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Peak Temperature Reached at any Point in Material Formula

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Peak Temperature Reached at Some Distance is the temperature reached at a distance of y from the fusion boundary. Check FAQs

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}

T_p - Peak Temperature Reached at Some Distance?t_a - Ambient Temperature?H_net - Net Heat Supplied Per Unit Length?T_m - Melting Temperature of Base Metal?ρ_m - Density of Metal?t - Thickness of Filler Metal?Q_c - Specific Heat Capacity?y - Distance from the Fusion Boundary?π - Archimedes' constant?

Peak Temperature Reached at any Point in Material Example

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Here is how the Peak Temperature Reached at any Point in Material equation looks like with Values.

Here is how the Peak Temperature Reached at any Point in Material equation looks like with Units.

Here is how the Peak Temperature Reached at any Point in Material equation looks like.

51.5875 = 37 + \frac{1000 \cdot (1500 - 37)}{(1500 - 37) \cdot \sqrt{2 \cdot 3.1416 \cdot e} \cdot 7850 \cdot 5 \cdot 4.184 \cdot 100 + 1000}

51.5875°C = 37°C + \frac{1000J/mm \cdot (1500°C - 37°C)}{(1500°C - 37°C) \cdot \sqrt{2 \cdot 3.1416 \cdot e} \cdot 7850kg/m³ \cdot 5mm \cdot 4.184kJ/kg*K \cdot 100mm + 1000J/mm}

51.5875 = 37 + \frac{1000 \cdot (1500 - 37)}{(1500 - 37) \cdot \sqrt{2 \cdot 3.1416 \cdot e} \cdot 7850 \cdot 5 \cdot 4.184 \cdot 100 + 1000}

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Peak Temperature Reached at any Point in Material Solution

Follow our step by step solution on how to calculate Peak Temperature Reached at any Point in Material?

FIRST Step Consider the formula

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}

Next Step Substitute values of Variables

∴

T p = 37°C + \frac{1000J/mm \cdot (1500°C - 37°C)}{(1500°C - 37°C) \cdot \sqrt{2 \cdot π \cdot e} \cdot 7850kg/m³ \cdot 5mm \cdot 4.184kJ/kg*K \cdot 100mm + 1000J/mm}

Next Step Substitute values of Constants

∴

T p = 37°C + \frac{1000J/mm \cdot (1500°C - 37°C)}{(1500°C - 37°C) \cdot \sqrt{2 \cdot 3.1416 \cdot e} \cdot 7850kg/m³ \cdot 5mm \cdot 4.184kJ/kg*K \cdot 100mm + 1000J/mm}

Next Step Convert Units

∴

T p = 310.15K + \frac{1E+6J/m \cdot (1773.15K - 310.15K)}{(1773.15K - 310.15K) \cdot \sqrt{2 \cdot 3.1416 \cdot e} \cdot 7850kg/m³ \cdot 0.005m \cdot 4184J/(kg*K) \cdot 0.1m + 1E+6J/m}

Next Step Prepare to Evaluate

∴

T p = 310.15 + \frac{1E+6 \cdot (1773.15 - 310.15)}{(1773.15 - 310.15) \cdot \sqrt{2 \cdot 3.1416 \cdot e} \cdot 7850 \cdot 0.005 \cdot 4184 \cdot 0.1 + 1E+6}

Next Step Evaluate

∴

T p = 324.737457789052K

Next Step Convert to Output's Unit

∴

T p = 51.5874577890518°C

LAST Step Rounding Answer

∴

T p = 51.5875°C

Peak Temperature Reached at any Point in Material Formula Elements

Variables

Constants

Functions

Peak Temperature Reached at Some Distance

Peak Temperature Reached at Some Distance is the temperature reached at a distance of y from the fusion boundary.

Symbol: T_p

Measurement: TemperatureUnit: °C

Note: Value should be greater than 0.

Formulas to find Peak Temperature Reached at Some Distance

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

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

Melting Temperature of Base Metal

Melting Temperature of Base Metal is the temperature at which its phase changes from liquid to solid.

