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ME 259 Heat Transfer Lecture Slides IV. Dr. Gregory A. Kallio Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology California State University, Chico. Natural (Free) Convection Heat Transfer. Natural Convection Fundamentals.

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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

Natural Convection Fundamentals

  • 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

Natural Convection Fundamentals, cont.

  • 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

Natural Convection Fundamentals, cont.

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

ME 259

Physics of Natural Convection

  • Consider a wood stove or fireplace:

    Buoyant force per unit area:

ME 259

Physics of Natural Convection, cont.

  • 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

Physics of Natural Convection, cont.

  • 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

Important Dimensionless Parameters in Natural Convection

  • 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

Empirical Correlations for Natural Convection Heat Transfer

  • 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

ME 259

Thermal Expansion Coefficient, b

  • 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

ME 259

Combined Natural and Forced Convection

  • 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

HXer Energy Balance Equations

  • Hot-side heat transfer rate

  • Cold-side heat transfer rate

  • Heat capacities

  • For an evaporating or condensing fluid:

ME 259

Log-Mean Temperature Difference (LMTD) Method of Analysis

  • For concentric tube hxers,

  • If hxer is shell-and-tube or cross flow type,

ME 259

Effectiveness()-NTU Method of Heat Exchanger Analysis

  • 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

Effectiveness-NTU Method, cont.

  • 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

Effectiveness-NTU Method, cont.

  • 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

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