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Cooling rate for relatively thin plates Formula

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Cooling Rate of Thin Plate is the rate of decrease of temperature of a particular material which has significantly less thickness. Check FAQs

R c = 2 \cdot π \cdot k \cdot ρ \cdot Q c \cdot ({(\frac{t}{H net})}^{2}) \cdot ({(T c - t a)}^{3})

R_c - Cooling Rate of Thin Plate?k - Thermal Conductivity?ρ - Density of Electrode?Q_c - Specific Heat Capacity?t - Thickness of Filler Metal?H_net - Net Heat Supplied Per Unit Length?T_c - Temperature for Cooling Rate?t_a - Ambient Temperature?π - Archimedes' constant?

Cooling rate for relatively thin plates Example

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Here is how the Cooling rate for relatively thin plates equation looks like with Values.

Here is how the Cooling rate for relatively thin plates equation looks like with Units.

Here is how the Cooling rate for relatively thin plates equation looks like.

0.6621 = 2 \cdot 3.1416 \cdot 10.18 \cdot 997 \cdot 4.184 \cdot ({(\frac{5}{1000})}^{2}) \cdot ({(500 - 37)}^{3})

0.6621°C/s = 2 \cdot 3.1416 \cdot 10.18W/(m*K) \cdot 997kg/m³ \cdot 4.184kJ/kg*K \cdot ({(\frac{5mm}{1000J/mm})}^{2}) \cdot ({(500°C - 37°C)}^{3})

0.6621 = 2 \cdot 3.1416 \cdot 10.18 \cdot 997 \cdot 4.184 \cdot ({(\frac{5}{1000})}^{2}) \cdot ({(500 - 37)}^{3})

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Cooling rate for relatively thin plates Solution

Follow our step by step solution on how to calculate Cooling rate for relatively thin plates?

FIRST Step Consider the formula

R c = 2 \cdot π \cdot k \cdot ρ \cdot Q c \cdot ({(\frac{t}{H net})}^{2}) \cdot ({(T c - t a)}^{3})

Next Step Substitute values of Variables

∴

R c = 2 \cdot π \cdot 10.18W/(m*K) \cdot 997kg/m³ \cdot 4.184kJ/kg*K \cdot ({(\frac{5mm}{1000J/mm})}^{2}) \cdot ({(500°C - 37°C)}^{3})

Next Step Substitute values of Constants

∴

R c = 2 \cdot 3.1416 \cdot 10.18W/(m*K) \cdot 997kg/m³ \cdot 4.184kJ/kg*K \cdot ({(\frac{5mm}{1000J/mm})}^{2}) \cdot ({(500°C - 37°C)}^{3})

Next Step Convert Units

∴

R c = 2 \cdot 3.1416 \cdot 10.18W/(m*K) \cdot 997kg/m³ \cdot 4184J/(kg*K) \cdot ({(\frac{0.005m}{1E+6J/m})}^{2}) \cdot ({(773.15K - 310.15K)}^{3})

Next Step Prepare to Evaluate

∴

R c = 2 \cdot 3.1416 \cdot 10.18 \cdot 997 \cdot 4184 \cdot ({(\frac{0.005}{1E+6})}^{2}) \cdot ({(773.15 - 310.15)}^{3})

Next Step Evaluate

∴

R c = 0.662060171595046K/s

Next Step Convert to Output's Unit

∴

R c = 0.662060171595046°C/s

LAST Step Rounding Answer

∴

R c = 0.6621°C/s

Cooling rate for relatively thin plates Formula Elements

Variables

Constants

Cooling Rate of Thin Plate

Cooling Rate of Thin Plate is the rate of decrease of temperature of a particular material which has significantly less thickness.

Symbol: R_c

Measurement: Rate of Temperature ChangeUnit: °C/s

Note: Value can be positive or negative.

Formulas to find Cooling Rate of Thin Plate

Thermal Conductivity

Thermal Conductivity is the rate at which heat passes through a material, defined as heat flow per unit time per unit area with a temperature gradient of one degree per unit distance.

Symbol: k

Measurement: Thermal ConductivityUnit: W/(m*K)

Note: Value can be positive or negative.

Formulas to find Thermal Conductivity

Density of Electrode

The Density of Electrode in welding refers to the mass per unit volume of the electrode material, it is the filling material of the weld.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density of Electrode

Specific Heat Capacity

Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.

