---
title: "Whitaker Correlation | Heat and Mass Transfer"
description: "Whitaker Correlation estimates the Nusselt number for forced convection around a sphere, linking Reynolds and Prandtl numbers to heat transfer in flow problems."
canonical: "https://fiveable.me/heat-mass-transfer/key-terms/whitaker-correlation"
type: "key-term"
subject: "Heat and Mass Transfer"
unit: "Unit 3"
---

# Whitaker Correlation | Heat and Mass Transfer

## Definition

The Whitaker Correlation is an empirical formula in Heat and Mass Transfer for estimating the average Nusselt number around a sphere in forced convection. You use it to predict the convective heat transfer coefficient from flow and fluid properties.

## What It Is

The Whitaker Correlation is an empirical heat transfer correlation used to estimate the average Nusselt number for forced convection around a spherical object. In Heat and Mass Transfer, that usually means you have fluid flowing past a sphere and you want a practical way to estimate the convection coefficient without solving the full boundary-layer equations.

The correlation connects the heat transfer behavior to dimensionless groups such as Reynolds number and Prandtl number. Reynolds number tells you whether inertia or viscosity is dominating the flow pattern, while Prandtl number compares momentum diffusion to thermal diffusion. Whitaker wraps those effects into a single usable expression, which is why it shows up so often in textbook problem sets.

A common form is written with terms like Re raised to a fraction, Pr raised to a fraction, and a viscosity correction that accounts for the difference between the fluid properties in the free stream and at the surface. That last piece matters because the fluid right next to the hot or cold surface can behave differently from the bulk fluid, especially when viscosity changes a lot with temperature.

The big idea is not that Whitaker is a universal law. It is an experimentally fitted relationship, so it works best in the range of conditions it was built for. If the flow is highly irregular, the geometry is not close to a sphere, the surface is unusually rough, or the property variation is extreme, you may need a different correlation or a more detailed model.

In a problem, Whitaker usually appears after you identify the geometry and the flow regime. You find Re from the fluid speed and sphere diameter, find Pr from the fluid properties, evaluate the Nusselt number from the correlation, and then convert Nu into the heat transfer coefficient with h = Nu k / L, using the characteristic length for the sphere. That sequence is the real skill, not memorizing a standalone formula.

## Why It Matters

Whitaker Correlation matters because many Heat and Mass Transfer problems are not asking you to solve the full Navier-Stokes and energy equations. They are asking for a realistic engineering estimate, and this is one of the shortcuts that turns fluid motion into a usable heat transfer rate.

It also teaches you how dimensionless numbers work together. Reynolds number tells you about the flow field, Prandtl number tells you about the fluid’s thermal behavior, and the resulting Nusselt number tells you how strong convection is compared with pure conduction across the boundary layer.

That makes the correlation useful in design-style questions. If you are estimating heat loss from a particle, a droplet, or a ball-shaped component in a fluid stream, Whitaker can give you the convection coefficient needed for energy balance calculations.

It also helps you interpret model limits. If your answer changes a lot when viscosity or velocity changes, Whitaker gives you a way to predict the direction of that change before you ever plug numbers into a calculator.

## Connections

### [Nusselt Number](/heat-mass-transfer/key-terms/nusselt-number)

Whitaker is built around the Nusselt number, so Nu is the output you are usually solving for first. Once you have Nu, you can back out the convection coefficient with the thermal conductivity and a characteristic length. If a problem asks which correlation to use, checking whether it wants Nu is often the first clue.

### [Reynolds Number](/heat-mass-transfer/key-terms/reynolds-number)

Reynolds number controls the flow pattern in the correlation because it measures how strongly inertia competes with viscosity. A higher Re usually means thinner boundary layers and stronger convection. When you compute Whitaker, getting Re right is a must, because a small mistake there can shift the predicted heat transfer a lot.

### [Convective Heat Transfer Coefficient](/heat-mass-transfer/key-terms/convective-heat-transfer-coefficient)

Whitaker is often used as a bridge to the convective heat transfer coefficient, h. The correlation gives you Nusselt number first, then you convert that into h with the right fluid conductivity and geometry. That makes it especially useful in energy balance and heat loss calculations.

