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ME 259 Heat Transfer Lecture Slides IV

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ME 259Heat TransferLecture Slides IV

Dr. Gregory A. Kallio

Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology

California State University, Chico

ME 259

Natural (Free) Convection Heat Transfer

ME 259

- Heat transfer is due to fluid motion by buoyancy forces
- Buoyancy arises from a density variation in the fluid, most commonly due to a temperature gradient:
- Velocities are generally much smaller than those associated with forced convection, hence
- For air, h = 2 – 10 W/m2-K
- For H2O, h = 50 – 1000 W/m2-K

ME 259

- Radiation and natural convection heat transfer are comparable in most applications
- Analysis often leads to an iterative solution technique ( IHT ! ) since qrad = f (T4) and qconv = f (T4/3) or f (T5/4)
- Natural convection strongly influences
- Heating & cooling of rooms
- Cooling of electronics, engines, refrigeration coils, transmission lines
- Human and animal comfort
- Environmental pollution
- Atmospheric motions
- Oceanic currents

ME 259

- Physical considerations – consider a quiescent fluid between parallel, heated horizontal plates:

ME 259

- Consider a wood stove or fireplace:
Buoyant force per unit area:

ME 259

- Now consider a vertical heated plate:
Buoyant force per unit area:

- The quantity (-) is related to a thermodynamic property called the volumetric thermal expansion coefficient ( ):

ME 259

- This buoyant force will cause fluid motion that is resisted by viscous forces:
- The ratio is important in determining the magnitude of natural convection - known as the Grashof number (Gr):

ME 259

- For a particular geometric shape and orientation,
- Dimensional analysis shows that
- The Grashof number plays a similar role to the Reynolds number in forced convection
- The product Gr •Pr appears frequently in analysis of natural convection, so we also define the Rayleigh number (Ra):

ME 259

- Many natural convection geometries have been studied; the correlations are typically written as
- Geometries:
- vertical plate, vertical cylinder
- horizontal plate
- horizontal cylinder
- sphere
- array of horizontal cylinders
- inclined plate
- parallel plates, or channel
- rectangular cavity, or enclosure
- annular cavity

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- For an ideal gas, r = P/RT, so
- For liquids and non-ideal gases, b is found from Appendix tables in text, e.g., A.4 - A.6

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- Both types of convection are comparable when
- the resulting flow field is complicated and difficult to predict; it is strongly influenced by the direction of the buoyancy relative to that of the flow; the effect on NuL can be estimated for three special cases by
- wheren = 3for vertical plates & cylinders
n = 3.5for horizontal plates

n = 4for horizontal cylinders & spheres

and+ refers to assisting and transverse flows

- refers to opposing flows

ME 259

Heat Exchangers

ME 259

- Heat exchangersenable efficient heat transfer between two fluids at different temperatures, separated by a solid wall.
- Boilers, condensers, regenerators, recuperators, preheaters, intercoolers, economizers, feedwater heaters, “radiators”, are all HXers.
- Types of HXers:
- Concentric tube – simple, inexpensive, easy to analyze
- Shell and tube – high efficiency, expensive, common for large-scale liquid-liquid heat exchange; difficult to analyze; performance based on empirical data
- Cross Flow – high-efficency, moderately expensive, common for gas-liquid heat exchange; difficult to analyze; performance based on empirical data.

ME 259

- Hot-side heat transfer rate
- Cold-side heat transfer rate
- Heat capacities
- For an evaporating or condensing fluid:

ME 259

- For concentric tube hxers,
- If hxer is shell-and-tube or cross flow type,

ME 259

- LMTD method requires an iterative procedure if only the inlet temperatures are known; in such cases, the -NTU method is preferred.
- Effectiveness () is defined as
- qmax corresponds to a CF hxer of infinite length where the fluid with the least heat capacity experiences the maximum possible temperature change, Thi-Tci .
- Thus, the actual heat transfer rate is found by

ME 259

- For any hxer, it can be shown that
- Cmin/Cmax is equal to Ch/Cc or Cc/Ch, depending on the relative magnitudes of the fluid mass flow rates and specific heats; the number of transfer units (NTU) is a dimensionless parameter given by
- NTU typically has values between 0 - 5 and indicates the relative size, or heat exchange area, of the hxer.

ME 259

- Relations for = f(NTU) and NTU = f() are given in Tables 11.3 and 11.4, respectively, for the three types of hxers.
- Figures 11.14 - 11.19 give this same information in graphical form.
- In summary, either the LMTD or -NTU methods may be used to solve hxer problems and both will yield identical values. However, the LMTD method is best-suited for design calculations, i.e., where one outlet temperature is known and the required heat exchange area (A) is sought.

ME 259