate of length x to the local heat transfer coefficient, hx, at x.
Example 3
Solution:
Department of Chemical Engineering
Hea
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July 2014
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by T
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Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
Example 4Consider the correlation below, obtained experimentally heat transfer over a flat plate with rough surface:
where Nux is the local value of Nusselt number at position x from the leading edge of the plate. Develop an expression for ratio of average heat transfer coefficient, h, for a plate of length x to the local heat transfer coefficient, hx, at x.
Solution:
Department of Chemical Engineering
Hea
t Tra
nsfe
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July 2014
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by T
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Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
Exercise 1Consider that the local heat transfer coefficient, hx, determined experimentally for flow over a flat plate with rough surface as
where a is a constant and x is a distance from the leading edge of the plate. Develop an expression for ratio of average heat transfer coefficient, h, for a plate of length x=0 to x = L, to the local heat transfer coefficient, hx.
Department of Chemical Engineering
Hea
t Tra
nsfe
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July 2014
19
by T
unde
Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
A thermocouple is used to measure the temperature of a gas flowing through a hot duct. The heat transfer coefficient, h, is proportional to u0.8, where u is the gas velocity and heat transfer rate by radiation from the walls to the thermocouple is proportional to temperature difference. when the gas is flowing at 5m/s, the thermocouple reads 323K and when it flows at 10 m/s, it reads 313K. Calculate the appropriate wall temperature at a gas temperature of 298K. What temperature will the thermometer indicate when the gas velocity is 20 m/s
Example 4
SolutionIt can be shown that:
Department of Chemical Engineering
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July 2014
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by T
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Oju
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(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria Fluid flow classification
We can infer that convection heat transfer is closely tied with fluid mechanics, which is the science that deals with the behaviour of fluids at rest or in motion, and the interaction of fluids with solids or other fluids at the boundaries.
There is a wide variety of fluid flow problems encountered in practice, and it is usually convenient to classify them on the basis of some common characteristics to make it feasible to study them in groups.
There are many ways to classify fluid flow problems, and here we present some general categories
» Viscous versus Inviscid region of flow» internal versus external flow» Compressible versus incompressible flow» Laminar versus turbulent flow» Natural (free) versus forced flow» Steady versus unsteady flow» 1-, 2- and 3 dimensional flow
Class reading
Department of Chemical Engineering
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(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria Convection boundary layers
Velocity boundary layers:The quantity is termed the boundary layer thickness, and it is typically defined as the value of y for which
The boundary layer velocity profile refers to the manner in which u varies with y through the boundary layer.
Accordingly, the fluid flow is characterized by two distinct regions, a thin fluid layer (the boundary layer) in which velocity gradients and shear stresses are large and a region outside the boundary layer in which velocity gradients and shear stresses are negligible.
With increasing distance from the leading edge, the effects of viscosity penetrate farther into the free stream and the boundary layer grows ( increases with x).
The relationship of velocity boundary layer to shear stress allows the calculation of friction coefficient
Department of Chemical Engineering
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July 2014
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by T
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Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
Thermal boundary layers:If the fluid flowing on a surface has a different temperature than the surface, the thermal boundary layer is similar to that of the velocity boundary layer
The thickness of thermal boundary layer, at any location along the length of flow is defined as a distance, y, from the surface at which:
where T is local temperature in the thermal boundary layer, a function of x and y directions
Department of Chemical Engineering
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July 2014
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by T
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Oju
mu
(PhD
) Obafemi Awolowo University, Ile-Ife, Nigeria
For flow over any surface, there will always exist a velocity boundary layer and hence surface friction. Likewise, a thermal boundary layer, and hence convection heat transfer, will always exist if the surface and free stream temperatures differ. Similarly, a concentration boundary layer and convection mass transfer will exist if the fluid’s species concentration at the surface differs from its species concentration in the free stream. The velocity boundary layer is of extent and is characterized by the presence of velocity gradients and shear stresses. The thermal boundary layer is of extent and is characterized by temperature gradients and heat transfer. Finally, the concentration boundary layer is of extent and is characterized by concentration gradients and species transfer. Situations can arise in which all three boundary layers are present. In such cases, the boundary layers rarely grow at the same rate, and their values at any given location are not the same.
Significance of the Boundary Layers