### [Churchill-Bernstein Correlation](/heat-mass-transfer/key-terms/churchill-bernstein-correlation)

Churchill-Bernstein is another empirical convection correlation, but it is commonly used for external flow over cylinders rather than spheres. Comparing it with Whitaker helps you match the right geometry to the right formula. A lot of errors in problem solving come from using a good correlation on the wrong shape.

## On the AP Exam

A quiz problem will usually give you a fluid, a sphere diameter, a surface temperature, and a free-stream velocity, then ask for the heat transfer coefficient or heat loss. Your job is to choose Whitaker, calculate Re and Pr from the given properties, evaluate Nu, and convert Nu to h. If the problem includes a surface viscosity or property-at-surface value, that is your cue to use the viscosity correction instead of ignoring it.

In a longer homework or lab write-up, you may also have to justify why Whitaker fits the geometry better than a flat-plate or cylinder correlation. The main mistake is using the wrong characteristic length or forgetting that Whitaker is for external convection around a sphere, not generic turbulent flow everywhere.

## Whitaker Correlation vs Churchill-Bernstein Correlation

These two are easy to mix up because both are empirical convection correlations and both use Reynolds-type and Nusselt-type thinking. The difference is geometry. Whitaker is the classic choice for flow around a sphere, while Churchill-Bernstein is commonly used for crossflow over a cylinder. If the object is round but not spherical, stop and check the shape before plugging anything in.

## Key Takeaways

- Whitaker Correlation is an empirical formula used to estimate the average Nusselt number for forced convection around a sphere.
- It links heat transfer to Reynolds number, Prandtl number, and often a viscosity correction between the free stream and the surface.
- The correlation is most useful when you want a practical estimate of the convection coefficient without solving the full boundary-layer equations.
- After you find Nu, you convert it to the convective heat transfer coefficient with the fluid conductivity and the sphere’s characteristic length.
- The biggest mistake is using Whitaker for the wrong geometry, since it is meant for spherical external flow, not every convection problem.

## FAQs

### What is Whitaker Correlation in Heat and Mass Transfer?

Whitaker Correlation is an empirical equation for estimating the average Nusselt number for forced convection around a sphere. It connects flow conditions and fluid properties to the heat transfer coefficient. In problems, you use it when a spherical object is moving through or exposed to a fluid stream.

### What numbers do you use in the Whitaker Correlation?

The main inputs are Reynolds number and Prandtl number, and many versions include a viscosity ratio to correct for property changes near the surface. Re reflects the flow regime, and Pr reflects how quickly heat diffuses relative to momentum. If either number is off, the heat transfer estimate will be off too.

### Is Whitaker Correlation for flat plates or spheres?

Whitaker is classically used for spheres, especially in external forced convection. If you are working with a flat plate, you usually need a different boundary-layer correlation. Shape matters here, so the first step is matching the geometry to the formula.

### How do you use Whitaker Correlation to find heat transfer coefficient?

First calculate Reynolds number and Prandtl number from the problem data. Then use the correlation to get Nusselt number, and convert Nu to h with h = Nu k / L using the correct characteristic length. That is the standard move in homework problems and design calculations.

## Related Study Guides

- [3.1 Boundary Layers and Convection Coefficients](/heat-mass-transfer/unit-3/boundary-layers-convection-coefficients/study-guide/QKnBMxoehYZs43wA)

## About This Document

Canonical Fiveable pages are available as Markdown at the same path plus `.md`.

