Heat Transfer Equations Basic Heat Transfer Equation

The rate of heat transfer through a given surface is given by the equation:

Q = U x A x LMTD

Where Q = total heat exchangedU = overall heat transfer coefficientA = exchanger surface areaLMTD = log mean temperature difference

Rearranging the equation for area calculation gives:

A = Q / (U x LMTD)

For compact heat exchangers, U is generally the clean U value. The heat exchanger area is generally 5 to 20% more than the calculated area (A) from above to allow for fouling. Please refer to fouling for more information and details.

Other TopicsLaminar Flow EquationLog Mean Temperature DifferenceOverall Heat Transfer CoefficientThermal BalanceTurbulent Flow Equation

Heat Transfer Equations Laminar Flow Equation

Laminar flow is generally avoided in most applications in compact heat exchangers due to the corrugations in plate. However, in certain applications with extremely low allowable pressure drops or very high heat recovery applications, laminar flow is unavoidable. The most common widely accepted equation for laminar flow is:

where

and

and

and

Nu = Nusselt's number = (h x d) / h = film coefficient, d = equivalent hydraulic diameter, = thermal conductivity

Re = Reynolds number = (G x d) / G = mass flow rate, d = equivalent hydraulic diameter, = viscosity

Pr = Prandtl Number = (c x ) / c = specific heat, = viscosity, = thermal conductivity

L= plate length or flow lengtha and b are constants depending on plate geometrya = 1.86 to 4.50 .... b = usually 0.333

y is a constant derived from Seider Tate modification or correction for viscosity and modified for corrugated plates - usual value ranges from 0.05 to 0.20. is average viscosity and w is wall viscosity.

Other TopicsBasic Heat Transfer EquationLog Mean Temperature DifferenceOverall Heat Transfer CoefficientThermal BalanceTurbulent Flow Equation

Heat Transfer Equations Log Mean Temperature Difference

The term LMTD refers to the "true" driving force for heat transfer (rather than the arithmetic temperature difference) and is derived as follows:

Where GTD = larger of (T1 - t2) or (T2 - t1)LTD = smaller of (T2 - t1) or (T1 - t2)

T1 - hot side temp inlet T2 - hot side temp outlett1 - cold side temp inlet t2 - cold side temp outlet

CF is correction factor depending on flow arrangement, heat exchanger type, number of passes. For compact heat exchangers, CF is usually very close to 1.

Other TopicsBasic Heat Transfer EquationLaminar Flow EquationOverall Heat Transfer CoefficientThermal BalanceTurbulent Flow Equation

Heat Transfer Equations Overall Heat Transfer Coefficient

This is often referred to as the U value. This can be clean U value (without fouling factors or excess area for fouling) and dirty U value which includes allowance for fouling.

Where Uc = clean U value Btu / hr - sq. ft. Fh1 = film coefficient side #1 Btu / hr - sq ft. Fh2 - film coefficient side #2 Btu / hr - sq ft Fy = heat transfer surface metal wall thickness in inchesk= thermal conductivity of heat transfer surface material Btu / hr - F - inch

The film coefficients are calculated based on flow characteristic, the heat transfer surface geometry and fluid properties. They are generally calculated for Turbulent flow or Laminar flow.

Compact heat exchangers (gasketed and welded) have corrugated heat transfer plates. The Reynold's number at which flow becomes turbulent is dependent on the "hardness" of the corrugation. For example, smooth surface shell and tubes have turbulent flow at Reynolds numbers greater than 2,100 while the hardest chevron corrugation plate can be turbulent flow at Reynold's numbers as low as 150.

Other TopicsBasic Heat Transfer EquationLaminar Flow EquationLog Mean Temperature DifferenceThermal BalanceTurbulent Flow Equation

Heat Transfer Equations Thermal Balance

Heat cannot be created or destroyed. Therefore, heat given off by one fluid must equal heat gained by the other fluid in a heat exchanger.

Heat loss / gain - no phase change

Qs (Btu / hr) = flow rate (lbs / hr) x specific heat (Btu / lb - F) x temp rise / fall (F)

Flow rate (lbs/hr) = flow rate (USGPM) x 500 x specific gravity

Heat loss / gain - phase change

Qp (Btu / hr) = flow - phase change (lbs / hr) x latent heat (Btu / lb)

Total Q = Qs + Qp

Where Qp = O for liquid - liquid or gas-liquid or gas-gas heat transfer with no phase change

Phase Change - Condenser - (heat loss)

When a fluid (such as steam) changes from gas to liquid (water)

Phase Change - Evaporator (heat gain)

When a fluid (such as water) changes from liquid to gas (steam)

Other TopicsBasic Heat Transfer EquationLaminar Flow EquationLog Mean Temperature DifferenceOverall Heat Transfer CoefficientTurbulent Flow Equation

Heat Transfer Equations Turbulent Flow Equation

For relatively non-viscous fluids, the most common, and proven equations is Dittus Boelter Equation, modified for compact heat exchangers.

Where

and

and

Nu = Nusselt's Number = (h x d) / h = film coefficient, d = equivalent hydraulic diameter, = thermal conductivity

Re = Reynold's Number = (G x d) / G = mass flow rate, d = equivalent hydraulic diameter, = viscosity

Pr = Prandtl Number = (c x ) / kc = specific heat, = viscosity, - thermal conductivity

a, n, and m are constants depending on plate geometrya = 0.15 to 0.4 .... n = 0.65 to 0.85 .... m = 0.30 to 0.45

y is a constant derived from Seider Tate modification or correction for viscosity and modified for corrugated plates - usual value ranges from 0.05 to 0.20. is average viscosity and w is wall viscosity.

Other TopicsBasic Heat Transfer EquationLaminar Flow EquationLog Mean Temperature DifferenceOverall Heat Transfer CoefficientThermal Balance