Symbol: T_m

Measurement: TemperatureUnit: °C

Note: Value should be greater than 0.

Formulas to find Melting Temperature of Base Metal

Density of Metal

Density of Metal is the mass per unit volume of the given metal.

Symbol: ρ_m

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density of Metal

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

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

Distance from the Fusion Boundary

Distance from the Fusion Boundary refers to the measurement of space between a specific point and the location where two materials have been joined together through the process of fusion.

Symbol: y

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from the Fusion Boundary

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Heat Flow in Welded Joints category

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}

Go Net Heat Supplied to Weld Area to Raise it to given Temperature from Fusion Boundary

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

How to Evaluate Peak Temperature Reached at any Point in Material?

Peak Temperature Reached at any Point in Material evaluator uses Peak Temperature Reached at Some Distance = Ambient Temperature+(Net Heat Supplied Per Unit Length*(Melting Temperature of Base Metal-Ambient Temperature))/((Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Metal*Thickness of Filler Metal*Specific Heat Capacity*Distance from the Fusion Boundary+Net Heat Supplied Per Unit Length) to evaluate the Peak Temperature Reached at Some Distance, The Peak Temperature reached at any point in material formula is defined as the temperature reached during welding in the heat affected zone. Peak Temperature Reached at Some Distance is denoted by T_p symbol.

How to evaluate Peak Temperature Reached at any Point in Material using this online evaluator? To use this online evaluator for Peak Temperature Reached at any Point in Material, enter Ambient Temperature (t_a), Net Heat Supplied Per Unit Length (H_net), Melting Temperature of Base Metal (T_m), Density of Metal (ρ_m), Thickness of Filler Metal (t), Specific Heat Capacity (Q_c) & Distance from the Fusion Boundary (y) and hit the calculate button.

FAQs on Peak Temperature Reached at any Point in Material

What is the formula to find Peak Temperature Reached at any Point in Material?

The formula of Peak Temperature Reached at any Point in Material is expressed as Peak Temperature Reached at Some Distance = Ambient Temperature+(Net Heat Supplied Per Unit Length*(Melting Temperature of Base Metal-Ambient Temperature))/((Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Metal*Thickness of Filler Metal*Specific Heat Capacity*Distance from the Fusion Boundary+Net Heat Supplied Per Unit Length). Here is an example- -221.562548 = 310.15+(1000000*(1773.15-310.15))/((1773.15-310.15)*sqrt(2*pi*e)*7850*0.005*4184*0.09999996+1000000).

How to calculate Peak Temperature Reached at any Point in Material?

With Ambient Temperature (t_a), Net Heat Supplied Per Unit Length (H_net), Melting Temperature of Base Metal (T_m), Density of Metal (ρ_m), Thickness of Filler Metal (t), Specific Heat Capacity (Q_c) & Distance from the Fusion Boundary (y) we can find Peak Temperature Reached at any Point in Material using the formula - Peak Temperature Reached at Some Distance = Ambient Temperature+(Net Heat Supplied Per Unit Length*(Melting Temperature of Base Metal-Ambient Temperature))/((Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Metal*Thickness of Filler Metal*Specific Heat Capacity*Distance from the Fusion Boundary+Net Heat Supplied Per Unit Length). This formula also uses Archimedes' constant and Square Root Function function(s).

Can the Peak Temperature Reached at any Point in Material be negative?

No, the Peak Temperature Reached at any Point in Material, measured in Temperature cannot be negative.

Which unit is used to measure Peak Temperature Reached at any Point in Material?

Peak Temperature Reached at any Point in Material is usually measured using the Celsius[°C] for Temperature. Kelvin[°C], Fahrenheit[°C], Rankine[°C] are the few other units in which Peak Temperature Reached at any Point in Material can be measured.

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Peak Temperature Reached at any Point in Material Formula

Peak Temperature Reached at any Point in Material Example

Peak Temperature Reached at any Point in Material Solution

Peak Temperature Reached at any Point in Material Formula Elements

Other formulas in Heat Flow in Welded Joints category

How to Evaluate Peak Temperature Reached at any Point in Material?

FAQs on Peak Temperature Reached at any Point in Material

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