- [llms.txt](https://fiveable.me/llms.txt): index of Fiveable's sections and URL patterns
- [llms-full.txt](https://fiveable.me/llms-full.txt): complete subject and unit listing
- [MCP server](https://fiveable.me/mcp): call Fiveable as tools instead of fetching pages (`https://fiveable.me/api/mcp`)
- [MCP server for AP teachers](https://fiveable.me/mcp/teachers): a teacher's classes, assignments and AP-rubric grading (`https://fiveable.me/api/mcp/teacher`)

## Structured Data

```json
{"@context":"https://schema.org","@graph":[{"@type":"LearningResource","@id":"https://fiveable.me/heat-mass-transfer/key-terms/whitaker-correlation#resource","name":"Whitaker Correlation | Heat and Mass Transfer","url":"https://fiveable.me/heat-mass-transfer/key-terms/whitaker-correlation","learningResourceType":"Concept explainer","educationalLevel":"AP® / High School","about":{"@id":"https://fiveable.me/heat-mass-transfer/key-terms/whitaker-correlation#term"},"audience":{"@type":"EducationalAudience","educationalRole":"student"},"dateModified":"2026-07-03T02:21:35.298Z","isPartOf":{"@type":"Collection","name":"Heat and Mass Transfer Key Terms","url":"https://fiveable.me/heat-mass-transfer/key-terms"},"author":{"@type":"Organization","@id":"https://fiveable.me/editorial#content-team","name":"Fiveable Content Team","url":"https://fiveable.me/editorial","parentOrganization":{"@id":"https://fiveable.me/#organization"},"member":[{"@type":"Person","name":"Amanda DoAmaral","sameAs":["https://www.linkedin.com/in/adoamaral"]},{"@type":"Person","name":"Becky Bahr","sameAs":["https://www.linkedin.com/in/becky-bahr-b52743132"]}]},"publisher":{"@type":"Organization","name":"Fiveable","url":"https://fiveable.me"}},{"@type":"DefinedTerm","@id":"https://fiveable.me/heat-mass-transfer/key-terms/whitaker-correlation#term","name":"Whitaker Correlation","description":"The Whitaker Correlation is an empirical formula in Heat and Mass Transfer for estimating the average Nusselt number around a sphere in forced convection. You use it to predict the convective heat transfer coefficient from flow and fluid properties.","url":"https://fiveable.me/heat-mass-transfer/key-terms/whitaker-correlation","inDefinedTermSet":{"@type":"DefinedTermSet","name":"Heat and Mass Transfer Key Terms","url":"https://fiveable.me/heat-mass-transfer/key-terms"}},{"@type":"FAQPage","mainEntity":[{"@type":"Question","name":"What is Whitaker Correlation in Heat and Mass Transfer?","acceptedAnswer":{"@type":"Answer","text":"Whitaker Correlation is an empirical equation for estimating the average Nusselt number for forced convection around a sphere. It connects flow conditions and fluid properties to the heat transfer coefficient. In problems, you use it when a spherical object is moving through or exposed to a fluid stream."}},{"@type":"Question","name":"What numbers do you use in the Whitaker Correlation?","acceptedAnswer":{"@type":"Answer","text":"The main inputs are Reynolds number and Prandtl number, and many versions include a viscosity ratio to correct for property changes near the surface. Re reflects the flow regime, and Pr reflects how quickly heat diffuses relative to momentum. If either number is off, the heat transfer estimate will be off too."}},{"@type":"Question","name":"Is Whitaker Correlation for flat plates or spheres?","acceptedAnswer":{"@type":"Answer","text":"Whitaker is classically used for spheres, especially in external forced convection. If you are working with a flat plate, you usually need a different boundary-layer correlation. Shape matters here, so the first step is matching the geometry to the formula."}},{"@type":"Question","name":"How do you use Whitaker Correlation to find heat transfer coefficient?","acceptedAnswer":{"@type":"Answer","text":"First calculate Reynolds number and Prandtl number from the problem data. Then use the correlation to get Nusselt number, and convert Nu to h with h = Nu k / L using the correct characteristic length. That is the standard move in homework problems and design calculations."}}]},{"@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Heat and Mass Transfer","item":"https://fiveable.me/heat-mass-transfer"},{"@type":"ListItem","position":2,"name":"Key Terms","item":"https://fiveable.me/heat-mass-transfer/key-terms"},{"@type":"ListItem","position":3,"name":"Unit 3","item":"https://fiveable.me/heat-mass-transfer/unit-3"},{"@type":"ListItem","position":4,"name":"Whitaker Correlation"}]}]}
```