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**Heat Transfer to Solids in a Flowing Fluid**

The heat transfer is dependent on: Geometry of the body. The position or orientation of the body (parallel, perpendicular to flow). Proximity of other bodies. The heat transfer coefficient varies across the surface of the object. But the average heat transfer coefficient can be determined from an equation of the form:

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**Flow Parallel to a Flat Plate**

Use fluid properties at average film temperature = (Ave. temp. of Wall + Ave. temp. of fluid)/2

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**Flow Perpendicular to a Single Cylinder**

Use properties at the film temperature. Velocity is free field velocity of fluid.

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**Flow Past a Single Sphere**

Use properties at film temperature.

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**Flow Thru Tube Banks Very important for heat exchanger design!**

Flow around the first bank is essentially the same as for a single tube. For subsequent rows, flow depends on the tube bank arrangement. The convection coefficient of a row increases with increasing row number until about the 5th row, after which there is little change. For aligned tubes, the front row shields the back rows, particularly for short distances between tubes. In general, heat transfer is encouraged by the staggered arrangement.

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Flow Thru Tube Banks In-Line Tubes Staggered Tubes

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Flow Thru Tube Banks Only for more than ten rows. Tables are available for non-equal ratios.

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Flow Thru Tube Banks Correction factors for banks of less than ten tubes.

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**Flow Thru Tube Banks Procedure for solving tube bank problems:**

Given: tube geometry, inlet temperature, tube surface temp., fluid velocity. Assume an outlet temperature. Determine properties of the fluid at the average temperature. Calculate max. velocity based on geometry. Calculate Reynolds number based on max. velocity. Determine average heat transfer coefficent. Determine overall q from total area of all tubes using temperature difference between tube wall and average fluid temperature. Determine mass flow rate from: Use to determine temperature drop. Continue until guessed = calculated.

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**Heat Transfer for Flow in Packed Beds**

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**Convective Heat Transfer**

Natural convection occurs when a quiescent fluid is exposed to a hot or cold surface. If the surface is hot, the fluid next to the surface will be heated, its temperature will increase and its density will decrease. Due to the decreased density of the fluid next to the surface, it will rise due to buoyancy. If the surface is cold, then the temperature of the fluid will be colder than the bulk fluid, its density will decrease and will fall due to buoyancy.

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**Convective Heat Transfer**

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**Convective Heat Transfer**

Typical chemical engineering problems involving convective heat transfer: If a hot fluid is transported thru a pipe from process A to process B, how much will its temperature drop? If a hot fluid is stored in a storage vessel, how much will the temperature drop each day? What are the convective heat losses from my process unit, i.e., distillation column? If a hot solid is cooled in the open, how long will it take to cool the solid to room temperature?

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**Convective Heat Transfer**

Natural convection heat transfer involves an additional dimensionless parameter called the Grashof number. The Grashof number represents the buoyancy force.

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**Convective Heat Transfer**

The volumetric expansion coefficient is defined as: Ethyl alcohol: 112 x 10-5 /deg. C Methyl alcohol: “ Benzene: “ Glycerin: “ Air: “

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**Convective Heat Transfer**

True for any material Ideal gas only

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**Convective Heat Transfer**

Most natural convection geometries are represented by the equation: The physical properties are evaluated at the film temperature. For vertical and horizontal plates and cylinders use Table (handout). For horizontal plates the length, L, is used. For cylinders L is replaced by D. For horizontal rectangles the average of the two dimensions is used. For a horizontal circular disk, the diameter is multiplied by 0.9. Simplified equations for various types of surfaces are provided in Table (handout).

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**Convective Heat Transfer**

For natural convection at pressures other than 1 atm, the heat transfer coefficients are multiplied by a correction factor:

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**Example - Convective Heat Transfer**

A vertical cylinder 76.2 mm in diameter and mm high is maintained at K at its surface. It loses heat by natural convection to air at K. Heat is lost from the sides and top – the bottom is insulated. Calculate the total heat loses neglecting radiation.

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**Example - Convective Heat Transfer**

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**Example - Convective Heat Transfer**

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**Example - Convective Heat Transfer**

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**Example - Convective Heat Transfer**

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**Example - Convective Heat Transfer**

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