Symbol: Q_c

Measurement: Specific Heat CapacityUnit: kJ/kg*K

Note: Value can be positive or negative.

Formulas to find Specific Heat Capacity

Thickness of Filler Metal

Thickness of Filler Metal refers to the distance between two opposite surfaces of a piece of metal where the filler metal is set.

Symbol: t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness of Filler Metal

Net Heat Supplied Per Unit Length

Net Heat Supplied Per Unit Length refers to the amount of heat energy transferred per unit length along a material or medium.

Symbol: H_net

Measurement: Energy per Unit LengthUnit: J/mm

Note: Value should be greater than 0.

Formulas to find Net Heat Supplied Per Unit Length

Temperature for Cooling Rate

Temperature for Cooling Rate is the temperature at which the cooling rate is calculated.

Symbol: T_c

Measurement: TemperatureUnit: °C

Note: Value can be positive or negative.

Formulas to find Temperature for Cooling Rate

Ambient Temperature

Ambient Temperature Ambient temperature refers to the air temperature of any object or environment where equipment is stored. In a more general sense, it is the temperature of the surrounding.

Symbol: t_a

Measurement: TemperatureUnit: °C

Note: Value should be greater than -273.15.

Formulas to find Ambient Temperature

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Heat Flow in Welded Joints category

Go Peak Temperature Reached at any Point in Material

T p = t a + \frac{H net \cdot (T m - t a)}{(T m - t a) \cdot \sqrt{2 \cdot π \cdot e} \cdot ρ m \cdot t \cdot Q c \cdot y + H net}

Go Position of Peak Temperature from Fusion Boundary

y = \frac{(T m - T y) \cdot H net}{(T y - t a) \cdot (T m - t a) \cdot \sqrt{2 \cdot π \cdot e} \cdot ρ \cdot Q c \cdot t}

How to Evaluate Cooling rate for relatively thin plates?

Cooling rate for relatively thin plates evaluator uses Cooling Rate of Thin Plate = 2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3) to evaluate the Cooling Rate of Thin Plate, The Cooling Rate for Relatively Thin Plates formula is defined as the rate at which heat is lost to the surrounding from the weldment. Cooling Rate of Thin Plate is denoted by R_c symbol.

How to evaluate Cooling rate for relatively thin plates using this online evaluator? To use this online evaluator for Cooling rate for relatively thin plates, enter Thermal Conductivity (k), Density of Electrode (ρ), Specific Heat Capacity (Q_c), Thickness of Filler Metal (t), Net Heat Supplied Per Unit Length (H_net), Temperature for Cooling Rate (T_c) & Ambient Temperature (t_a) and hit the calculate button.

FAQs on Cooling rate for relatively thin plates

What is the formula to find Cooling rate for relatively thin plates?

The formula of Cooling rate for relatively thin plates is expressed as Cooling Rate of Thin Plate = 2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3). Here is an example- 0.659999 = 2*pi*10.18*997*4184*((0.005/1000000)^2)*((773.15-310.15)^3).

How to calculate Cooling rate for relatively thin plates?

With Thermal Conductivity (k), Density of Electrode (ρ), Specific Heat Capacity (Q_c), Thickness of Filler Metal (t), Net Heat Supplied Per Unit Length (H_net), Temperature for Cooling Rate (T_c) & Ambient Temperature (t_a) we can find Cooling rate for relatively thin plates using the formula - Cooling Rate of Thin Plate = 2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3). This formula also uses Archimedes' constant .

Can the Cooling rate for relatively thin plates be negative?

Yes, the Cooling rate for relatively thin plates, measured in Rate of Temperature Change can be negative.

Which unit is used to measure Cooling rate for relatively thin plates?

Cooling rate for relatively thin plates is usually measured using the Celsius per Second[°C/s] for Rate of Temperature Change. Kelvin per Second[°C/s], Kelvin per Minute[°C/s], Fahrenheit per Second[°C/s] are the few other units in which Cooling rate for relatively thin plates can be measured.

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Cooling rate for relatively thin plates Formula

Cooling rate for relatively thin plates Example

Cooling rate for relatively thin plates Solution

Cooling rate for relatively thin plates Formula Elements

Other formulas in Heat Flow in Welded Joints category

How to Evaluate Cooling rate for relatively thin plates?

FAQs on Cooling rate for relatively thin plates

Variable Name